A constrained, total-variation minimization algorithm for low-intensity x-ray CT

Tomographic Image Reconstruction Using an Advanced Score Function (ADSF)

Computed tomography (CT) reconstructs volumetric images using X-ray projection data acquired from multiple angles around an object. For low-dose or sparse-view CT scans, the classic image reconstruction algorithms often produce severe noise and artifacts. To address this issue, we develop a novel iterative image reconstruction method based on maximum a posteriori (MAP) estimation. In the MAP framework, the score function, i.e., the gradient of the logarithmic probability density distribution, plays a crucial role as an image prior in the iterative image reconstruction process. By leveraging the Gaussian mixture model, we derive a novel score matching formula to establish an advanced score function (ADSF) through deep learning. Integrating the new ADSF into the image reconstruction process, a new ADSF iterative reconstruction method is developed to improve image reconstruction quality. The convergence of the ADSF iterative reconstruction algorithm is proven through mathematical analysis. The performance of the ADSF reconstruction method is also evaluated on both public medical image datasets and clinical raw CT datasets. Our results show that the ADSF reconstruction method can achieve better denoising and deblurring effects than the state-of-the-art reconstruction methods, showing excellent generalizability and stability.

Autonomous Electron Tomography Reconstruction with Machine Learning

Modern electron tomography has progressed to higher resolution at lower doses by leveraging compressed sensing (CS) methods that minimize total variation (TV). However, these sparsity-emphasized reconstruction algorithms introduce tunable parameters that greatly influence the reconstruction quality. Here, Pareto front analysis shows that high-quality tomograms are reproducibly achieved when TV minimization is heavily weighted. However, in excess, CS tomography creates overly smoothed three-dimensional (3D) reconstructions. Adding momentum to the gradient descent during reconstruction reduces the risk of over-smoothing and better ensures that CS is well behaved. For simulated data, the tedious process of tomography parameter selection is efficiently solved using Bayesian optimization with Gaussian processes. In combination, Bayesian optimization with momentum-based CS greatly reduces the required compute time-an 80% reduction was observed for the 3D reconstruction of SrTiO3 nanocubes. Automated parameter selection is necessary for large-scale tomographic simulations that enable the 3D characterization of a wider range of inorganic and biological materials.

Bilateral Weighted Relative Total Variation for Low-Dose CT Reconstruction

Low-dose computed tomography (LDCT) has been widely used for various clinic applications to reduce the X-ray dose absorbed by patients. However, LDCT is usually degraded by severe noise over the image space. The image quality of LDCT has attracted aroused attentions of scholars. In this study, we propose the bilateral weighted relative total variation (BRTV) used for image restoration to simultaneously maintain edges and further reduce noise, then propose the BRTV-regularized projections onto convex sets (POCS-BRTV) model for LDCT reconstruction. Referring to the spacial closeness and the similarity of gray value between two pixels in a local rectangle, POCS-BRTV can adaptively extract sharp edges and minor details during the iterative reconstruction process. Evaluation indexes and visual effects are used to measure the performances among different algorithms. Experimental results indicate that the proposed POCS-BRTV model can achieve superior image quality than the compared algorithms in terms of the structure and texture preservation.

Structure-guided computed tomography reconstruction from limited-angle projections

Limited-angle computed tomography (CT) imaging is one of the common imaging problems. The reconstructed images often encounter obvious artifacts and structure degradation. In recent years, the recoverability prior of image structure has been widely explored in limited-angle CT reconstruction, and the image quality has been greatly improved. However, the artifacts and structure degradation still exist. In this study, we establish a new reconstruction model based on weighted relative structure (wRS) determined by image gradients, which serves as weights to guide image reconstruction in order to reduce artifacts and preserve structures. Then, we develop an efficient algorithm using a surrogate function to solve this model. Moreover, this method is compared with some of other popular reconstruction methods, such as anisotropic total variation method and image gradient L0 norm minimization method and so on. Experiments on digital phantoms, real carved cheese and walnut projection are reported to demonstrate its superiority. Several quantitative indices including RMSE, PSNR, and SSIM of the reconstruction images from 90°-data of FORBILD head phantom are 0.0120, 43.52, and 0.9961. The experimental results indicate that the image obtained by our method is the closest to reference image. By comparing reconstruction images or their residual images, images reconstructed from real CT data, the experimental results of the residual images and the respective quantitative data analysis also demonstrate that the images reconstructed using our new method suffer from less artifacts and structure degradation.

