A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT—helical scanning

A Systematic Literature Review of 3D Deep Learning Techniques in Computed Tomography Reconstruction

Computed tomography (CT) is used in a wide range of medical imaging diagnoses. However, the reconstruction of CT images from raw projection data is inherently complex and is subject to artifacts and noise, which compromises image quality and accuracy. In order to address these challenges, deep learning developments have the potential to improve the reconstruction of computed tomography images. In this regard, our research aim is to determine the techniques that are used for 3D deep learning in CT reconstruction and to identify the training and validation datasets that are accessible. This research was performed on five databases. After a careful assessment of each record based on the objective and scope of the study, we selected 60 research articles for this review. This systematic literature review revealed that convolutional neural networks (CNNs), 3D convolutional neural networks (3D CNNs), and deep learning reconstruction (DLR) were the most suitable deep learning algorithms for CT reconstruction. Additionally, two major datasets appropriate for training and developing deep learning systems were identified: 2016 NIH-AAPM-Mayo and MSCT. These datasets are important resources for the creation and assessment of CT reconstruction models. According to the results, 3D deep learning may increase the effectiveness of CT image reconstruction, boost image quality, and lower radiation exposure. By using these deep learning approaches, CT image reconstruction may be made more precise and effective, improving patient outcomes, diagnostic accuracy, and healthcare system productivity.

SHCT: segmented helical computed tomography based on multiple slant source-translation

Micro-computed tomography (Micro-CT) is inevitably required to inspect long large objects with high resolution. It is well known that helical CT solves the so-called "long object" problem, but it requires that the measured object be strictly located in the lateral field of view (FOV). Therefore, developing a novel scanning method to extend the FOV in both the lateral and axial directions (i.e., the large helical FOV) is necessary. Recently, due to the application of linearly distributed source arrays and the characteristics of easy extension of the FOV and engineering implementation, straight-line scanning systems have attracted much attention. In this paper, we propose a segmented helical computed tomography (SHCT) based on multiple slant source-translation. SHCT can readily extend the helical FOV by adjusting the source slant translation (SST) length, pitch (or elevation of the SST trajectory), and number of scanning circles. In SHCT, each projection view is truncated laterally and axially, but the projection data set within the cylindrical FOV region is complete. To ensure reconstruction efficiency and avoid the lateral truncation, we propose a generalized backprojection-filtration (G-BPF) algorithm for SHCT approximate reconstruction. Experimental results verify the effectiveness of the proposed SHCT methods for imaging large and long objects. As the pitch decreases, the proposed SHCT methods can reconstruct competitive, high-quality volumes.

Clinical Feasibility of Deep Learning-Based Image Reconstruction on Coronary Computed Tomography Angiography

This study evaluated the feasibility of deep-learning-based image reconstruction (DLIR) on coronary computed tomography angiography (CCTA). By using a 20 cm water phantom, the noise reduction ratio and noise power spectrum were evaluated according to the different reconstruction methods. Then 46 patients who underwent CCTA were retrospectively enrolled. CCTA was performed using the 16 cm coverage axial volume scan technique. All CT images were reconstructed using filtered back projection (FBP); three model-based iterative reconstructions (MBIR) of 40%, 60%, and 80%; and three DLIR algorithms: low (L), medium (M), and high (H). Quantitative and qualitative image qualities of CCTA were compared according to the reconstruction methods. In the phantom study, the noise reduction ratios of MBIR-40%, MBIR-60%, MBIR-80%, DLIR-L, DLIR-M, and DLIR-H were 26.7 ± 0.2%, 39.5 ± 0.5%, 51.7 ± 0.4%, 33.1 ± 0.8%, 43.2 ± 0.8%, and 53.5 ± 0.1%, respectively. The pattern of the noise power spectrum of the DLIR images was more similar to FBP images than MBIR images. In a CCTA study, CCTA yielded a significantly lower noise index with DLIR-H reconstruction than with the other reconstruction methods. DLIR-H showed a higher SNR and CNR than MBIR (p < 0.05). The qualitative image quality of CCTA with DLIR-H was significantly higher than that of MBIR-80% or FBP. The DLIR algorithm was feasible and yielded a better image quality than the FBP or MBIR algorithms on CCTA.

XCIST-an open access x-ray/CT simulation toolkit

Objective. X-ray-based imaging modalities including mammography and computed tomography (CT) are widely used in cancer screening, diagnosis, staging, treatment planning, and therapy response monitoring. Over the past few decades, improvements to these modalities have resulted in substantially improved efficacy and efficiency, and substantially reduced radiation dose and cost. However, such improvements have evolved more slowly than would be ideal because lengthy preclinical and clinical evaluation is required. In many cases, new ideas cannot be evaluated due to the high cost of fabricating and testing prototypes. Wider availability of computer simulation tools could accelerate development of new imaging technologies. This paper introduces the development of a new open-access simulation environment for x-ray-based imaging. The main motivation of this work is to publicly distribute a fast but accurate ray-tracing x-ray and CT simulation tool along with realistic phantoms and 3D reconstruction capability, building on decades of developments in industry and academia.Approach. The x-ray-based Cancer Imaging Simulation Toolkit (XCIST) is developed in the context of cancer imaging, but can more broadly be applied. XCIST is physics-based, written in Python and C/C++, and currently consists of three major subsets: digital phantoms, the simulator itself (CatSim), and image reconstruction algorithms; planned future features include a fast dose-estimation tool and rigorous validation. To enable broad usage and to model and evaluate new technologies, XCIST is easily extendable by other researchers. To demonstrate XCIST's ability to produce realistic images and to show the benefits of using XCIST for insight into the impact of separate physics effects on image quality, we present exemplary simulations by varying contributing factors such as noise and sampling.Main results. The capabilities and flexibility of XCIST are demonstrated, showing easy applicability to specific simulation problems. Geometric and x-ray attenuation accuracy are shown, as well as XCIST's ability to model multiple scanner and protocol parameters, and to attribute fundamental image quality characteristics to specific parameters.Significance. This work represents an important first step toward the goal of creating an open-access platform for simulating existing and emerging x-ray-based imaging systems. While numerous simulation tools exist, we believe the combined XCIST toolset provides a unique advantage in terms of modeling capabilities versus ease of use and compute time. We publicly share this toolset to provide an environment for scientists to accelerate and improve the relevance of their research in x-ray and CT.

Sparse Angle CBCT Reconstruction Based on Guided Image Filtering

Cone-beam Computerized Tomography (CBCT) has the advantages of high ray utilization and detection efficiency, short scan time, high spatial and isotropic resolution. However, the X-rays emitted by CBCT examination are harmful to the human body, so reducing the radiation dose without damaging the reconstruction quality is the key to the reconstruction of CBCT. In this paper, we propose a sparse angle CBCT reconstruction algorithm based on Guided Image FilteringGIF, which combines the classic Simultaneous Algebra Reconstruction Technique(SART) and the Total p-Variation (TpV) minimization. Due to the good edge-preserving ability of SART and noise suppression ability of TpV minimization, the proposed method can suppress noise and artifacts while preserving edge and texture information in reconstructed images. Experimental results based on simulated and real-measured CBCT datasets show the advantages of the proposed method.

High-performance reconstruction of CT medical images by using out-of-core methods in GPU

BACKGROUND AND OBJECTIVE

Since Computed Tomography (CT) is one of the most widely used medical imaging tests, it is essential to work on methods that reduce the radiation the patient is exposed to. Although there are several possible approaches to achieve this, we focus on reducing the exposure time through sparse sampling. With this approach, efficient algebraic methods are needed to be able to generate the images in real time, and since their computational cost is high, using high-performance computing is essential.

METHODS

In this paper we present a GPU (Graphics Processing Unit) software for solving the CT image reconstruction problem using the QR factorization performed with out-of-core (OOC) techniques. This implementation is optimized to reduce the data transfer times between disk, CPU, and GPU, as well as to overlap input/output operations and computations.

