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

Self-supervised learning for CT image denoising and reconstruction: a review

This article reviews the self-supervised learning methods for CT image denoising and reconstruction. Currently, deep learning has become a dominant tool in medical imaging as well as computer vision. In particular, self-supervised learning approaches have attracted great attention as a technique for learning CT images without clean/noisy references. After briefly reviewing the fundamentals of CT image denoising and reconstruction, we examine the progress of deep learning in CT image denoising and reconstruction. Finally, we focus on the theoretical and methodological evolution of self-supervised learning for image denoising and reconstruction.

Compressed-sensing-inspired reconstruction algorithms in low-dose computed tomography: A review

BACKGROUND

Optimization of the dose the patient receives during scanning is an important problem in modern medical X-ray computed tomography (CT). One of the basic ways to its solution is to reduce the number of views. Compressed sensing theory helped promote the development of a new class of effective reconstruction algorithms for limited data CT. These compressed-sensing-inspired (CSI) algorithms optimize the Lp (0 ≤ p ≤ 1) norm of images and can accurately reconstruct CT tomograms from a very few views. The paper presents a review of the CSI algorithms and discusses prospects for their further use in commercial low-dose CT.

METHODS

Many literature references with the CSI algorithms have been were searched. To structure the material collected the author gives a classification framework within which he describes Lp regularization methods, the basic CSI algorithms that are used most often in few-view CT, and some of their derivatives. Lots of examples are provided to illustrate the use of the CSI algorithms in few-view and low-dose CT.

RESULTS

A list of the CSI algorithms is compiled from the literature search. For better demonstrativeness they are summarized in a table. The inference is done that already today some of the algorithms are capable of reconstruction from 20 to 30 views with acceptable quality and dose reduction by a factor of 10.

DISCUSSION

In conclusion the author discusses how soon the CSI reconstruction algorithms can be introduced in the practice of medical diagnosis and used in commercial CT scanners.

Sparse-view cone-beam computed tomography iterative reconstruction based on new multi-gradient direction total variation

AIM

The accurate reconstruction of cone-beam computed tomography (CBCT) from sparse projections is one of the most important areas for study. The compressed sensing theory has been widely employed in the sparse reconstruction of CBCT. However, the total variation (TV) approach solely uses information from the i-coordinate, j-coordinate, and k-coordinate gradients to reconstruct the CBCT image.

MATERIALS AND METHODS

It is well recognized that the CBCT image can be reconstructed more accurately with more gradient information from different directions. Thus, this study introduces a novel approach, named the new multi-gradient direction total variation minimization method. The method uses gradient information from the ij-coordinate, ik-coordinate, and jk-coordinate directions to reconstruct CBCT images, which incorporates nine different types of gradient information from nine directions.

RESULTS

This study assessed the efficacy of the proposed methodology using under-sampled projections from four different experiments, including two digital phantoms, one patient's head dataset, and one physical phantom dataset. The results indicated that the proposed method achieved the lowest RMSE index and the highest SSIM index. Meanwhile, we compared the voxel intensity curves of the reconstructed images to assess the edge structure preservation. Among the various methods compared, the curves generated by the proposed method exhibited the highest level of consistency with the gold standard image curves.

CONCLUSION

In summary, the proposed method showed significant potential in enhancing the quality and accuracy of CBCT image reconstruction.

Exploration of differentiability in a proton computed tomography simulation framework

Objective.Gradient-based optimization using algorithmic derivatives can be a useful technique to improve engineering designs with respect to a computer-implemented objective function. Likewise, uncertainty quantification through computer simulations can be carried out by means of derivatives of the computer simulation. However, the effectiveness of these techniques depends on how 'well-linearizable' the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications.Approach.This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques.Main results.The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. However, the observed high density and magnitude of jumps was likely to preclude most meaningful uses of the derivatives. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path, and could be reduced in magnitude by a 'fuzzy voxels' approach. The investigated jumps in the MC function arose from local changes in the control flow that affected the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem.Significance.Besides the technical challenges of merely applying AD to existing software projects, the MC and MBIR codes must be adapted to compute smoother functions. For the MBIR code, we presented one possible approach for this while for the MC code, this will be subject to further research. For the tracking subprocedure, further research on surrogate models is necessary.

Self-supervised denoising of projection data for low-dose cone-beam CT

BACKGROUND

Convolutional neural networks (CNNs) have shown promising results in image denoising tasks. While most existing CNN-based methods depend on supervised learning by directly mapping noisy inputs to clean targets, high-quality references are often unavailable for interventional radiology such as cone-beam computed tomography (CBCT).

PURPOSE

In this paper, we propose a novel self-supervised learning method that reduces noise in projections acquired by ordinary CBCT scans.

METHODS

With a network that partially blinds input, we are able to train the denoising model by mapping the partially blinded projections to the original projections. Additionally, we incorporate noise-to-noise learning into the self-supervised learning by mapping the adjacent projections to the original projections. With standard image reconstruction methods such as FDK-type algorithms, we can reconstruct high-quality CBCT images from the projections denoised by our projection-domain denoising method.

RESULTS

In the head phantom study, we measure peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) values of the proposed method along with the other denoising methods and uncorrected low-dose CBCT data for a quantitative comparison both in projection and image domains. The PSNR and SSIM values of our self-supervised denoising approach are 27.08 and 0.839, whereas those of uncorrected CBCT images are 15.68 and 0.103, respectively. In the retrospective study, we assess the quality of interventional patient CBCT images to evaluate the projection-domain and image-domain denoising methods. Both qualitative and quantitative results indicate that our approach can effectively produce high-quality CBCT images with low-dose projections in the absence of duplicate clean or noisy references.