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.

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.

Segmental limited-angle CT reconstruction based on image structural prior

CT reconstruction from incomplete projection data is one of the key researches of X-ray CT imaging. The projection data acquired by few-view and limited-angle sampling are incomplete. In addition, few-view sampling often requires turning on and off the tube voltage, but rapid switching of tube voltage demands for high technical requirements. Limited-angle sampling is easy to realize. However, reconstructed images may encounter obvious artifacts. In this study we investigate a new segmental limited-angle (SLA) sampling strategy, which avoids rapid switching of tube voltage. Thus, the projection data has lower data correlation than limited-angle CT, which is conducive to reconstructing high-quality images. To suppress potential artifacts, we incorporate image structural prior into reconstruction model to present a reconstruction method. The limited-angle CT reconstruction experiments on digital phantoms, real carved cheese and walnut projections are used to test and verify the effectiveness of the proposed method. Several image quality evaluation indices including RMSE, PSNR, and SSIM of the reconstructions in simulation experiments are calculated and listed to show the superiority of our method. The experimental results indicate that the CT image reconstructed using the proposed new method is closer to the reference image. Images from real CT data and their residual images also show that applying the proposed new method can more effectively reduce artifacts and image structures are well preserved.

A generalized simultaneous algebraic reconstruction technique (GSART) for dual-energy X-ray computed tomography

BACKGROUND

Dual-energy computed tomography (DECT) is a widely used and actively researched imaging modality that can estimate the physical properties of an object more accurately than single-energy CT (SECT). Recently, iterative reconstruction methods called one-step methods have received attention among various approaches since they can resolve the intermingled limitations of the conventional methods. However, the one-step methods typically have expensive computational costs, and their material decomposition performance is largely affected by the accuracy in the spectral coefficients estimation.

OBJECTIVE

In this study, we aim to develop an efficient one-step algorithm that can effectively decompose into the basis material maps and is less sensitive to the accuracy of the spectral coefficients.

METHODS

By use of a new loss function that employs the non-linear forward model and the weighted squared errors, we propose a one-step reconstruction algorithm named generalized simultaneous algebraic reconstruction technique (GSART). The proposed algorithm was compared with the image-domain material decomposition and other existing one-step reconstruction algorithm.

RESULTS

In both simulation and experimental studies, we demonstrated that the proposed algorithm effectively reduced the beam-hardening artifacts thereby increasing the accuracy in the material decomposition.

CONCLUSIONS

The proposed one-step reconstruction for material decomposition in dual-energy CT outperformed the image-domain approach and the existing one-step algorithm. We believe that the proposed method is a practically very useful addition to the material-selective image reconstruction field.

Deep Interactive Denoiser (DID) for X-Ray Computed Tomography

Low-dose computed tomography (LDCT) is desirable for both diagnostic imaging and image-guided interventions. Denoisers are widely used to improve the quality of LDCT. Deep learning (DL)-based denoisers have shown state-of-the-art performance and are becoming mainstream methods. However, there are two challenges to using DL-based denoisers: 1) a trained model typically does not generate different image candidates with different noise-resolution tradeoffs, which are sometimes needed for different clinical tasks; and 2) the model's generalizability might be an issue when the noise level in the testing images differs from that in the training dataset. To address these two challenges, in this work, we introduce a lightweight optimization process that can run on top of any existing DL-based denoiser during the testing phase to generate multiple image candidates with different noise-resolution tradeoffs suitable for different clinical tasks in real time. Consequently, our method allows users to interact with the denoiser to efficiently review various image candidates and quickly pick the desired one; thus, we termed this method deep interactive denoiser (DID). Experimental results demonstrated that DID can deliver multiple image candidates with different noise-resolution tradeoffs and shows great generalizability across various network architectures, as well as training and testing datasets with various noise levels.