RESULTS

The experimental study shows that a block cache stored on main page-locked memory is more efficient than using a cache on GPU memory or mirroring it in both GPU and CPU memory. Compared to a CPU version, this implementation is up to 6.5 times faster, providing an improved image quality when compared to other reconstruction methods.

CONCLUSIONS

The software developed is an optimized version of the QR factorization for GPU that allows the algebraic reconstruction of CT images with high quality and resolution, with a performance that can be compared with state-of-the-art methods used in clinical practice. This approach allows reducing the exposure time of the patient and thus the radiation dose.

Exact gram filtering and efficient back projection for iterative CT reconstruction

PURPOSE

Forward and back-projections are the basis of all model-based iterative reconstruction (MBIR) methods. However, computing these accurately is time consuming. In this paper, we present a method for model-based iterative reconstruction in parallel X-ray beam geometry that utilizes a Gram filter to efficiently implement forward and back projection.

METHODS

We propose using voxel-basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of back-projection. In the special case of parallel X-ray beam geometry, the forward and back-projection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel-basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of back-projection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realistic scenarios.

RESULTS

The proposed method is tested on both phantom and real CT images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state-of-the-art projection models in terms of speed and accuracy for both back-projection and reconstruction.

CONCLUSIONS

We proposed a iterative reconstruction methodology for 3D parallel-beam X-ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state-of-the-art projection models on both back-projection and reconstruction results significantly. This article is protected by copyright. All rights reserved.

A new weighting scheme for arc based circle cone-beam CT reconstruction

In this paper, we present an arc based fan-beam computed tomography (CT) reconstruction algorithm by applying Katsevich's helical CT image reconstruction formula to 2D fan-beam CT scanning data. Specifically, we propose a new weighting function to deal with the redundant data. Our weighting function ϖ(x_,λ) is an average of two characteristic functions, where each characteristic function indicates whether the projection data of the scanning angle contributes to the intensity of the pixel x_. In fact, for every pixel x_, our method uses the projection data of two scanning angle intervals to reconstruct its intensity, where one interval contains the starting angle and another contains the end angle. Each interval corresponds to a characteristic function. By extending the fan-beam algorithm to the circle cone-beam geometry, we also obtain a new circle cone-beam CT reconstruction algorithm. To verify the effectiveness of our method, the simulated experiments are performed for 2D fan-beam geometry with straight line detectors and 3D circle cone-beam geometry with flat-plan detectors, where the simulated sinograms are generated by the open-source software "ASTRA toolbox." We compare our method with the other existing algorithms. Our experimental results show that our new method yields the lowest root-mean-square-error (RMSE) and the highest structural-similarity (SSIM) for both reconstructed 2D and 3D fan-beam CT images.

Deep learning enabled ultra-fast-pitch acquisition in clinical X-ray computed tomography

OBJECTIVE

In X-raycomputed tomography (CT), many important clinical applications may benefit from a fast acquisition speed. The helical scan is the most widely used acquisition mode in clinical CT, where a fast helical pitch can improve the acquisition speed. However, on a typical single-source helical CT (SSCT) system, the helical pitch p typically cannot exceed 1.5; otherwise, reconstruction artifacts will result from data insufficiency. The purpose of this work is to develop a deep convolutional neural network (CNN) to correct for artifacts caused by an ultra-fast pitch, which can enable faster acquisition speed than what is currently achievable.

METHODS

A customized CNN (denoted as ultra-fast-pitch network (UFP-net)) was developed to restore the underlying anatomical structure from the artifact-corrupted post-reconstruction data acquired from SSCT with ultra-fast pitch (i.e., p ≥ 2). UFP-net employed residual learning to capture the features of image artifacts. UFP-net further deployed in-house-customized functional blocks with spatial-domain local operators and frequency-domain non-local operators, to explore multi-scale feature representation. Images of contrast-enhanced patient exams (n = 83) with routine pitch setting (i.e., p < 1) were retrospectively collected, which were used as training and testing datasets. This patient cohort involved CT exams over different scan ranges of anatomy (chest, abdomen, and pelvis) and CT systems (Siemens Definition, Definition Flash, Definition AS+, Siemens Healthcare, Inc.), and the corresponding base CT scanning protocols used consistent settings of major scan parameters (e.g., collimation and pitch). Forward projection of the original images was calculated to synthesize helical CT scans with one regular pitch setting (p = 1) and two ultra-fast-pitch setting (p = 2 and 3). All patient images were reconstructed using the standard filtered-back-projection (FBP) algorithm. A customized multi-stage training scheme was developed to incrementally optimize the parameters of UFP-net, using ultra-fast-pitch images as network inputs and regular pitch images as labels. Visual inspection was conducted to evaluate image quality. Structural similarity index (SSIM) and relative root-mean-square error (rRMSE) were used as quantitative quality metrics.

RESULTS

The UFP-net dramatically improved image quality over standard FBP at both ultra-fast-pitch settings. At p = 2, UFP-net yielded higher mean SSIM (> 0.98) with lower mean rRMSE (< 2.9%), compared to FBP (mean SSIM < 0.93; mean rRMSE > 9.1%). Quantitative metrics at p = 3: UFP-net-mean SSIM [0.86, 0.94] and mean rRMSE [5.0%, 8.2%]; FBP-mean SSIM [0.36, 0.61] and mean rRMSE [36.0%, 58.6%].

CONCLUSION

The proposed UFP-net has the potential to enable ultra-fast data acquisition in clinical CT without sacrificing image quality. This method has demonstrated reasonable generalizability over different body parts when the corresponding CT exams involved consistent base scan parameters.

Computed tomography medical image reconstruction on affordable equipment by using Out-Of-Core techniques

BACKGROUND AND OBJECTIVE

As Computed Tomography scans are an essential medical test, many techniques have been proposed to reconstruct high-quality images using a smaller amount of radiation. One approach is to employ algebraic factorization methods to reconstruct the images, using fewer views than the traditional analytical methods. However, their main drawback is the high computational cost and hence the time needed to obtain the images, which is critical in the daily clinical practice. For this reason, faster methods for solving this problem are required.

METHODS

In this paper, we propose a new reconstruction method based on the QR factorization that is very efficient on affordable equipment (standard multicore processors and standard Solid-State Drives) by using Out-Of-Core techniques.

RESULTS

Combining both affordable hardware and the new software proposed in our work, the images can be reconstructed very quickly and with high quality. We analyze the reconstructions using real Computed Tomography images selected from a dataset, comparing the QR method to the LSQR and FBP. We measure the quality of the images using the metrics Peak Signal-To-Noise Ratio and Structural Similarity Index, obtaining very high values. We also compare the efficiency of using spinning disks versus Solid-State Drives, showing how the latter performs the Input/Output operations in a significantly lower amount of time.

CONCLUSIONS

The results indicate that our proposed me thod and software are valid to efficiently solve large-scale systems and can be applied to the Computed Tomography reconstruction problem to obtain high-quality images.

Head Motion Correction Based on Filtered Backprojection in Helical CT Scanning

Head motion may unexpectedly occur during a CT scan. It thereby results in motion artifacts in a reconstructed image and may lead to a false diagnosis or a failure of diagnosis. To alleviate this motion problem, as a hardware approach, increasing the gantry rotation speed or using an immobilization device is usually considered. These approaches, however, cannot completely resolve the motion problem. Hence, motion estimation (ME) and compensation for it have been explored as a software approach instead. In this paper, adopting the latter approach, we propose a head motion correction algorithm in helical CT scanning, based on filtered backprojection (FBP). For the motion correction, we first introduce a new motion-compensated (MC) reconstruction scheme based on FBP, which is applicable to helical scanning. We then estimate the head motion parameters by using an iterative nonlinear optimization algorithm, or the L-BFGS. Note here that an objective function for the optimization is defined on reconstructed images in each iteration, which are obtained by using the proposed MC reconstruction scheme. Using the estimated motion parameters, we then obtain the final MC reconstructed image. Using numerical and physical phantom datasets along with simulated head motions, we demonstrate that the proposed algorithm can provide significantly improved quality to MC reconstructed images by alleviating motion artifacts.