CONCLUSIONS

Our self-supervised learning strategy is capable of restoring anatomical information while efficiently removing noise in CBCT projection data.

NeRP: Implicit Neural Representation Learning With Prior Embedding for Sparsely Sampled Image Reconstruction

Image reconstruction is an inverse problem that solves for a computational image based on sampled sensor measurement. Sparsely sampled image reconstruction poses additional challenges due to limited measurements. In this work, we propose a methodology of implicit Neural Representation learning with Prior embedding (NeRP) to reconstruct a computational image from sparsely sampled measurements. The method differs fundamentally from previous deep learning-based image reconstruction approaches in that NeRP exploits the internal information in an image prior and the physics of the sparsely sampled measurements to produce a representation of the unknown subject. No large-scale data is required to train the NeRP except for a prior image and sparsely sampled measurements. In addition, we demonstrate that NeRP is a general methodology that generalizes to different imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI). We also show that NeRP can robustly capture the subtle yet significant image changes required for assessing tumor progression.

De-aliased depth-range-extended optical coherence tomography based on dual under-sampling

We demonstrate a dual under-sampling (DUS) method to achieve de-aliased and depth-range-extended optical coherence tomography (OCT) imaging. The spectral under-sampling can significantly reduce the data size but causes well-known aliasing artifacts. A change in the sampling frequency used to acquire the interference spectrum alters the aliasing period within the output window except for the true image; this feature is utilized to distinguish the true image from the aliasing artifacts. We demonstrate that with DUS, the data size is reduced to 37% at an extended depth range of 24 mm, over which the true depth can be precisely measured without ambiguity. This reduction in data size and precise measuring capability would be beneficial for reducing the acquisition time for OCT imaging in various biomedical and industrial applications.

Fluoroscopic 3D Image Generation from Patient-Specific PCA Motion Models Derived from 4D-CBCT Patient Datasets: A Feasibility Study

A method for generating fluoroscopic (time-varying) volumetric images using patient-specific motion models derived from four-dimensional cone-beam CT (4D-CBCT) images was developed. 4D-CBCT images acquired immediately prior to treatment have the potential to accurately represent patient anatomy and respiration during treatment. Fluoroscopic 3D image estimation is performed in two steps: (1) deriving motion models and (2) optimization. To derive motion models, every phase in a 4D-CBCT set is registered to a reference phase chosen from the same set using deformable image registration (DIR). Principal components analysis (PCA) is used to reduce the dimensionality of the displacement vector fields (DVFs) resulting from DIR into a few vectors representing organ motion found in the DVFs. The PCA motion models are optimized iteratively by comparing a cone-beam CT (CBCT) projection to a simulated projection computed from both the motion model and a reference 4D-CBCT phase, resulting in a sequence of fluoroscopic 3D images. Patient datasets were used to evaluate the method by estimating the tumor location in the generated images compared to manually defined ground truth positions. Experimental results showed that the average tumor mean absolute error (MAE) along the superior–inferior (SI) direction and the 95th percentile in two patient datasets were 2.29 and 5.79 mm for patient 1, and 1.89 and 4.82 mm for patient 2. This study demonstrated the feasibility of deriving 4D-CBCT-based PCA motion models that have the potential to account for the 3D non-rigid patient motion and localize tumors and other patient anatomical structures on the day of treatment.

Continuously streaming compressed high-speed photography using time delay integration

An imaging system capable of acquiring high-resolution data at a high speed is in demand. However, the amount of optical information captured by a modern camera is limited by the data transfer bandwidth of electronics, resulting in a reduced spatial and temporal resolution. To overcome this problem, we developed continuously streaming compressed high-speed photography, which can record a dynamic scene with an unprecedented space-bandwidth-time product. By performing compressed imaging in a time-delay-integration manner, we continuously recorded a 0.85 megapixel video at 200 kHz, corresponding to an information flux of 170 gigapixels per second.

Computed tomography for distributed Brillouin sensing

A method to reconstruct the spatial distribution of Brillouin gain spectrum from its Radon transform is proposed, which is a type of optical computed tomography. To verify the concept, an experiment was performed on distributed Brillouin fiber sensing, which succeeded in detecting a 55-cm strain section along a 10-m fiber. The experimental system to obtain the Radon transform of the Brillouin gain spectrum is based on a Brillouin optical correlation-domain analysis with a linear frequency-modulated continuous-wave laser. Combining distributed fiber sensing with computed tomography, this method can realize a high signal-to-noise ratio Brillouin sensing.

Utilizing the Wavelet Transform's Structure in Compressed Sensing

Compressed sensing has empowered quality image reconstruction with fewer data samples than previously thought possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is commonly used for this purpose. In this work, we take advantage of the structure of this wavelet transform and identify an affine transformation that increases the sparsity of the result. After inclusion of this affine transformation, we modify the resulting optimization problem to comply with the form of the Basis Pursuit Denoising problem. Finally, we show theoretically that this yields a lower bound on the error of the reconstruction and present results where solving this modified problem yields images of higher quality for the same sampling patterns using both magnetic resonance and optical images.