Image quality guided iterative reconstruction for low-dose CT based on CT image statistics

Iterative reconstruction framework shows predominance in low dose and incomplete data situation. In the iterative reconstruction framework, there are two components, i.e., fidelity term aims to maintain the structure details of the reconstructed object, and the regularization term uses prior information to suppress the artifacts such as noise. A regularization parameter balances them, aiming to find a good trade-off between noise and resolution. Currently, the regularization parameters are selected as a rule of thumb or some prior knowledge assumption is required, which limits practical uses. Furthermore, the computation cost of regularization parameter selection is also heavy. In this paper, we address this problem by introducing CT image quality assessment (IQA) into the iterative reconstruction framework. Several steps are involved during the study. First, we analyze the CT image statistics using the dual dictionary method. Regularities are observed and concluded, revealing the relationship among the regularization parameter, iterations, and CT image quality. Second, with derivation and simplification of DDL procedure, a CT IQA metric named SODVAC is designed. The SODVAC locates the optimal regularization parameter that results in the reconstructed image with distinct structures and with no noise or little noise. Third, we introduce SODVAC into the iterative reconstruction framework and then propose a general image-quality-guided iterative reconstruction (QIR) framework and give a specific framework example (sQIR) by introducing SODVAC into the iterative reconstruction framework. sQIR simultaneously optimizes the reconstructed image and the regularization parameter during the iterations. Results confirm the effectiveness of the proposed method. No prior information needed and low computation cost are the advantages of our method compared with existing state-of-theart L-curve and ZIP selection strategies.

Noise2Context: Context-assisted learning 3D thin-layer for low-dose CT

PURPOSE

Computed tomography (CT) has played a vital role in medical diagnosis, assessment, and therapy planning, etc. In clinical practice, concerns about the increase of x-ray radiation exposure attract more and more attention. To lower the x-ray radiation, low-dose CT (LDCT) has been widely adopted in certain scenarios, while it will induce the degradation of CT image quality. In this paper, we proposed a deep learning-based method that can train denoising neural networks without any clean data.

METHODS

In this work, for 3D thin-slice LDCT scanning, we first drive an unsupervised loss function which was equivalent to a supervised loss function with paired noisy and clean samples when the noise in the different slices from a single scan was uncorrelated and zero-mean. Then, we trained the denoising neural network to map one noise LDCT image to its two adjacent LDCT images in a single 3D thin-layer LDCT scanning, simultaneously. In essence, with some latent assumptions, we proposed an unsupervised loss function to train the denoising neural network in an unsupervised manner, which integrated the similarity between adjacent CT slices in 3D thin-layer LDCT.

RESULTS

Further experiments on Mayo LDCT dataset and a realistic pig head were carried out. In the experiments using Mayo LDCT dataset, our unsupervised method can obtain performance comparable to that of the supervised baseline. With the realistic pig head, our method can achieve optimal performance at different noise levels as compared to all the other methods that demonstrated the superiority and robustness of the proposed Noise2Context.

CONCLUSIONS

In this work, we present a generalizable LDCT image denoising method without any clean data. As a result, our method not only gets rid of the complex artificial image priors but also amounts of paired high-quality training datasets.