Three-Dimensional Weighting in Cone Beam FBP Reconstruction and Its Transformation Over Geometries

GOALS

With substantially increased number of detector rows in multidetector CT (MDCT), axial scan with projection data acquired along a circular source trajectory has become the method-of-choice in increasing clinical applications. Recognizing the practical relevance of image reconstruction directly from the projection data acquired in the native cone beam (CB) geometry, especially in scenarios wherein the most achievable in-plane resolution is desirable, we present a three-dimensional (3-D) weighted CB-FBP algorithm in such geometry in this paper.

METHODS

We start the algorithm's derivation in the cone-parallel geometry. Via changing of variables, taking the Jacobian into account and making heuristic and empirical assumptions, we arrive at the formulas for 3-D weighted image reconstruction in the native CB geometry.

RESULTS

Using the projection data simulated by computer and acquired by an MDCT scanner, we evaluate and verify performance of the proposed algorithm for image reconstruction directly from projection data acquired in the native CB geometry.

CONCLUSION

The preliminary data show that the proposed algorithm performs as well as the 3-D weighted CB-FBP algorithm in the cone-parallel geometry.

SIGNIFICANCE

The proposed algorithm is anticipated to find its utility in extensive clinical and preclinical applications wherein the reconstruction of images in the native CB geometry, i.e., the geometry for data acquisition, is of relevance.

A fast iteration approach to undersampled cone-beam CT reconstruction

BACKGROUND

Due to large dimensional matrix multiplications, the existing iterative algorithms for cone beam computed tomography (CBCT) reconstruction often face problems of heavy computational workload and large volume of memory usage.

OBJECTIVE

This study proposes and tests an iterative algorithm of 3DA-TVAL3 for fast reconstruction of CBCT images using undersampled measurement data and the reduced amount of computer memories.

METHODS

In order to reduce computational workload and computer memories based on the sparsity of the CBCT measurement matrix, the proposed iterative algorithm applies elementwise scalar multiplications in the iterative computation to search for optimal solution. Through a number of tests on three different CT data sets with different number of projections, the reconstruction performance of the proposed algorithm is compared with that of two accelerated iterative algorithms and the conventional FDK algorithm.

RESULTS

The visual and quantitative evaluations using the normalized mean square error, peak signal to noise ratio and structural similarity metrics demonstrated the faster computational time and the higher image quality of using the proposed 3DA-TVAL3 algorithm than using other conventional algorithms under comparison.

CONCLUSIONS

The proposed 3DA-TVAL3 algorithm can perform efficient and fast computation of CBCT reconstruction using the reduced amount of computer memories.

On the data acquisition, image reconstruction, cone beam artifacts, and their suppression in axial MDCT and CBCT - A review

PURPOSE

In the clinic, computed tomography (CT) has evolved into an essential modality for diagnostic imaging by multidetector row CT (MDCT) and image guided intervention by cone beam CT (CBCT). Recognizing the increasing importance of axial MDCT/CBCT in clinical and preclinical applications, and the existence of CB artifacts in MDCT/CBCT images, we provide a review of CB artifacts' root causes, rendering mechanisms and morphology, and possible solutions for elimination and/or reduction of the artifacts.

METHODS

By examining the null space in Radon and Fourier domain, the root cause of CB artifacts (i.e., data insufficiency) in axial MDCT/CBCT is analytically investigated, followed by a review of the data sufficiency conditions and the "circle +" source trajectories. The rendering mechanisms and morphology of CB artifacts in axial MDCT/CBCT and their special cases (e.g., half/short scan and full scan with latitudinally displaced detector) are then analyzed, followed by a survey of the potential solutions to suppress the artifacts. The phenomenon of imaged zone indention and its variation over FBP, BPF/DBPF, two-pass and iterative CB reconstruction algorithms and/or schemes are discussed in detail.

RESULTS

An interdomain examination of the null space provides an insightful understanding of the root cause of CB artifacts in axial MDCT/CBCT. The decomposition of CB artifacts rendering mechanisms facilitates understanding of the artifacts' behavior under different conditions and the potential solutions to suppress them. An inspection of the imaged zone intention phenomenon provides guidance on the design and implementation of CB image reconstruction algorithms and schemes for CB artifacts suppression in axial MDCT/CBCT.

CONCLUSIONS

With increasing importance of axial MDCT/CBCT in clinical and preclinical applications, this review article can update the community with in-depth information and clarification on the latest progress in dealing with CB artifacts and thus increase clinical/preclinical confidence.

Cardiac Motion Correction for Helical CT Scan With an Ordinary Pitch

Cardiac X-ray computed tomography (CT) imaging is still challenging due to the cardiac motion during CT scanning, which leads to the presence of motion artifacts in the reconstructed image. In response, many cardiac X-ray CT imaging algorithms have been proposed, based on motion estimation (ME) and motion compensation (MC), to improve the image quality by alleviating the motion artifacts in the reconstructed image. However, these ME/MC algorithms are mainly based on an axial scan or a low-pitch helical scan. In this paper, we propose a ME/MC-based cardiac imaging algorithm for the data set acquired from a helical scan with an ordinary pitch of around 1.0 so as to obtain the whole cardiac image within a single scan of short time without ECG gating. In the proposed algorithm, a sequence of partial angle reconstructed (PAR) images is generated by using consecutive parts of the sinogram, each of which has a small angular span. Subsequently, an initial 4-D motion vector field (MVF) is obtained using multiple pairs of conjugate PAR images. The 4-D MVF is then refined based on an image quality metric so as to improve the quality of the motion-compensated image. Finally, a time-resolved cardiac image is obtained by performing motion-compensated image reconstruction by using the refined 4-D MVF. Using digital XCAT phantom data sets and a human data set commonly obtained via a helical scan with a pitch of 1.0, we demonstrate that the proposed algorithm significantly improves the image quality by alleviating motion artifacts.

Evaluation of an Analytic Reconstruction Method as a Platform for Spectral Cone-beam CT

With the fast development of photon counting detection techniques, spectral CT with a photon counting detector has attracted considerable attention by increasing energy-resolution to identify and discriminate materials. The conventional analytic reconstruction algorithms can be directly applied to reconstruct spectral CT images for each spectrum or energy bin. However, a comprehensive evaluation of analytic reconstruction algorithms for spectral CT has not been reported yet. This motivates us to evaluate the analytic spiral cone-beam CT algorithms and to provide a fair comparison platform for the state-of-the-art iterative spectral CT reconstruction algorithms. Considering the fact that a narrow energy bin has high noise which degrades the imaging quality of spectral CT, an adaptive maximum a posterior (MAP) projection restoration algorithm is first used to reduce the noise, and then a 2D/3D weighted spiral Feldkamp-Davis-Kress (FDK) algorithm is implemented to reconstruct the spectral CT images at different energy bins. Finally, the principle component analysis (PCA) is employed to render the spectral reconstruction results into a color space. Our numerical results show that the analytic reconstruction approach is fast and it can provide high spatial resolution, high contrast resolution and high signal-noise-ratio (SNR) under higher helical pitches. This makes it possible to serve as a platform to evaluate the state-of-the-art iterative spectral CT algorithms.