A Model-Based Optimization Framework for Iterative Digital Breast Tomosynthesis Image Reconstruction

Digital Breast Tomosynthesis is an X-ray imaging technique that allows a volumetric reconstruction of the breast, from a small number of low-dose two-dimensional projections. Although it is already used in the clinical setting, enhancing the quality of the recovered images is still a subject of research. The aim of this paper was to propose and compare, in a general optimization framework, three slightly different models and corresponding accurate iterative algorithms for Digital Breast Tomosynthesis image reconstruction, characterized by a convergent behavior. The suggested model-based implementations are specifically aligned to Digital Breast Tomosynthesis clinical requirements and take advantage of a Total Variation regularizer. We also tune a fully-automatic strategy to set a proper regularization parameter. We assess our proposals on real data, acquired from a breast accreditation phantom and a clinical case. The results confirm the effectiveness of the presented framework in reconstructing breast volumes, with particular focus on the masses and microcalcifications, in few iterations and in enhancing the image quality in a prolonged execution.

Sparse-view imaging of a fiber internal structure in holographic diffraction tomography via a convolutional neural network

Deep learning has recently shown great potential in computational imaging. Here, we propose a deep-learning-based reconstruction method to realize the sparse-view imaging of a fiber internal structure in holographic diffraction tomography. By taking the sparse-view sinogram as the input and the cross-section image obtained by the dense-view sinogram as the ground truth, the neural network can reconstruct the cross-section image from the sparse-view sinogram. It performs better than the corresponding filtered back-projection algorithm with a sparse-view sinogram, both in the case of simulated data and real experimental data.

Learning Sub-Sampling and Signal Recovery With Applications in Ultrasound Imaging

Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-optimal. In addition, real-time recovery is hampered by the iterative and time-consuming nature of sparse recovery algorithms. Recently, deep learning methods have shown promise for fast recovery from compressed measurements, but the design of adequate and practical sensing strategies remains a challenge. Here, we propose a deep learning solution termed Deep Probabilistic Sub-sampling (DPS), that enables joint optimization of a task-adaptive sub-sampling pattern and a subsequent neural task model in an end-to-end fashion. Once learned, the task-based sub-sampling patterns are fixed and straightforwardly implementable, e.g. by non-uniform analog-to-digital conversion, sparse array design, or slow-time ultrasound pulsing schemes. The effectiveness of our framework is demonstrated in-silico for sparse signal recovery from partial Fourier measurements, and in-vivo for both anatomical image and tissue-motion (Doppler) reconstruction from sub-sampled medical ultrasound imaging data.

Sparse-view CBCT reconstruction via weighted Schatten p-norm minimization

A novel iterative algorithm is proposed for sparse-view cone beam computed tomography (CBCT) reconstruction based on the weighted Schatten p-norm minimization (WSNM). By using the half quadratic splitting, the sparse-view CBCT reconstruction task is decomposed into two sub-problems that can be solved through alternating iteration: simple reconstruction and image denoising. The WSNM that fits well with the low-rank hypothesis of CBCT data is introduced to improve the denoising sub-problem as a regularization term. The experimental results based on the digital brain phantom and clinical CT data indicated the advantages of the proposed algorithm in both structural information preservation and artifacts suppression, which performs better than the classical algorithms in quantitative and qualitative evaluations.

Statistical Image Restoration for Low-Dose CT using Convolutional Neural Networks

Deep learning has recently attracted widespread interest as a means of reducing noise in low-dose CT (LDCT) images. Deep convolutional neural networks (CNNs) are typically trained to transfer high-quality image features of normal-dose CT (NDCT) images to LDCT images. However, existing deep learning approaches for denoising LDCT images often overlook the statistical property of CT images. In this paper, we propose an approach to statistical image restoration for LDCT using deep learning (StatCNN). We introduce a loss function to incorporate the noise property in the image domain derived from the noise statistics in the sinogram domain. In order to capture the spatially-varying statistics of axial CT images, we increase the receptive fields of the proposed network to cover full-size CT slices. In addition, the proposed network utilizes z-directional correlation by taking multiple consecutive CT slices as input. For performance evaluation, the proposed network was thoroughly trained and tested by leave-one-out cross-validation with a dataset consisting of LDCT-NDCT image pairs. The experimental results showed that the denoising networks successfully reduced the noise level and restored the image details without adding artifacts. This study demonstrates that the statistical deep learning approach can transfer the image style from NDCT images to LDCT images without loss of anatomical information.

Verification of the machine delivery parameters of a treatment plan via deep learning

We developed a generative adversarial network (GAN)-based deep learning approach to estimate the multileaf collimator (MLC) aperture and corresponding monitor units (MUs) from a given 3D dose distribution. The proposed design of the adversarial network, which integrates a residual block into pix2pix framework, jointly trains a 'U-Net'-like architecture as the generator and a convolutional 'PatchGAN' classifier as the discriminator. 199 patients, including nasopharyngeal, lung and rectum, treated with intensity-modulated radiotherapy and volumetric-modulated arc therapy techniques were utilized to train the network. An additional 47 patients were used to test the prediction accuracy of the proposed deep learning model. The Dice similarity coefficient (DSC) was calculated to evaluate the similarity between the MLC aperture shapes obtained from the treatment planning system (TPS) and the deep learning prediction. The average and standard deviation of the bias between the TPS-generated MUs and predicted MUs was calculated to evaluate the MU prediction accuracy. In addition, the differences between TPS and deep learning-predicted MLC leaf positions were compared. The average and standard deviation of DSC was 0.94 ± 0.043 for 47 testing patients. The average deviation of predicted MUs from the planned MUs normalized to each beam or arc was within 2% for all the testing patients. The average deviation of the predicted MLC leaf positions was around one pixel for all the testing patients. Our results demonstrated the feasibility and reliability of the proposed approach. The proposed technique has strong potential to improve the efficiency and accuracy of the patient plan quality assurance process.