Probabilistic self-learning framework for low-dose CT denoising

PURPOSE

Despite the indispensable role of x-ray computed tomography (CT) in diagnostic medicine, the associated harmful ionizing radiation dose is a major concern, as it may cause genetic diseases and cancer. Decreasing patients' exposure can reduce the radiation dose and hence the related risks, but it would inevitably induce higher quantum noise. Supervised deep learning techniques have been used to train deep neural networks for denoising low-dose CT (LDCT) images, but the success of such strategies requires massive sets of pixel-level paired LDCT and normal-dose CT (NDCT) images, which are rarely available in real clinical practice. Our purpose is to mitigate the data scarcity problem for deep learning-based LDCT denoising.

METHODS

To solve this problem, we devised a shift-invariant property-based neural network that uses only the LDCT images to characterize both the inherent pixel correlations and the noise distribution, shaping into our probabilistic self-learning (PSL) framework. The AAPM Low-dose CT Challenge dataset was used to train the network. Both simulated datasets and real dataset were employed to test the denoising performance as well as the model generalizability. The performance was compared to a conventional method (total variation (TV)-based), a popular self-learning method (noise2void (N2V)), and a well-known unsupervised learning method (CycleGAN) by using both qualitative visual inspection and quantitative metrics including peak signal-noise-ratio (PSNR), structural similarity index (SSIM) and contrast-to-noise-ratio (CNR). The standard deviations (STD) of selected flat regions were also calculated for comparison.

RESULTS

The PSL method can improve the averaged PSNR/SSIM values from 27.61/0.5939 (LDCT) to 30.50/0.6797. By contrast, the averaged PSNR/SSIM values were 31.49/0.7284 (TV), 29.43/0.6699 (N2V), and 29.79/0.6992 (CycleGAN). The averaged STDs of selected flat regions were calculated to be 132.3 HU (LDCT), 25.77 HU (TV), 19.95 HU (N2V), 75.06 HU (CycleGAN), 60.62 HU (PSL) and 57.28 HU (NDCT). As for the low-contrast lesion detectability quantification, the CNR were calculated to be 0.202 (LDCT), 0.356 (TV), 0.372 (N2V), 0.383 (CycleGAN), 0.399 (PSL), and 0.359 (NDCT). By visual inspection, we observed that the proposed PSL method can deliver a noise-suppressed and detail-preserved image, while the TV-based method would lead to the blocky artifact, the N2V method would produce over-smoothed structures and CT value biased effect, and the CycleGAN method would generate slightly noisy results with inaccurate CT values. We also verified the generalizability of the PSL method, which exhibited superior denoising performance among various testing datasets with different data distribution shifts.

CONCLUSIONS

A deep learning-based convolutional neural network can be trained without paired datasets. Qualitatively visual inspection showed the proposed PSL method can achieve superior denoising performance than all the competitors, despite that the employed quantitative metrics in terms of PSNR, SSIM and CNR did not always show consistently better values.

Feasibility of Total Variation Noise Reduction Algorithm According to Various MR-Based PET Images in a Simultaneous PET/MR System: A Phantom Study

Recently, the total variation (TV) algorithm has been used for noise reduction distribution in degraded nuclear medicine images. To acquire positron emission tomography (PET) to correct the attenuation region in the PET/magnetic resonance (MR) system, the MR Dixon pulse sequence, which is based on controlled aliasing in parallel imaging, results from higher acceleration (CAIPI; MR-AC_Dixon-CAIPI) and generalized autocalibrating partially parallel acquisition (GRAPPA; MR-AC_Dixon-GRAPPA) algorithms are used. Therefore, this study aimed to evaluate the image performance of the TV noise reduction algorithm for PET/MR images using the Jaszczak phantom by injecting ¹⁸F radioisotopes with PET/MR, which is called mMR (Siemens, Germany), compared with conventional noise-reduction techniques such as Wiener and median filters. The contrast-to-noise (CNR) and coefficient of variation (COV) were used for quantitative analysis. Based on the results, PET images with the TV algorithm were improved by approximately 7.6% for CNR and decreased by approximately 20.0% for COV compared with conventional noise-reduction techniques. In particular, the image quality for the MR-AC_Dixon-CAIPI PET image was better than that of the MR-AC_Dixon-GRAPPA PET image. In conclusion, the TV noise-reduction algorithm is efficient for improving the PET image quality in PET/MR systems.