Task-based statistical image reconstruction for high-quality cone-beam CT

Task-based analysis of medical imaging performance underlies many ongoing efforts in the development of new imaging systems. In statistical image reconstruction, regularization is often formulated in terms to encourage smoothness and/or sharpness (e.g. a linear, quadratic, or Huber penalty) but without explicit formulation of the task. We propose an alternative regularization approach in which a spatially varying penalty is determined that maximizes task-based imaging performance at every location in a 3D image. We apply the method to model-based image reconstruction (MBIR-viz., penalized weighted least-squares, PWLS) in cone-beam CT (CBCT) of the head, focusing on the task of detecting a small, low-contrast intracranial hemorrhage (ICH), and we test the performance of the algorithm in the context of a recently developed CBCT prototype for point-of-care imaging of brain injury. Theoretical predictions of local spatial resolution and noise are computed via an optimization by which regularization (specifically, the quadratic penalty strength) is allowed to vary throughout the image to maximize local task-based detectability index ([Formula: see text]). Simulation studies and test-bench experiments were performed using an anthropomorphic head phantom. Three PWLS implementations were tested: conventional (constant) penalty; a certainty-based penalty derived to enforce constant point-spread function, PSF; and the task-based penalty derived to maximize local detectability at each location. Conventional (constant) regularization exhibited a fairly strong degree of spatial variation in [Formula: see text], and the certainty-based method achieved uniform PSF, but each exhibited a reduction in detectability compared to the task-based method, which improved detectability up to ~15%. The improvement was strongest in areas of high attenuation (skull base), where the conventional and certainty-based methods tended to over-smooth the data. The task-driven reconstruction method presents a promising regularization method in MBIR by explicitly incorporating task-based imaging performance as the objective. The results demonstrate improved ICH conspicuity and support the development of high-quality CBCT systems.

Optimization of data acquisition in axial CT under the framework of sampling on lattice for suppression of aliasing artifacts with algorithmic detector interlacing

PURPOSE

We present the methodology for analyzing and optimizing the sampling structure of projection data acquisition in axial multidetector CT (MDCT) and cone beam CT (CBCT) under the framework of sampling on lattice. Specifically, we propose and evaluate the scheme of interlaced detector cell binning for suppression of longitudinal aliasing artifacts. In addition, we investigate the proposed scheme's capability of mitigating shift variation in spatial resolution and possibility of improving CB image reconstruction accuracy.

METHODS

Under the framework of sampling on lattice, the proposed scheme is evaluated using an axial MDCT with its architecture similar to that of state-of-the-art CT scanners for diagnostic imaging in the clinic. The widely used FDK algorithm is adopted for image reconstruction, in which either horizontal/latitudinal or vertical/longitudinal interpolation is used for lining-up of projection data between interlaced detector cells. Using a spiral clock phantom, the capability of suppressing aliasing artifacts and possibility of improving reconstruction accuracy is quantitatively investigated. The in-plane spatial resolution, as assessed by the modulation transfer function (MTF), and its shift-variant property are quantitatively assessed using wire phantoms, while the through-plane spatial resolution and its shift-variant behavior are assessed by the slice sensitivity profile (SSP) using thin foil phantoms.

RESULTS

The preliminary results show that the interlaced detector cell binning can suppress longitudinal aliasing artifacts effectively, while the shift variation in spatial resolution and reconstruction inaccuracy can be mitigated moderately. In addition, the direction, along which the interpolation is carried out to line up projection data between the interlaced detector cells for image reconstruction, plays a significant role in determining the in-plane and through-plane spatial resolution.

CONCLUSIONS

The scheme of interlaced detector cell binning with longitudinal interpolation for data lining-up is an effective solution for suppression of longitudinal aliasing artifacts in axial MDCT and CBCT.

Cardiac Image Reconstruction via Nonlinear Motion Correction Based on Partial Angle Reconstructed Images

Even though the X-ray Computed Tomography (CT) scan is considered suitable for fast imaging, motion-artifact-free cardiac imaging is still an important issue, because the gantry rotation speed is not fast enough compared with the heart motion. To obtain a heart image with less motion artifacts, a motion estimation (ME) and motion compensation (MC) approach is usually adopted. In this paper, we propose an ME/MC algorithm that can estimate a nonlinear heart motion model from a sinogram with a rotation angle of less than 360°. In this algorithm, we first assume the heart motion to be nonrigid but linear, and thereby estimate an initial 4-D motion vector field (MVF) during a half rotation by using conjugate partial angle reconstructed images, as in our previous ME/MC algorithm. We then refine the MVF to determine a more accurate nonlinear MVF by maximizing the information potential of a motion-compensated image. Finally, MC is performed by incorporating the determined MVF into the image reconstruction process, and a time-resolved heart image is obtained. By using a numerical phantom, a physical cardiac phantom, and an animal data set, we demonstrate that the proposed algorithm can noticeably improve the image quality by reducing motion artifacts throughout the image.

Technical Note: FreeCT_wFBP: A robust, efficient, open-source implementation of weighted filtered backprojection for helical, fan-beam CT

PURPOSE

With growing interest in quantitative imaging, radiomics, and CAD using CT imaging, the need to explore the impacts of acquisition and reconstruction parameters has grown. This usually requires extensive access to the scanner on which the data were acquired and its workflow is not designed for large-scale reconstruction projects. Therefore, the authors have developed a freely available, open-source software package implementing a common reconstruction method, weighted filtered backprojection (wFBP), for helical fan-beam CT applications.

METHODS

FreeCT_wFBP is a low-dependency, GPU-based reconstruction program utilizing c for the host code and Nvidia CUDA C for GPU code. The software is capable of reconstructing helical scans acquired with arbitrary pitch-values, and sampling techniques such as flying focal spots and a quarter-detector offset. In this work, the software has been described and evaluated for reconstruction speed, image quality, and accuracy. Speed was evaluated based on acquisitions of the ACR CT accreditation phantom under four different flying focal spot configurations. Image quality was assessed using the same phantom by evaluating CT number accuracy, uniformity, and contrast to noise ratio (CNR). Finally, reconstructed mass-attenuation coefficient accuracy was evaluated using a simulated scan of a FORBILD thorax phantom and comparing reconstructed values to the known phantom values.

RESULTS

The average reconstruction time evaluated under all flying focal spot configurations was found to be 17.4 ± 1.0 s for a 512 row × 512 column × 32 slice volume. Reconstructions of the ACR phantom were found to meet all CT Accreditation Program criteria including CT number, CNR, and uniformity tests. Finally, reconstructed mass-attenuation coefficient values of water within the FORBILD thorax phantom agreed with original phantom values to within 0.0001 mm(2)/g (0.01%).

CONCLUSIONS

FreeCT_wFBP is a fast, highly configurable reconstruction package for third-generation CT available under the GNU GPL. It shows good performance with both clinical and simulated data.

Optimization of an on-board imaging system for extremely rapid radiation therapy

PURPOSE

Next-generation extremely rapid radiation therapy systems could mitigate the need for motion management, improve patient comfort during the treatment, and increase patient throughput for cost effectiveness. Such systems require an on-board imaging system that is competitively priced, fast, and of sufficiently high quality to allow good registration between the image taken on the day of treatment and the image taken the day of treatment planning. In this study, three different detectors for a custom on-board CT system were investigated to select the best design for integration with an extremely rapid radiation therapy system.

METHODS

Three different CT detectors are proposed: low-resolution (all 4×4 mm pixels), medium-resolution (a combination of 4×4 mm pixels and 2×2 mm pixels), and high-resolution (all 1×1 mm pixels). An in-house program was used to generate projection images of a numerical anthropomorphic phantom and to reconstruct the projections into CT datasets, henceforth called "realistic" images. Scatter was calculated using a separate Monte Carlo simulation, and the model included an antiscatter grid and bowtie filter. Diagnostic-quality images of the phantom were generated to represent the patient scan at the time of treatment planning. Commercial deformable registration software was used to register the diagnostic-quality scan to images produced by the various on-board detector configurations. The deformation fields were compared against a "gold standard" deformation field generated by registering initial and deformed images of the numerical phantoms that were used to make the diagnostic and treatment-day images. Registrations of on-board imaging system data were judged by the amount their deformation fields differed from the corresponding gold standard deformation fields--the smaller the difference, the better the system. To evaluate the registrations, the pointwise distance between gold standard and realistic registration deformation fields was computed.