Explorative Imaging and Its Implementation at the FleX-ray Laboratory

In tomographic imaging, the traditional process consists of an expert and an operator collecting data, the expert working on the reconstructed slices and drawing conclusions. The quality of reconstructions depends heavily on the quality of the collected data, except that, in the traditional process of imaging, the expert has very little influence over the acquisition parameters, experimental plan or the collected data. It is often the case that the expert has to draw limited conclusions from the reconstructions, or adapt a research question to data available. This method of imaging is static and sequential, and limits the potential of tomography as a research tool. In this paper, we propose a more dynamic process of imaging where experiments are tailored around a sample or the research question; intermediate reconstructions and analysis are available almost instantaneously, and expert has input at any stage of the process (including during acquisition) to improve acquisition or image reconstruction. Through various applications of 2D, 3D and dynamic 3D imaging at the FleX-ray Laboratory, we present the unexpected journey of exploration a research question undergoes, and the surprising benefits it yields.

Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm

Low dose computed tomography (CT) has drawn much attention in the medical imaging field because of its ability to reduce the radiation dose. Recently, statistical iterative reconstruction (SIR) with total variation (TV) penalty has been developed to low dose CT image reconstruction. Nevertheless, the TV penalty has the drawback of creating blocky effects in the reconstructed images. To overcome the limitations of TV, in this paper we firstly introduce the structure tensor total variation (STV₁) penalty into SIR framework for low dose CT image reconstruction. Then, an accelerated fast iterative shrinkage thresholding algorithm (AFISTA) is developed to minimize the objective function. The proposed AFISTA reconstruction algorithm was evaluated using numerical simulated low dose projection based on two CT images and realistic low dose projection data of a sheep lung CT perfusion. The experimental results demonstrated that our proposed STV₁-based algorithm outperform FBP and TV-based algorithm in terms of removing noise and restraining blocky effects.

Semi-Supervised Learning for Low-Dose CT Image Restoration with Hierarchical Deep Generative Adversarial Network (HD-GAN)

In the absence of duplicate high-dose CT data, it is challenging to restore high-quality images based on deep learning with only low-dose CT (LDCT) data. When different reconstruction algorithms and settings are adopted to prepare high-quality images, LDCT datasets for deep learning can be unpaired. To address this problem, we propose hierarchical deep generative adversarial networks (HD-GANs) for semi-supervised learning with the unpaired datasets. We first cluster each patient's CT images into multiple categories, and then collect the images in the same categories across different patients to build an imageset for denoising. Each imageset is fed into a generative adversarial network that consists of a denoising network and a following classification network. The denoising network efficiently reuses feature maps from the lower layers for end-to-end learning with full-size images. The classifier is trained to distinguish between the denoised images and the high-quality images. Evaluated with a clinical LDCT dataset, the proposed semi-supervised learning approach efficiently reduces the noise level of LDCT images without loss of information, thereby addressing the major shortcomings of IR such as computation time and anatomical inaccuracy.

Patient-specific reconstruction of volumetric computed tomography images from a single projection view via deep learning

Tomographic imaging via penetrating waves generates cross-sectional views of the internal anatomy of a living subject. For artefact-free volumetric imaging, projection views from a large number of angular positions are required. Here, we show that a deep-learning model trained to map projection radiographs of a patient to the corresponding 3D anatomy can subsequently generate volumetric tomographic X-ray images of the patient from a single projection view. We demonstrate the feasibility of the approach with upper-abdomen, lung, and head-and-neck computed tomography scans from three patients. Volumetric reconstruction via deep learning could be useful in image-guided interventional procedures such as radiation therapy and needle biopsy, and might help simplify the hardware of tomographic imaging systems.

GWRA: grey wolf based reconstruction algorithm for compressive sensing signals

The recent advances in compressive sensing (CS) based solutions make it a promising technique for signal acquisition, image processing and other types of data compression needs. In CS, the most challenging problem is to design an accurate and efficient algorithm for reconstructing the original data. Greedy-based reconstruction algorithms proved themselves as a good solution to this problem because of their fast implementation and low complex computations. In this paper, we propose a new optimization algorithm called grey wolf reconstruction algorithm (GWRA). GWRA is inspired from the benefits of integrating both the reversible greedy algorithm and the grey wolf optimizer algorithm. The effectiveness of GWRA technique is demonstrated and validated through rigorous simulations. The simulation results show that GWRA significantly exceeds the greedy-based reconstruction algorithms such as sum product, orthogonal matching pursuit, compressive sampling matching pursuit and filtered back projection and swarm based techniques such as BA and PSO in terms of reducing the reconstruction error, the mean absolute percentage error and the average normalized mean squared error.

SparseCT: System concept and design of multislit collimators

PURPOSE

SparseCT, an undersampling scheme for compressed sensing (CS) computed tomography (CT), has been proposed to reduce radiation dose by acquiring undersampled projection data from clinical CT scanners (Koesters et al. in, SparseCT: Interrupted-Beam Acquisition and Sparse Reconstruction for Radiation Dose Reduction; 2017). SparseCT partially blocks the x-ray beam with a multislit collimator (MSC) to perform a multidimensional undersampling along the view and detector row dimensions. SparseCT undersamples the projection data within each view and moves the MSC along the z-direction during gantry rotation to change the undersampling pattern. It enables reconstruction of images from undersampled data using CS algorithms. The purpose of this work is to design the spacing and width of the MSC slits and the MSC motion patterns based on beam separation, undersampling efficiency, and image quality. The development and testing of a SparseCT prototype with the designed MSC will be described in a following paper.