Anisotropic structure property based image reconstruction method for limited-angle computed tomography

Limited-angle computed tomography (CT) may appear in restricted CT scans. Since the available projection data is incomplete, the images reconstructed by filtered back-projection (FBP) or algebraic reconstruction technique (ART) often encounter shading artifacts. However, using the anisotropy property of the shading artifacts that coincide with the characteristic of limited-angle CT images can reduce the shading artifacts. Considering this concept, we combine the anisotropy property of the shading artifacts with the anisotropic structure property of an image to develop a new algorithm for image reconstruction. Specifically, we propose an image reconstruction method based on adaptive weighted anisotropic total variation (AwATV). This method, termed as AwATV method for short, is designed to preserve image structures and then remove the shading artifacts. It characterizes both of above properties. The anisotropy property of the shading artifacts accounts for reducing artifacts, and the anisotropic structure property of an image accounts for preserving structures. In order to evaluate the performance of AwATV, we use the simulation projection data of FORBILD head phantom and real CT data for image reconstruction. Experimental results show that AwATV can always reconstruct images with higher SSIM and PSNR, and smaller RMSE, which means that AwATV enables to reconstruct images with higher quality in term of artifact reduction and structure preservation.

Dynamic compressed sensing for real-time tomographic reconstruction

Electron tomography has achieved higher resolution and quality at reduced doses with recent advances in compressed sensing. Compressed sensing (CS) exploits the inherent sparse signal structure to efficiently reconstruct three-dimensional (3D) volumes at the nanoscale from undersampled measurements. However, the process bottlenecks 3D reconstruction with computation times that run from hours to days. Here we demonstrate a framework for dynamic compressed sensing that produces a 3D specimen structure that updates in real-time as new specimen projections are collected. Researchers can begin interpreting 3D specimens as data is collected to facilitate high-throughput and interactive analysis. Using scanning transmission electron microscopy (STEM), we show that dynamic compressed sensing accelerates the convergence speed by ~3-fold while also reducing its error by 27% for a Au/SrTiO₃ nanoparticle specimen. Before a tomography experiment is completed, the 3D tomogram has interpretable structure within ~33% of completion and fine details are visible as early as ~66%. Upon completion of an experiment, a high-fidelity 3D visualization is produced without further delay. Additionally, reconstruction parameters that tune data fidelity can be manipulated throughout the computation without re-running the entire process.

Quantifying day-to-day variations in 4DCBCT-based PCA motion models

The aim of this paper is to quantify the day-to-day variations of motion models derived from pre-treatment 4-dimensional cone beam CT (4DCBCT) fractions for lung cancer stereotactic body radiotherapy (SBRT) patients. Motion models are built by (1) applying deformable image registration (DIR) on each 4DCBCT image with respect to a reference image from that day, resulting in a set of displacement vector fields (DVFs), and (2) applying principal component analysis (PCA) on the DVFs to obtain principal components representing a motion model. Variations were quantified by comparing the PCA eigenvectors of the motion model built from the first day of treatment to the corresponding eigenvectors of the other motion models built from each successive day of treatment. Three metrics were used to quantify the variations: root mean squared (RMS) difference in the vectors, directional similarity, and an introduced metric called the Euclidean Model Norm (EMN). EMN quantifies the degree to which a motion model derived from the first fraction can represent the motion models of subsequent fractions. Twenty-one 4DCBCT scans from five SBRT patient treatments were used in this retrospective study. Experimental results demonstrated that the first two eigenvectors of motion models across all fractions have smaller RMS (0.00017), larger directional similarity (0.528), and larger EMN (0.678) than the last three eigenvectors (RMS: 0.00025, directional similarity: 0.041, and EMN: 0.212). The study concluded that, while the motion model eigenvectors varied from fraction to fraction, the first few eigenvectors were shown to be more stable across treatment fractions than others. This supports the notion that a pre-treatment motion model built from the first few PCA eigenvectors may remain valid throughout a treatment course. Future work is necessary to quantify how day-to-day variations in these models will affect motion reconstruction accuracy for specific clinical tasks.