RESULTS

By most global metrics (e.g., mean, median, and maximum pointwise distance), the high-resolution detector had the best performance but the medium-resolution detector was comparable. For all medium- and high-resolution detector registrations, mean error between the realistic and gold standard deformation fields was less than 4 mm. By pointwise metrics (e.g., tracking a small lesion), the high- and medium-resolution detectors performed similarly. For these detectors, the smallest error between the realistic and gold standard registrations was 0.6 mm and the largest error was 3.6 mm.

CONCLUSIONS

The medium-resolution CT detector was selected as the best for an extremely rapid radiation therapy system. In essentially all test cases, data from this detector produced a significantly better registration than data from the low-resolution detector and a comparable registration to data from the high-resolution detector. The medium-resolution detector provides an appropriate compromise between registration accuracy and system cost.

Cardiac motion correction based on partial angle reconstructed images in x-ray CT

PURPOSE

Cardiac x-ray CT imaging is still challenging due to heart motion, which cannot be ignored even with the current rotation speed of the equipment. In response, many algorithms have been developed to compensate remaining motion artifacts by estimating the motion using projection data or reconstructed images. In these algorithms, accurate motion estimation is critical to the compensated image quality. In addition, since the scan range is directly related to the radiation dose, it is preferable to minimize the scan range in motion estimation. In this paper, the authors propose a novel motion estimation and compensation algorithm using a sinogram with a rotation angle of less than 360°. The algorithm estimates the motion of the whole heart area using two opposite 3D partial angle reconstructed (PAR) images and compensates the motion in the reconstruction process.

METHODS

A CT system scans the thoracic area including the heart over an angular range of 180° + α + β, where α and β denote the detector fan angle and an additional partial angle, respectively. The obtained cone-beam projection data are converted into cone-parallel geometry via row-wise fan-to-parallel rebinning. Two conjugate 3D PAR images, whose center projection angles are separated by 180°, are then reconstructed with an angular range of β, which is considerably smaller than a short scan range of 180° + α. Although these images include limited view angle artifacts that disturb accurate motion estimation, they have considerably better temporal resolution than a short scan image. Hence, after preprocessing these artifacts, the authors estimate a motion model during a half rotation for a whole field of view via nonrigid registration between the images. Finally, motion-compensated image reconstruction is performed at a target phase by incorporating the estimated motion model. The target phase is selected as that corresponding to a view angle that is orthogonal to the center view angles of two conjugate PAR images. To evaluate the proposed algorithm, digital XCAT and physical dynamic cardiac phantom datasets are used. The XCAT phantom datasets were generated with heart rates of 70 and 100 bpm, respectively, by assuming a system rotation time of 300 ms. A physical dynamic cardiac phantom was scanned using a slowly rotating XCT system so that the effective heart rate will be 70 bpm for a system rotation speed of 300 ms.

RESULTS

In the XCAT phantom experiment, motion-compensated 3D images obtained from the proposed algorithm show coronary arteries with fewer motion artifacts for all phases. Moreover, object boundaries contaminated by motion are well restored. Even though object positions and boundary shapes are still somewhat different from the ground truth in some cases, the authors see that visibilities of coronary arteries are improved noticeably and motion artifacts are reduced considerably. The physical phantom study also shows that the visual quality of motion-compensated images is greatly improved.

CONCLUSIONS

The authors propose a novel PAR image-based cardiac motion estimation and compensation algorithm. The algorithm requires an angular scan range of less than 360°. The excellent performance of the proposed algorithm is illustrated by using digital XCAT and physical dynamic cardiac phantom datasets.

Cardiac CT: A system architecture study

BACKGROUND

We are interested in exploring dedicated, high-performance cardiac CT systems optimized to provide the best tradeoff between system cost, image quality, and radiation dose.

OBJECTIVE

We sought to identify and evaluate a broad range of CT architectures that could provide an optimal, dedicated cardiac CT solution.

METHODS

We identified and evaluated thirty candidate architectures using consistent design choices. We defined specific evaluation metrics related to cost and performance. We then scored the candidates versus the defined metrics. Lastly, we applied a weighting system to combine scores for all metrics into a single overall score for each architecture. CT experts with backgrounds in cardiovascular radiology, x-ray physics, CT hardware and CT algorithms performed the scoring and weighting.

RESULTS

We found nearly a twofold difference between the most and the least promising candidate architectures. Architectures employed by contemporary commercial diagnostic CT systems were among the highest-scoring candidates. We identified six architectures that show sufficient promise to merit further in-depth analysis and comparison.

CONCLUSION

Our results suggest that contemporary diagnostic CT system architectures outperform most other candidates that we evaluated, but the results for a few alternatives were relatively close. We selected six representative high-scoring candidates for more detailed design and further comparative evaluation.

Axial Cone-Beam Reconstruction by Weighted BPF/DBPF and Orthogonal Butterfly Filtering

GOAL

The backprojection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical reconstruction from cone-beam (CB) scan data and axial reconstruction from fan beam data, respectively. These two algorithms can be heuristically extended for image reconstruction from axial CB scan data, but induce severe artifacts in images located away from the central plane, determined by the circular source trajectory. We propose an algorithmic solution herein to eliminate the artifacts.

METHODS

The solution is an integration of three-dimensional (3-D) weighted axial CB-BPF/DBPF algorithm with orthogonal butterfly filtering, namely axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering. Using the computer simulated Forbild head and thoracic phantoms that are rigorous in inspecting the reconstruction accuracy, and an anthropomorphic thoracic phantom with projection data acquired by a CT scanner, we evaluate the performance of the proposed algorithm.

RESULTS

Preliminary results show that the orthogonal butterfly filtering can eliminate the severe streak artifacts existing in the images reconstructed by the 3-D weighted axial CB-BPF/DBPF algorithm located at off-central planes.

CONCLUSION

Integrated with orthogonal butterfly filtering, the 3-D weighted CB-BPF/DBPF algorithm can perform at least as well as the 3-D weighted CB-FBP algorithm in image reconstruction from axial CB scan data.

SIGNIFICANCE

The proposed 3-D weighted axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering can be an algorithmic solution for CT imaging in extensive clinical and preclinical applications.

An algorithm to estimate the object support in truncated images

PURPOSE

Truncation artifacts in CT occur if the object to be imaged extends past the scanner field of view (SFOV). These artifacts impede diagnosis and could possibly introduce errors in dose plans for radiation therapy. Several approaches exist for correcting truncation artifacts, but existing correction algorithms do not accurately recover the skin line (or support) of the patient, which is important in some dose planning methods. The purpose of this paper was to develop an iterative algorithm that recovers the support of the object.

METHODS

The authors assume that the truncated portion of the image is made up of soft tissue of uniform CT number and attempt to find a shape consistent with the measured data. Each known measurement in the sinogram is interpreted as an estimate of missing mass along a line. An initial estimate of the object support is generated by thresholding a reconstruction made using a previous truncation artifact correction algorithm (e.g., water cylinder extrapolation). This object support is iteratively deformed to reduce the inconsistency with the measured data. The missing data are estimated using this object support to complete the dataset. The method was tested on simulated and experimentally truncated CT data.

RESULTS

The proposed algorithm produces a better defined skin line than water cylinder extrapolation. On the experimental data, the RMS error of the skin line is reduced by about 60%. For moderately truncated images, some soft tissue contrast is retained near the SFOV. As the extent of truncation increases, the soft tissue contrast outside the SFOV becomes unusable although the skin line remains clearly defined, and in reformatted images it varies smoothly from slice to slice as expected.

CONCLUSIONS

The support recovery algorithm provides a more accurate estimate of the patient outline than thresholded, basic water cylinder extrapolation, and may be preferred in some radiation therapy applications.

Control algorithms for dynamic attenuators

PURPOSE

The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator.

METHODS

The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen.

RESULTS

The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution.