METHODS

We chose a few initial MSC designs based on the guidance from two metrics: beam separation and undersampling efficiency. Both beam separation and undersampling efficiency were measured from numerically simulated photon distribution with MSC taken into consideration. Beam separation measures the separation between x-ray beams from consecutive slits, taking into account penumbra effects on both sides of each slit. Undersampling efficiency measures the dose-weighted similarity between penumbra undersampling and binary undersampling, in other words, the effective contribution of the incident dose to the signal to noise ratio of the projection data. We then compared the initially chosen MSC designs in terms of their reconstruction image quality. SparseCT projections were simulated from fully sampled patient projection data according to the MSC design and motion pattern, reconstructed iteratively using a sparsity-enforcing penalized weighted least squares cost function with ordered subsets/momentum algorithm, and compared visually and quantitatively.

RESULTS

Simulated photon distributions indicate that the size of the penumbra is dominated by the size of the focal spot. Therefore, a wider MSC slit and a smaller focal spot lead to increased beam separation and undersampling efficiency. For fourfold undersampling with a 1.2 mm focal spot, a minimum MSC slit width of three detector rows (projected to the detector surface) is needed for beam separation; for threefold undersampling, a minimum slit width of four detector rows is needed. Simulations of SparseCT projection and reconstruction indicate that the motion pattern of the MSC does not have a visible impact on image quality. An MSC slit width of three or four detector rows yields similar image quality.

CONCLUSION

The MSC is the key component of the SparseCT method. Simulations of MSC designs incorporating x-ray beam penumbra effects showed that for threefold and fourfold dose reductions, an MSC slit width of four detector rows provided reasonable beam separation, undersampling efficiency, and image quality.

Image quality and dose characteristics for an O-arm intraoperative imaging system with model-based image reconstruction

PURPOSE

To assess the imaging performance and radiation dose characteristics of the O-arm CBCT imaging system (Medtronic Inc., Littleton MA) and demonstrate the potential for improved image quality and reduced dose via model-based image reconstruction (MBIR).

METHODS

Two main studies were performed to investigate previously unreported characteristics of the O-arm system. First is an investigation of dose and 3D image quality achieved with filtered back-projection (FBP) - including enhancements in geometric calibration, handling of lateral truncation and detector saturation, and incorporation of an isotropic apodization filter. Second is implementation of an MBIR algorithm based on Huber-penalized likelihood estimation (PLH) and investigation of image quality improvement at reduced dose. Each study involved measurements in quantitative phantoms as a basis for analysis of contrast-to-noise ratio and spatial resolution as well as imaging of a human cadaver to test the findings under realistic imaging conditions.

RESULTS

View-dependent calibration of system geometry improved the accuracy of reconstruction as quantified by the full-width at half maximum of the point-spread function - from 0.80 to 0.65 mm - and yielded subtle but perceptible improvement in high-contrast detail of bone (e.g., temporal bone). Standard technique protocols for the head and body imparted absorbed dose of 16 and 18 mGy, respectively. For low-to-medium contrast (<100 HU) imaging at fixed spatial resolution (1.3 mm edge-spread function) and fixed dose (6.7 mGy), PLH improved CNR over FBP by +48% in the head and +35% in the body. Evaluation at different dose levels demonstrated 30% increase in CNR at 62% of the dose in the head and 90% increase in CNR at 50% dose in the body.

CONCLUSIONS

A variety of improvements in FBP implementation (geometric calibration, truncation and saturation effects, and isotropic apodization) offer the potential for improved image quality and reduced radiation dose on the O-arm system. Further gains are possible with MBIR, including improved soft-tissue visualization, low-dose imaging protocols, and extension to methods that naturally incorporate prior information of patient anatomy and/or surgical instrumentation.

Regularization strategies in statistical image reconstruction of low-dose x-ray CT: A review

Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose x-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (a) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

A Compressed-Sensing Based Blind Deconvolution Method for Image Deblurring in Dental Cone-Beam Computed Tomography

In cone-beam computed tomography (CBCT), reconstructed images are inherently degraded, restricting its image performance, due mainly to imperfections in the imaging process resulting from detector resolution, noise, X-ray tube's focal spot, and reconstruction procedure as well. Thus, the recovery of CBCT images from their degraded version is essential for improving image quality. In this study, we investigated a compressed-sensing (CS)-based blind deconvolution method to solve the blurring problem in CBCT where both the image to be recovered and the blur kernel (or point-spread function) of the imaging system are simultaneously recursively identified. We implemented the proposed algorithm and performed a systematic simulation and experiment to demonstrate the feasibility of using the algorithm for image deblurring in dental CBCT. In the experiment, we used a commercially available dental CBCT system that consisted of an X-ray tube, which was operated at 90 kV_p and 5 mA, and a CMOS flat-panel detector with a 200-μm pixel size. The image characteristics were quantitatively investigated in terms of the image intensity, the root-mean-square error, the contrast-to-noise ratio, and the noise power spectrum. The results indicate that our proposed method effectively reduced the image blur in dental CBCT, excluding repetitious measurement of the system's blur kernel.