TGV-regularized inversion of the Radon transform for photoacoustic tomography

We propose and study a reconstruction method for photoacoustic tomography (PAT) based on total generalized variation (TGV) regularization for the inversion of the slice-wise 2D-Radon transform in 3D. The latter problem occurs for recently-developed PAT imaging techniques with parallelized integrating ultrasound detection where projection data from various directions is sequentially acquired. As the imaging speed is presently limited to 20 seconds per 3D image, the reconstruction of temporally-resolved 3D sequences of, e.g., one heartbeat or breathing cycle, is very challenging and currently, the presence of motion artifacts in the reconstructions obstructs the applicability for biomedical research. In order to push these techniques forward towards real time, it thus becomes necessary to reconstruct from less measured data such as few-projection data and consequently, to employ sophisticated reconstruction methods in order to avoid typical artifacts. The proposed TGV-regularized Radon inversion is a variational method that is shown to be capable of such artifact-free inversion. It is validated by numerical simulations, compared to filtered back projection (FBP), and performance-tested on real data from phantom as well as in-vivo mouse experiments. The results indicate that a speed-up factor of four is possible without compromising reconstruction quality.

CT IMAGE RECONSTRUCTION ON A LOW DIMENSIONAL MANIFOLD

The patch manifold of a natural image has a low dimensional structure and accommodates rich structural information. Inspired by the recent work of the low-dimensional manifold model (LDMM), we apply the LDMM for regularizing X-ray computed tomography (CT) image reconstruction. This proposed method recovers detailed structural information of images, significantly enhancing spatial and contrast resolution of CT images. Both numerically simulated data and clinically experimental data are used to evaluate the proposed method. The comparative studies are also performed over the simultaneous algebraic reconstruction technique (SART) incorporated the total variation (TV) regularization to demonstrate the merits of the proposed method. Results indicate that the LDMM-based method enables a more accurate image reconstruction with high fidelity and contrast resolution.

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.

Derivative-free superiorization with component-wise perturbations

Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints compatibility. This is done by taking a solely feasibility-seeking algorithm, analyzing its perturbation resilience, and proactively perturbing its iterates accordingly to steer them toward a feasible point with reduced value of the target function. When the perturbation steps are computationally efficient, this enables generation of a superior result with essentially the same computational cost as that of the original feasibility-seeking algorithm. In this work, we refine previous formulations of the superiorization method to create a more general framework, enabling target function reduction steps that do not require partial derivatives of the target function. In perturbations that use partial derivatives, the step-sizes in the perturbation phase of the superiorization method are chosen independently from the choice of the nonascent directions. This is no longer true when component-wise perturbations are employed. In that case, the step-sizes must be linked to the choice of the nonascent direction in every step. Besides presenting and validating these notions, we give a computational demonstration of superiorization with component-wise perturbations for a problem of computerized tomography image reconstruction.

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.