CONCLUSIONS

Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods.

Dose reduction using a dynamic, piecewise-linear attenuator

PURPOSE

The authors recently proposed a dynamic, prepatient x-ray attenuator capable of producing a piecewise-linear attenuation profile customized to each patient and viewing angle. This attenuator was intended to reduce scatter-to-primary ratio (SPR), dynamic range, and dose by redistributing flux. In this work the authors tested the ability of the attenuator to reduce dose and SPR in simulations.

METHODS

The authors selected four clinical applications, including routine full field-of-view scans of the thorax and abdomen, and targeted reconstruction tasks for an abdominal aortic aneurysm and the pancreas. Raw data were estimated by forward projection of the image volume datasets. The dynamic attenuator was controlled to reduce dose while maintaining peak variance by solving a convex optimization problem, assuminga priori knowledge of the patient anatomy. In targeted reconstruction tasks, the noise in specific regions was given increased weighting. A system with a standard attenuator (or "bowtie filter") was used as a reference, and used either convex optimized tube current modulation (TCM) or a standard TCM heuristic. The noise of the scan was determined analytically while the dose was estimated using Monte Carlo simulations. Scatter was also estimated using Monte Carlo simulations. The sensitivity of the dynamic attenuator to patient centering was also examined by shifting the abdomen in 2 cm intervals.

RESULTS

Compared to a reference system with optimized TCM, use of the dynamic attenuator reduced dose by about 30% in routine scans and 50% in targeted scans. Compared to the TCM heuristics which are typically used withouta priori knowledge, the dose reduction is about 50% for routine scans. The dynamic attenuator gives the ability to redistribute noise and variance and produces more uniform noise profiles than systems with a conventional bowtie filter. The SPR was also modestly reduced by 10% in the thorax and 24% in the abdomen. Imaging with the dynamic attenuator was relatively insensitive to patient centering, showing a 17% increase in peak variance for a 6 cm shift of the abdomen, instead of an 82% increase in peak variance for a fixed bowtie filter.

CONCLUSIONS

A dynamic prepatient x-ray attenuator consisting of multiple wedges is capable of achieving substantial dose reductions and modest SPR reductions.

The piecewise-linear dynamic attenuator reduces the impact of count rate loss with photon-counting detectors

Photon counting x-ray detectors (PCXDs) offer several advantages compared to standard energy-integrating x-ray detectors, but also face significant challenges. One key challenge is the high count rates required in CT. At high count rates, PCXDs exhibit count rate loss and show reduced detective quantum efficiency in signal-rich (or high flux) measurements. In order to reduce count rate requirements, a dynamic beam-shaping filter can be used to redistribute flux incident on the patient. We study the piecewise-linear attenuator in conjunction with PCXDs without energy discrimination capabilities. We examined three detector models: the classic nonparalyzable and paralyzable detector models, and a 'hybrid' detector model which is a weighted average of the two which approximates an existing, real detector (Taguchi et al 2011 Med. Phys. 38 1089-102). We derive analytic expressions for the variance of the CT measurements for these detectors. These expressions are used with raw data estimated from DICOM image files of an abdomen and a thorax to estimate variance in reconstructed images for both the dynamic attenuator and a static beam-shaping ('bowtie') filter. By redistributing flux, the dynamic attenuator reduces dose by 40% without increasing peak variance for the ideal detector. For non-ideal PCXDs, the impact of count rate loss is also reduced. The nonparalyzable detector shows little impact from count rate loss, but with the paralyzable model, count rate loss leads to noise streaks that can be controlled with the dynamic attenuator. With the hybrid model, the characteristic count rates required before noise streaks dominate the reconstruction are reduced by a factor of 2 to 3. We conclude that the piecewise-linear attenuator can reduce the count rate requirements of the PCXD in addition to improving dose efficiency. The magnitude of this reduction depends on the detector, with paralyzable detectors showing much greater benefit than nonparalyzable detectors.

The feasibility of an inverse geometry CT system with stationary source arrays

PURPOSE

Inverse geometry computed tomography (IGCT) has been proposed as a new system architecture that combines a small detector with a large, distributed source. This geometry can suppress cone-beam artifacts, reduce scatter, and increase dose efficiency. However, the temporal resolution of IGCT is still limited by the gantry rotation time. Large reductions in rotation time are in turn difficult due to the large source array and associated power electronics. We examine the feasibility of using stationary source arrays for IGCT in order to achieve better temporal resolution. We anticipate that multiple source arrays are necessary, with each source array physically separated from adjacent ones.

METHODS

Key feasibility issues include spatial resolution, artifacts, flux, noise, collimation, and system timing clashes. The separation between the different source arrays leads to missing views, complicating reconstruction. For the special case of three source arrays, a two-stage reconstruction algorithm is used to estimate the missing views. Collimation is achieved using a rotating collimator with a small number of holes. A set of equally spaced source spots are designated on the source arrays, and a source spot is energized when a collimator hole is aligned with it. System timing clashes occur when multiple source spots are scheduled to be energized simultaneously. We examine flux considerations to evaluate whether sufficient flux is available for clinical applications.

RESULTS

The two-stage reconstruction algorithm suppresses cone-beam artifacts while maintaining resolution and noise characteristics comparable to standard third generation systems. The residual artifacts are much smaller in magnitude than the cone-beam artifacts eliminated. A mathematical condition is given relating collimator hole locations and the number of virtual source spots for which system timing clashes are avoided. With optimization, sufficient flux may be achieved for many clinical applications.

CONCLUSIONS

IGCT with stationary source arrays could be an imaging platform potentially capable of imaging a complete 16-cm thick volume within a tenth of a second.

Interesting detector shapes for third generation CT scanners

PURPOSE

To discuss options in designing detector shapes in third generation CT and to quantify potential cost savings for compact third generation CT systems, and to extend the work from two-dimensional fan-beam CT to three-dimensional cone-beam CT for circular, sequential, and spiral scan trajectories.

METHODS

Third generation CT scanners typically comprise detectors which are flat or whose shape is the segment of a cylinder or a sphere that is focused onto the focal spot of the x-ray source. There appear to be two design criteria that favor this choice of detector shape. One is the possibility of performing fan-beam and cone-beam filtered backprojection in the native geometry (without rebinning) and the other criterion could be to enable the early use of focused antiscatter grids. It is less known, however, that other detector shapes may also have these properties. While these designs have been evaluated for 2D CT from a theoretical standpoint more than one decade ago the authors revisit and generalize these considerations, extend them to 3D circular, sequential, and spiral cone-beam CT and propose an optimal design in terms of detector costs while keeping image quality constant. Their considerations and conclusions are based on considering the sampling density of the x-rays, including the effects of finite focal spot and finite detector element size. Proposing image reconstruction algorithms or numerically evaluating the results by reconstructing simulated projection data is not within the scope of this work.

RESULTS

If the detector arc is curved to be nearly concentric with the circle describing the edge of the field of measurement significantly less detector area and detector pixels are required compared to today's third generation CT systems where the detector arc is centered about the focal spot. Combined with a detector that just covers the spiral Tam window cost savings of 60% or more are possible in compact CT systems. In terms of practicability the new designs appear to be nearly as easy to realize as today's third generation systems.

CONCLUSIONS

Compact CT systems, which require the focal spot to be mounted close to the edge of the field of measurement, may significantly benefit from using detector shapes other than the typical equiangular detector that is focused onto the focal spot.

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT: spectrum of noise equivalent quanta NEQ(k)

PURPOSE

Differential phase contrast CT (DPC-CT) is emerging as a new technology to improve the contrast sensitivity of conventional attenuation-based CT. The noise equivalent quanta as a function over spatial frequency, i.e., the spectrum of noise equivalent quanta NEQ(k), is a decisive indicator of the signal and noise transfer properties of an imaging system. In this work, we derive the functional form of NEQ(k) in DPC-CT. Via system modeling, analysis, and computer simulation, we evaluate and verify the derived NEQ(k) and compare it with that of the conventional attenuation-based CT.