Assessment of prior image induced nonlocal means regularization for low-dose CT reconstruction: Change in anatomy

PURPOSE

Repeated computed tomography (CT) scans are prescribed for some clinical applications such as lung nodule surveillance. Several studies have demonstrated that incorporating a high-quality prior image into the reconstruction of subsequent low-dose CT (LDCT) acquisitions can either improve image quality or reduce data fidelity requirements. Our proposed previous normal-dose image induced nonlocal means (ndiNLM) regularization method for LDCT is an example of such a method. However, one major concern with prior image based methods is that they might produce false information when the prior image and the current LDCT image show different structures (for example, if a lung nodule emerges, grows, shrinks, or disappears over time). This study aims to assess the performance of the ndiNLM regularization method in situations with change in anatomy.

METHOD

We incorporated the ndiNLM regularization into the statistical image reconstruction (SIR) framework for reconstruction of subsequent LDCT images. Because of its patch-based search mechanism, a rough registration between the prior image and the current LDCT image is adequate for the SIR-ndiNLM method. We assessed the performance of the SIR-ndiNLM method in lung nodule surveillance for two different scenarios: (a) the nodule was not found in a baseline exam but appears in a follow-up LDCT scan; (b) the nodule was present in a baseline exam but disappears in a follow-up LDCT scan. We further investigated the effect of nodule size on the performance of the SIR-ndiNLM method.

RESULTS

We found that a relatively large search-window (e.g., 33 × 33) should be used for the SIR-ndiNLM method to account for misalignment between the prior image and the current LDCT image, and to ensure that enough similar patches can be found in the prior image. With proper selection of other parameters, experimental results with two patient datasets demonstrated that the SIR-ndiNLM method did not miss true nodules nor introduce false nodules in the lung nodule surveillance scenarios described above. We also found that the SIR-ndiNLM reconstruction shows improved image quality when the prior image is similar to the current LDCT image in anatomy. These gains in image quality might appear small upon visual inspection, but they can be detected using quantitative measures. Finally, the SIR-ndiNLM method also performed well in ultra-low-dose conditions and with different nodule sizes.

CONCLUSIONS

This study assessed the performance of the SIR-ndiNLM method in situations in which the prior image and the current LDCT image show substantial anatomical differences, specifically, changes in lung nodules. The experimental results demonstrate that the SIR-ndiNLM method does not introduce false lung nodules nor miss true nodules, which relieves the concern that this method might produce false information. However, there is insufficient evidence that these findings will hold true for all kinds of anatomical changes.

Statistical Iterative CBCT Reconstruction Based on Neural Network

Cone-beam computed tomography (CBCT) plays an important role in radiation therapy. Statistical iterative reconstruction (SIR) algorithms with specially designed penalty terms provide good performance for low-dose CBCT imaging. Among others, the total variation (TV) penalty is the current state-of-the-art in removing noises and preserving edges, but one of its well-known limitations is its staircase effect. Recently, various penalty terms with higher order differential operators were proposed to replace the TV penalty to avoid the staircase effect, at the cost of slightly blurring object edges. We developed a novel SIR algorithm using a neural network for CBCT reconstruction. We used a data-driven method to learn the "potential regularization term" rather than design a penalty term manually. This approach converts the problem of designing a penalty term in the traditional statistical iterative framework to designing and training a suitable neural network for CBCT reconstruction. We proposed using transfer learning to overcome the data deficiency problem and an iterative deblurring approach specially designed for the CBCT iterative reconstruction process during which the noise level and resolution of the reconstructed images may change. Through experiments conducted on two physical phantoms, two simulation digital phantoms, and patient data, we demonstrated the excellent performance of the proposed network-based SIR for CBCT reconstruction, both visually and quantitatively. Our proposed method can overcome the staircase effect, preserve both edges and regions with smooth intensity transition, and provide reconstruction results at high resolution and low noise level.

Computational study of estimating 3D trabecular bone microstructure for the volume of interest from CT scan data

Inspired by the self-optimizing capabilities of bone, a new concept of bone microstructure reconstruction has been recently introduced by using 2D synthetic skeletal images. As a preliminary clinical study, this paper proposes a topology optimization-based method that can estimate 3D trabecular bone microstructure for the volume of interest (VOI) from 3D computed tomography (CT) scan data with enhanced computational efficiency and phenomenological accuracy. For this purpose, a localized finite element (FE) model is constructed by segmenting a target bone from CT scan data and determining the physiological local loads for the VOI. Then, topology optimization is conducted with multiresolution bone mineral density (BMD) deviation constraints to preserve the patient-specific spatial bone distribution obtained from the CT scan data. For the first time, to our knowledge, this study has demonstrated that 60-μm resolution trabecular bone images can be reconstructed from 600-μm resolution CT scan data (a 62-year-old woman with no metabolic bone disorder) for the 4 VOIs in the proximal femur. The reconstructed trabecular bone includes the characteristic trabecular patterns and has morphometric indices that are in good agreement with the anatomical data in the literature. As for computational efficiency, the localization for the VOI reduces the number of FEs by 99%, compared with that of the full FE model. Compared with the previous single-resolution BMD deviation constraint, the proposed multiresolution BMD deviation constraints enable at least 65% and 47% reductions in the number of iterations and computing time, respectively. These results demonstrate the clinical feasibility and potential of the proposed method.