METHODS

The DPC-CT is implemented with x-ray tube and gratings. The x-ray propagation and data acquisition are modeled and simulated through Fresnel and Fourier analysis. A monochromatic x-ray source (30 keV) is assumed to exclude any system imperfection and interference caused by scatter and beam hardening, while a 360° full scan is carried out in data acquisition to avoid any weighting scheme that may disrupt noise randomness. Adequate upsampling is implemented to simulate the x-ray beam's propagation through the gratings G(1) and G(2) with periods 8 and 4 μm, respectively, while the intergrating distance is 193.6 mm (1∕16 of the Talbot distance). The dimensions of the detector cell for data acquisition are 32 × 32, 64 × 64, 96 × 96, and 128 × 128 μm(2), respectively, corresponding to a 40.96 × 40.96 mm(2) field of view in data acquisition. An air phantom is employed to obtain the noise power spectrum NPS(k), spectrum of noise equivalent quanta NEQ(k), and detective quantum efficiency DQE(k). A cylindrical water phantom at 5.1 mm diameter and complex refraction coefficient n = 1 - δ + iβ = 1 -2.5604 × 10(-7) + i1.2353 × 10(-10) is placed in air to measure the edge transfer function, line spread function and then modulation transfer function MTF(k), of both DPC-CT and the conventional attenuation-based CT. The x-ray flux is set at 5 × 10(6) photon∕cm(2) per projection and observes the Poisson distribution, which is consistent with that of a micro-CT for preclinical applications. Approximately 360 regions, each at 128 × 128 matrix, are used to calculate the NPS(k) via 2D Fourier transform, in which adequate zero padding is carried out to avoid aliasing in noise.

RESULTS

The preliminary data show that the DPC-CT possesses a signal transfer property [MTF(k)] comparable to that of the conventional attenuation-based CT. Meanwhile, though there exists a radical difference in their noise power spectrum NPS(k) (trait 1∕|k| in DPC-CT but |k| in the conventional attenuation-based CT) the NEQ(k) and DQE(k) of DPC-CT and the conventional attenuation-based CT are in principle identical.

CONCLUSIONS

Under the framework of ideal observer study, the joint signal and noise transfer property NEQ(k) and detective quantum efficiency DQE(k) of DPC-CT are essentially the same as those of the conventional attenuation-based CT. The findings reported in this paper may provide insightful guidelines on the research, development, and performance optimization of DPC-CT for extensive preclinical and clinical applications in the future.

Completeness map evaluation demonstrated with candidate next-generation cardiac CT architectures

PURPOSE

In this report, the authors introduce the general concept of the completeness map, as a means to evaluate the completeness of data acquired by a given CT system design (architecture and scan mode). They illustrate the utility of completeness map by applying the completeness map concept to a number of candidate CT system designs, as part of a study to advance the state-of-the-art in cardiac CT.

METHODS

In order to optimally reconstruct a point within a volume of interest (VOI), the Radon transform on all possible planes through that point should be measured. The authors quantified the extent to which this ideal condition is satisfied for the entire image volume. They first determined a Radon completeness number for each point in the VOI, as the percentage of possible planes that is actually measured. A completeness map is then defined as a 3D matrix of the completeness numbers for the entire VOI. The authors proposed algorithms to analyze the projection datasets in Radon space and compute the completeness number for a fixed point and apply these algorithms to various architectures and scan modes that they are evaluating. In this report, the authors consider four selected candidate architectures, operating with different scan modes, for a total of five system design alternatives. Each of these alternatives is evaluated using completeness map.

RESULTS

If the detector size and cone angle are large enough to cover the entire cardiac VOI, a single-source circular scan can have ≥99% completeness over the entire VOI. However, only the central z-slice can be exactly reconstructed, which corresponds to 100% completeness. For a typical single-source architecture, if the detector is limited to an axial dimension of 40 mm, a helical scan needs about five rotations to form an exact reconstruction region covering the cardiac VOI, while a triple-source helical scan only requires two rotations, leading to a 2.5x improvement in temporal resolution. If the source and detector of an inverse-geometry (IGCT) system have the same axial extent, and the spacing of source points in the axial and transaxial directions is sufficiently small, the IGCT can also form an exact reconstruction region for the cardiac VOI. If the VOI can be covered by the x-ray beam in any view, a composite-circling scan can generate an exact reconstruction region covering the VOI.

CONCLUSIONS

The completeness map evaluation provides useful information for selecting the next-generation cardiac CT system design. The proposed completeness map method provides a practical tool for analyzing complex scanning trajectories, where the theoretical image quality for some complex system designs is impossible to predict, without yet-undeveloped reconstruction algorithms.

FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT

We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hu's and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hu's algorithm, T-FDK, and Zhu et al.'s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.'s algorithm while one of the efficient algorithms outperforms Zhu et al.'s algorithm in terms of computational complexity.

Scatter correction for full-fan volumetric CT using a stationary beam blocker in a single full scan

PURPOSE

Applications of volumetric CT (VCT) are hampered by shading and streaking artifacts in the reconstructed images. These artifacts are mainly due to strong x-ray scatter signals accompanied with the large illumination area within one projection, which lead to CT number inaccuracy, image contrast loss and spatial nonuniformity. Although different scatter correction algorithms have been proposed in literature, a standard solution still remains unclear. Measurement-based methods use a beam blocker to acquire scatter samples. These techniques have unrivaled advantages over other existing algorithms in that they are simple and efficient, and achieve high scatter estimation accuracy without prior knowledge of the imaged object. Nevertheless, primary signal loss is inevitable in the scatter measurement, and multiple scans or moving the beam blocker during data acquisition are typically employed to compensate for the missing primary data. In this paper, we propose a new measurement-based scatter correction algorithm without primary compensation for full-fan VCT. An accurate reconstruction is obtained with one single-scan and a stationary x-ray beam blocker, two seemingly incompatible features which enable simple and efficient scatter correction without increase of scan time or patient dose.

METHODS

Based on the CT reconstruction theory, we distribute the blocked data over the projection area where primary signals are considered approximately redundant in a full scan, such that the CT image quality is not degraded even with primary loss. Scatter is then accurately estimated by interpolation and scatter-corrected CT images are obtained using an FDK-based reconstruction algorithm.

RESULTS

The proposed method is evaluated using two phantom studies on a tabletop CBCT system. On the Catphan©600 phantom, our approach reduces the reconstruction error from 207 Hounsfield unit (HU) to 9 HU in the selected region of interest, and improves the image contrast by a factor of 2.0 in the high-contrast regions. On an anthropomorphic head phantom, the reconstruction error is reduced from 97 HU to 6 HU in the soft tissue region and image spatial nonuniformity decreases from 27% to 5% after correction.

CONCLUSIONS

Our method inherits the main advantages of measurement-based methods while avoiding their shortcomings. It has the potential to become a practical scatter correction solution widely implementable on different VCT systems.

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT--noise power spectrum NPS(k)

PURPOSE

The differential phase contrast CT is emerging as a new technology to improve the contrast sensitivity of the conventional CT. Via system analysis, modeling, and computer simulation, the authors study the noise power spectrum (NPS)--an imaging performance indicator-of the differential phase contrast CT and compare it with that of the conventional CT.