Low dose CT reconstruction via L1 norm dictionary learning using alternating minimization algorithm and balancing principle

Excessive radiation exposure in computed tomography (CT) scans increases the chance of developing cancer and has become a major clinical concern. Recently, statistical iterative reconstruction (SIR) with l0-norm dictionary learning regularization has been developed to reconstruct CT images from the low dose and few-view dataset in order to reduce radiation dose. Nonetheless, the sparse regularization term adopted in this approach is l0-norm, which cannot guarantee the global convergence of the proposed algorithm. To address this problem, in this study we introduced the l1-norm dictionary learning penalty into SIR framework for low dose CT image reconstruction, and developed an alternating minimization algorithm to minimize the associated objective function, which transforms CT image reconstruction problem into a sparse coding subproblem and an image updating subproblem. During the image updating process, an efficient model function approach based on balancing principle is applied to choose the regularization parameters. The proposed alternating minimization algorithm was evaluated first using real projection data of a sheep lung CT perfusion and then using numerical simulation based on sheep lung CT image and chest image. Both visual assessment and quantitative comparison using terms of root mean square error (RMSE) and structural similarity (SSIM) index demonstrated that the new image reconstruction algorithm yielded similar performance with l0-norm dictionary learning penalty and outperformed the conventional filtered backprojection (FBP) and total variation (TV) minimization algorithms.

Image reconstruction in region-of-interest (or interior) digital tomosynthesis (DTS) based on compressed-sensing (CS)

BACKGROUND AND OBJECTIVE

Digital tomosynthesis (DTS) based on filtered-backprojection (FBP) reconstruction requires a full field-of-view (FOV) scan and relatively dense projections, which results in high doses for medical imaging purposes. To overcome these difficulties, we investigated region-of-interest (ROI) or interior DTS reconstruction where the x-ray beam span covers only a small ROI containing a target area.

METHODS

An iterative method based on compressed-sensing (CS) scheme was compared with the FBP-based algorithm for ROI-DTS reconstruction. We implemented both algorithms and performed a systematic simulation and experiments on body and skull phantoms. The image characteristics were evaluated and compared.

RESULTS

The CS-based algorithm yielded much better reconstruction quality in ROI-DTS compared to the FBP-based algorithm, preserving superior image homogeneity, edge sharpening, and in-plane resolution. The image characteristics of the CS-reconstructed images in ROI-DTS were not significantly different from those in full-FOV DTS. The measured CNR value of the CS-reconstructed ROI-DTS image was about 12.3, about 1.9 times larger than that of the FBP-reconstructed ROI-DTS image.

CONCLUSIONS

ROI-DTS images of substantially high accuracy were obtained using the CS-based algorithm and at reduced imaging doses and less computational cost, compared to typical full-FOV DTS images. We expect that the proposed method will be useful for the development of new DTS systems.

Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data

Recent work in CT image reconstruction has seen increasing interest in the use of total variation (TV) and related penalties to regularize problems involving reconstruction from undersampled or incomplete data. Superiorization is a recently proposed heuristic which provides an automatic procedure to 'superiorize' an iterative image reconstruction algorithm with respect to a chosen objective function, such as TV. Under certain conditions, the superiorized algorithm is guaranteed to find a solution that is as satisfactory as any found by the original algorithm with respect to satisfying the constraints of the problem; this solution is also expected to be superior with respect to the chosen objective. Most work on superiorization has used reconstruction algorithms which assume a linear measurement model, which in the case of CT corresponds to data generated from a monoenergetic x-ray beam. Many CT systems generate x-rays from a polyenergetic spectrum, however, in which the measured data represent an integral of object attenuation over all energies in the spectrum. This inconsistency with the linear model produces the well-known beam hardening artifacts, which impair analysis of CT images. In this work we superiorize an iterative algorithm for reconstruction from polyenergetic data, using both TV and an anisotropic TV (ATV) penalty. We apply the superiorized algorithm in numerical phantom experiments modeling both sparse-view and limited-angle scenarios. In our experiments, the superiorized algorithm successfully finds solutions which are as constraints-compatible as those found by the original algorithm, with significantly reduced TV and ATV values. The superiorized algorithm thus produces images with greatly reduced sparse-view and limited angle artifacts, which are also largely free of the beam hardening artifacts that would be present if a superiorized version of a monoenergetic algorithm were used.

Combining Acceleration Techniques for Low-Dose X-Ray Cone Beam Computed Tomography Image Reconstruction

Background and Objective

Over the past decade, image quality in low-dose computed tomography has been greatly improved by various compressive sensing- (CS-) based reconstruction methods. However, these methods have some disadvantages including high computational cost and slow convergence rate. Many different speed-up techniques for CS-based reconstruction algorithms have been developed. The purpose of this paper is to propose a fast reconstruction framework that combines a CS-based reconstruction algorithm with several speed-up techniques.

Methods

First, total difference minimization (TDM) was implemented using the soft-threshold filtering (STF). Second, we combined TDM-STF with the ordered subsets transmission (OSTR) algorithm for accelerating the convergence. To further speed up the convergence of the proposed method, we applied the power factor and the fast iterative shrinkage thresholding algorithm to OSTR and TDM-STF, respectively.

Results

Results obtained from simulation and phantom studies showed that many speed-up techniques could be combined to greatly improve the convergence speed of a CS-based reconstruction algorithm. More importantly, the increased computation time (≤10%) was minor as compared to the acceleration provided by the proposed method.

Conclusions

In this paper, we have presented a CS-based reconstruction framework that combines several acceleration techniques. Both simulation and phantom studies provide evidence that the proposed method has the potential to satisfy the requirement of fast image reconstruction in practical CT.

Fast alternating projection methods for constrained tomographic reconstruction

The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification.

Applications of nonlocal means algorithm in low-dose X-ray CT image processing and reconstruction: A review

Low-dose X-ray computed tomography (LDCT) imaging is highly recommended for use in the clinic because of growing concerns over excessive radiation exposure. However, the CT images reconstructed by the conventional filtered back-projection (FBP) method from low-dose acquisitions may be severely degraded with noise and streak artifacts due to excessive X-ray quantum noise, or with view-aliasing artifacts due to insufficient angular sampling. In 2005, the nonlocal means (NLM) algorithm was introduced as a non-iterative edge-preserving filter to denoise natural images corrupted by additive Gaussian noise, and showed superior performance. It has since been adapted and applied to many other image types and various inverse problems. This paper specifically reviews the applications of the NLM algorithm in LDCT image processing and reconstruction, and explicitly demonstrates its improving effects on the reconstructed CT image quality from low-dose acquisitions. The effectiveness of these applications on LDCT and their relative performance are described in detail.

Compressed sensing laser scanning microscopy

We present a measurement and reconstruction method for laser-scanning microscopy based on compressed sensing, which enables significantly higher frame rates and reduced photobleaching. The image reconstruction accuracy is ensured by including a model of the physical imaging process into the compressed sensing reconstruction procedure. We demonstrate its applicability to unmodified commercial confocal fluorescence microscopy systems and for Raman imaging, showing a potential data reduction of 10-15 times, which directly leads to improvements in acquisition speed, or reduction of photobleaching, without significant loss of spatial resolution. Furthermore, the reconstruction model is also robust to noise, and effective for low-light applications. This method has promising applications for all imaging modalities based on laser-scanning acquisition, including fluorescence, Raman, and nonlinear microscopy.

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

PURPOSE

The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT.

METHODS

Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units.

RESULTS

The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min.

CONCLUSIONS

The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

The exposure of normal tissues to high radiation during cone-beam CT (CBCT) imaging increases the risk of cancer and genetic defects. Statistical iterative algorithms with the total variation (TV) penalty have been widely used for low dose CBCT reconstruction, with state-of-the-art performance in suppressing noise and preserving edges. However, TV is a first-order penalty and sometimes leads to the so-called staircase effect, particularly over regions with smooth intensity transition in the reconstruction images. A second-order penalty known as the Hessian penalty was recently used to replace TV to suppress the staircase effect in CBCT reconstruction at the cost of slightly blurring object edges. In this study, we proposed a new penalty, the TV-H, which combines TV and Hessian penalties for CBCT reconstruction in a structure-adaptive way. The TV-H penalty automatically differentiates the edges, gradual transition and uniform local regions within an image using the voxel gradient, and adaptively weights TV and Hessian according to the local image structures in the reconstruction process. Our proposed penalty retains the benefits of TV, including noise suppression and edge preservation. It also maintains the structures in regions with gradual intensity transition more successfully. A majorization-minimization (MM) approach was designed to optimize the objective energy function constructed with the TV-H penalty. The MM approach employed a quadratic upper bound of the original objective function, and the original optimization problem was changed to a series of quadratic optimization problems, which could be efficiently solved using the Gauss-Seidel update strategy. We tested the reconstruction algorithm on two simulated digital phantoms and two physical phantoms. Our experiments indicated that the TV-H penalty visually and quantitatively outperformed both TV and Hessian penalties.

[Impact of the Infrared Monitor Signal Pattern on Accuracy of Target Imaging in 4-dimensional Cone-beam Computed Tomography]

To realize the high precision radiotherapy, localized radiation field of the moving target is very important, and visualization of a temporal location of the target can help to improve the accuracy of the target localization. However, conditions of the breathing and the patient's own motion differ from the situation of the treatment planning. Therefore, positions of the tumor are affected by these changes. In this study, we implemented a method to reconstruct target motions obtained with the 4D CBCT using the sorted projection data according to the phase and displacement of the extracorporeal infrared monitor signal, and evaluated the proposed method with a moving phantom. In this method, motion cycles and positions of the marker were sorted to reconstruct the image, and evaluated the image quality affected by changes in the cycle, phase, and positions of the marker. As a result, we realized the visualization of the moving target using the sorted projection data according to the infrared monitor signal. This method was based on the projection binning, in which the signal of the infrared monitor was surrogate of the tumor motion. Thus, further major efforts are needed to ensure the accuracy of the infrared monitor signal.

Optimization of Proton CT Detector System and Image Reconstruction Algorithm for On-Line Proton Therapy

The purposes of this study were to optimize a proton computed tomography system (pCT) for proton range verification and to confirm the pCT image reconstruction algorithm based on projection images generated with optimized parameters. For this purpose, we developed a new pCT scanner using the Geometry and Tracking (GEANT) 4.9.6 simulation toolkit. GEANT4 simulations were performed to optimize the geometric parameters representing the detector thickness and the distance between the detectors for pCT. The system consisted of four silicon strip detectors for particle tracking and a calorimeter to measure the residual energies of the individual protons. The optimized pCT system design was then adjusted to ensure that the solution to a CS-based convex optimization problem would converge to yield the desired pCT images after a reasonable number of iterative corrections. In particular, we used a total variation-based formulation that has been useful in exploiting prior knowledge about the minimal variations of proton attenuation characteristics in the human body. Examinations performed using our CS algorithm showed that high-quality pCT images could be reconstructed using sets of 72 projections within 20 iterations and without any streaks or noise, which can be caused by under-sampling and proton starvation. Moreover, the images yielded by this CS algorithm were found to be of higher quality than those obtained using other reconstruction algorithms. The optimized pCT scanner system demonstrated the potential to perform high-quality pCT during on-line image-guided proton therapy, without increasing the imaging dose, by applying our CS based proton CT reconstruction algorithm. Further, we make our optimized detector system and CS-based proton CT reconstruction algorithm potentially useful in on-line proton therapy.