METHODS

The differential phase contrast CT is implemented with x-ray tube and gratings. The x-ray propagation and data acquisition are modeled and simulated with Fourier analysis and Fresnel analysis. To avoid any interference caused by scatter and beam hardening, a monochromatic x-ray source (30 keV) is assumed, which irradiates the object to be imaged by 360 degrees so that no weighting scheme is needed. A 20-fold up-sampling is assumed to simulate x-ray beam's propagation through the gratings Gl and G2 with periods 8 and 4 microm, respectively, while the intergrating distance is 193.6 mm (1/16 of the Tabolt distance). The dimension of the detector cell for data acquisition ranges from 32 x 32 to 128 x 128 microm2, while the field of view in data acquisition is 40.96 x 40.96 mm2. A uniform water phantom with a diameter 37.68 mm is employed to study the NPS, with its complex refraction coefficient n = 1 - delta + ibeta = 1 - 2.5604 x 10(-7) + i1.2353 x 10(-10). The x-ray flux ranges from 10(6) to 10(8) photon/cm2.projection and observes the Poisson distribution, which is consistent with that of micro-CT in preclinical applications. The image matrix of reconstructed water phantom is 1280 x 1280, and a total of 180 regions at 128 x 128 matrix are used for NPS calculation via 2D Fourier Transform in which adequate zero padding is applied to avoid aliasing.

RESULTS

The preliminary data show that the differential phase contrast CT manifests its NPS with a l/|k| trait, while the distribution of the conventional CTs NPS observes |k|. This accounts for the significant difference in their noise granularity and the differential phase contrast CTs substantial advantage in noise over the conventional CT, particularly, in the situations where the detector cell size for data acquisition is smaller than 100 microm.

CONCLUSIONS

The differential phase contrast CT detects the projection of refractive coefficient's derivative and uses the Hilbert filter for image reconstruction, which leads to the radical difference in its NPS and the advantage in noise in comparison to that of the conventional CT.

A fast CT reconstruction scheme for a general multi-core PC

Expensive computational cost is a severe limitation in CT reconstruction for clinical applications that need real-time feedback. A primary example is bolus-chasing computed tomography (CT) angiography (BCA) that we have been developing for the past several years. To accelerate the reconstruction process using the filtered backprojection (FBP) method, specialized hardware or graphics cards can be used. However, specialized hardware is expensive and not flexible. The graphics processing unit (GPU) in a current graphic card can only reconstruct images in a reduced precision and is not easy to program. In this paper, an acceleration scheme is proposed based on a multi-core PC. In the proposed scheme, several techniques are integrated, including utilization of geometric symmetry, optimization of data structures, single-instruction multiple-data (SIMD) processing, multithreaded computation, and an Intel C++ compilier. Our scheme maintains the original precision and involves no data exchange between the GPU and CPU. The merits of our scheme are demonstrated in numerical experiments against the traditional implementation. Our scheme achieves a speedup of about 40, which can be further improved by several folds using the latest quad-core processors.

Patient size compensated automatic tube current modulation in multi-detector row CT of the abdomen and pelvis

RATIONALE AND PURPOSE

To evaluate the performance of a patient size-compensated automatic tube current modulation (PSC-AutomA) technique from the perspectives of image quality and radiation dose in multi-detector-row computed tomography (MDCT) scan of the abdomen and pelvis.

MATERIALS AND METHODS

Institutional review board approval was obtained and the study was Health Insurance Portability and Accountability Act-compliant. One hundred and seventeen patients (mean age: 48.8 years; range: 17-89 years; male/female: 57/60) underwent abdominal-pelvic CT scan on a 64-slice MDCT using the noise indexes (NI) recommended by the PSC-AutomA technique. Two radiologists independently evaluated all examinations for noise, streak artifacts, and diagnostic acceptability at the dome of liver, porta hepatis, and the upper margin of acetabulum. The CT dose index (CTDI) volume and effective dose of the CT performed using a recommended NI were compared to the CT performed using a fixed NI of 12. Statistical analysis of the data was performed with nonparametric tests.

RESULTS

The NI recommended by the PSC-AutomA technique was strongly correlated with patient size (r = 0.98, P < .001) with a mean NI of 14.2 HU. The recommended NI of 98.2% (115/117) patients was different from the fixed NI of 12. Approximately 71.8% (84/117) subjects were scanned with a NI higher than 12, whereas 26.5% (31/117) subjects were scanned with a NI lower than 12. All examinations (100%; 117/117) were graded as possessing diagnostic image quality. Compared with the CT performed by using a fixed NI 12, the overall CTDI and effective dose reduction by the PSC-AutomA technique were 11.1% and 11.8%, respectively.

CONCLUSION

The PSC-AutomA technique can recommend an appropriate NI in MDCT scan of the abdomen and pelvis according to patient size, allowing a balanced optimization of both radiation dose and image quality, simultaneously.

Compressed sensing based cone-beam computed tomography reconstruction with a first-order method

PURPOSE

This article considers the problem of reconstructing cone-beam computed tomography (CBCT) images from a set of undersampled and potentially noisy projection measurements.

METHODS

The authors cast the reconstruction as a compressed sensing problem based on l1 norm minimization constrained by statistically weighted least-squares of CBCT projection data. For accurate modeling, the noise characteristics of the CBCT projection data are used to determine the relative importance of each projection measurement. To solve the compressed sensing problem, the authors employ a method minimizing total-variation norm, satisfying a prespecified level of measurement consistency using a first-order method developed by Nesterov.

RESULTS

The method converges fast to the optimal solution without excessive memory requirement, thanks to the method of iterative forward and back-projections. The performance of the proposed algorithm is demonstrated through a series of digital and experimental phantom studies. It is found a that high quality CBCT image can be reconstructed from undersampled and potentially noisy projection data by using the proposed method. Both sparse sampling and decreasing x-ray tube current (i.e., noisy projection data) lead to the reduction of radiation dose in CBCT imaging.

CONCLUSIONS

It is demonstrated that compressed sensing outperforms the traditional algorithm when dealing with sparse, and potentially noisy, CBCT projection views.

Algorithm for hyperfast cone-beam spiral backprojection

Cone-beam spiral backprojection is computationally highly demanding. At first sight, the backprojection requirements are similar to those of cone-beam backprojection from circular scans such as it is performed in the widely used Feldkamp algorithm. However, there is an additional complication: the illumination of each voxel, i.e. the range of angles the voxel is seen by the X-ray cone is a complex function of the voxel position. The weight function has no analytically closed form and must be numerically determined. Storage of the weights is prohibitive since the amount of memory required equals the number of voxels per spiral rotation times the number of projections a voxel receives contributions and therefore is in the order of 10(9) to 10(11) floating point values for typical spiral scans. We propose a new algorithm that combines the spiral symmetry with the ability of today's 64 bit CPUs to store large amounts of precomputed weights. Using the spiral symmetry in this way allows to exploit data-level parallelism and thereby to achieve a very high level of vectorization. An additional postprocessing step rotates these slices back to normal images. Our new backprojection algorithm achieves up to 24.6 Giga voxel updates per second (GUPS) on our systems that are equipped with two standard Intel X5570 quad core CPUs (Intel Xeon 5500 platform, 2.93 GHz, Intel Corporation). This equals the reconstruction of 410 images per second assuming each slice consists of 512 x 512 pixels, receiving contributions from 512 projections.

3D analytic cone-beam reconstruction for multiaxial CT acquisitions

A conventional 3rd generation Computed Tomography (CT) system with a single circular source trajectory is limited in terms of longitudinal scan coverage since extending the scan coverage beyond 40 mm results in significant cone-beam artifacts. A multiaxial CT acquisition is achieved by combining multiple sequential 3rd generation axial scans or by performing a single axial multisource CT scan with multiple longitudinally offset sources. Data from multiple axial scans or multiple sources provide complementary information. For full-scan acquisitions, we present a window-based 3D analytic cone-beam reconstruction algorithm by tessellating data from neighboring axial datasets. We also show that multi-axial CT acquisition can extend the axial scan coverage while minimizing cone-beam artifacts. For half-scan acquisitions, one cannot take advantage of conjugate rays. We propose a cone-angle dependent weighting approach to combine multi-axial half-scan data. We compute the relative contribution from each axial dataset to each voxel based on the X-ray beam collimation, the respective cone-angles, and the spacing between the axial scans. We present numerical experiments to demonstrate that the proposed techniques successfully reduce cone-beam artifacts at very large volumetric coverage.