Penalized-Likelihood Reconstruction With High-Fidelity Measurement Models for High-Resolution Cone-Beam Imaging

We present a novel reconstruction algorithm based on a general cone-beam CT forward model, which is capable of incorporating the blur and noise correlations that are exhibited in flat-panel CBCT measurement data. Specifically, the proposed model may include scintillator blur, focal-spot blur, and noise correlations due to light spread in the scintillator. The proposed algorithm (GPL-BC) uses a Gaussian Penalized-Likelihood objective function, which incorporates models of blur and correlated noise. In a simulation study, GPL-BC was able to achieve lower bias as compared with deblurring followed by FDK as well as a model-based reconstruction method without integration of measurement blur. In the same study, GPL-BC was able to achieve better line-pair reconstructions (in terms of segmented-image accuracy) as compared with deblurring followed by FDK, a model-based method without blur, and a model-based method with blur but not noise correlations. A prototype extremities quantitative cone-beam CT test-bench was used to image a physical sample of human trabecular bone. These data were used to compare reconstructions using the proposed method and model-based methods without blur and/or correlation to a registered CT image of the same bone sample. The GPL-BC reconstructions resulted in more accurate trabecular bone segmentation. Multiple trabecular bone metrics, including trabecular thickness (Tb.Th.) were computed for each reconstruction approach as well as the CT volume. The GPL-BC reconstruction provided the most accurate Tb.Th. measurement, 0.255 mm, as compared with the CT derived value of 0.193 mm, followed by the GPL-B reconstruction, the GPL-I reconstruction, and then the FDK reconstruction (0.271 mm, 0.309 mm, and 0.335 mm, respectively).

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.

An electron beam linear scanning mode for industrial limited-angle nano-computed tomography

Nano-computed tomography (nano-CT), which utilizes X-rays to research the inner structure of some small objects and has been widely utilized in biomedical research, electronic technology, geology, material sciences, etc., is a high spatial resolution and non-destructive research technique. A traditional nano-CT scanning model with a very high mechanical precision and stability of object manipulator, which is difficult to reach when the scanned object is continuously rotated, is required for high resolution imaging. To reduce the scanning time and attain a stable and high resolution imaging in industrial non-destructive testing, we study an electron beam linear scanning mode of nano-CT system that can avoid mechanical vibration and object movement caused by the continuously rotated object. Furthermore, to further save the scanning time and study how small the scanning range could be considered with acceptable spatial resolution, an alternating iterative algorithm based on ℓ₀ minimization is utilized to limited-angle nano-CT reconstruction problem with the electron beam linear scanning mode. The experimental results confirm the feasibility of the electron beam linear scanning mode of nano-CT system.

Structurally-sensitive Multi-scale Deep Neural Network for Low-Dose CT Denoising

Computed tomography (CT) is a popular medical imaging modality and enjoys wide clinical applications. At the same time, the x-ray radiation dose associated with CT scannings raises a public concern due to its potential risks to the patients. Over the past years, major efforts have been dedicated to the development of Low-Dose CT (LDCT) methods. However, the radiation dose reduction compromises the signal-to-noise ratio (SNR), leading to strong noise and artifacts that downgrade CT image quality. In this paper, we propose a novel 3D noise reduction method, called Structurally-sensitive Multi-scale Generative Adversarial Net (SMGAN), to improve the LDCT image quality. Specifically, we incorporate three-dimensional (3D) volumetric information to improve the image quality. Also, different loss functions for training denoising models are investigated. Experiments show that the proposed method can effectively preserve structural and textural information in reference to normal-dose CT (NDCT) images, and significantly suppress noise and artifacts. Qualitative visual assessments by three experienced radiologists demonstrate that the proposed method retrieves more information, and outperforms competing methods.

A review of GPU-based medical image reconstruction

Tomographic image reconstruction is a computationally demanding task, even more so when advanced models are used to describe a more complete and accurate picture of the image formation process. Such advanced modeling and reconstruction algorithms can lead to better images, often with less dose, but at the price of long calculation times that are hardly compatible with clinical workflows. Fortunately, reconstruction tasks can often be executed advantageously on Graphics Processing Units (GPUs), which are exploited as massively parallel computational engines. This review paper focuses on recent developments made in GPU-based medical image reconstruction, from a CT, PET, SPECT, MRI and US perspective. Strategies and approaches to get the most out of GPUs in image reconstruction are presented as well as innovative applications arising from an increased computing capacity. The future of GPU-based image reconstruction is also envisioned, based on current trends in high-performance computing.

Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using ℓ0-regularized gradient prior

Accurate images reconstructed from limited computed tomography (CT) data are desired when reducing the X-ray radiation exposure imposed on patients. The total variation (TV), known as the l₁-norm of the image gradient magnitudes, is popular in CT reconstruction from incomplete projection data. However, as the projection data collected are from a sparse-view of the limited scanning angular range, the results reconstructed by a TV-based method suffer from blocky artifact and gradual changed artifacts near the edges, which in turn make the reconstruction images degraded. Different from the TV, the ℓ₀-norm of an image gradient counts the number of its non-zero coefficients of the image gradient. Since the regularization based on the ℓ₀-norm of the image gradient will not penalize the large gradient magnitudes, the edge can be effectively retained. In this work, an edge-preserving image reconstruction method based on l₀-regularized gradient prior was investigated for limited-angle computed tomography from sparse projections. To solve the optimization model effectively, the variable splitting and the alternating direction method (ADM) were utilized. Experiments demonstrated that the ADM-like method used for the non-convex optimization problem has better performance than other classical iterative reconstruction algorithms in terms of edge preservation and artifact reduction.

Gamma-ray CT from incomplete projections for two-phase pipe flow

A low-energy low-dose γ-ray computed tomography (CT) system used in the gas-liquid two-phase pipe flow measurement has been studied at Tianjin University in recent years. The γ-ray CT system, having a third-generation X-ray CT scanning configuration, is comprised of one 300mCi ²⁴¹Am source and 17 CdZnTe detector units and achieves a spatial image resolution of about 7 mm. It is primarily intended to measure the two-phase pipe flow and provide improvement suggestions for industrial CT system. Recently we improve the design for image reconstruction from incomplete projection to optimize the scanning parameters and reduce the radiation dose. First, tomographic problem from incomplete projections is briefly described. Next, a system structure and a hardware circuit design are listed and explained, especially on time parameter setting of the pulse shaper. And then a detailed system analysis is provided in Section II, mainly focusing on spatial resolution, temporal resolution, system noise, and imaging algorithm. Finally, we carry on necessary static and dynamic experiments in a full scan (360°) and two sets of partial scan reconstruction tests to determine the feasibility of this γ-ray CT system for reconstructing the images from insufficient projections. And based on an A-variable algebraic reconstruction technique method, a specially designed algorithm, we evaluate the system performance and noise level of this CT system working quantitatively and qualitatively. Results of dynamic test indicate that the acceptable results can be acquired using a multi-source γ-ray CT system with the same parameters when the flow rate is less than 0.04 m/s and the imaging speed is slower than 33 frames/s.

A fast method based on NESTA to accurately reconstruct CT image from highly undersampled projection measurements

BACKGROUND

The CT image reconstruction algorithm based compressed sensing (CS) can be formulated as an optimization problem that minimizes the total-variation (TV) term constrained by the data fidelity and image nonnegativity. There are a lot of solutions to this problem, but the computational efficiency and reconstructed image quality of these methods still need to be improved.

OBJECTIVE

To investigate a faster and more accurate mathematical algorithm to settle TV term minimization problem of CT image reconstruction.

METHOD

A Nesterov's algorithm (NESTA) is a fast and accurate algorithm for solving TV minimization problem, which can be ascribed to the use of most notably Nesterov's smoothing technique and a subtle averaging of sequences of iterates, which has been shown to improve the convergence properties of standard gradient-descent algorithms. In order to demonstrate the superior performance of NESTA on computational efficiency and image quality, a comparison with Simultaneous Algebraic Reconstruction Technique-TV (SART-TV) and Split-Bregman (SpBr) algorithm is made using a digital phantom study and two physical phantom studies from highly undersampled projection measurements.

RESULTS

With only 25% of conventional full-scan dose and, NESTA method reduces the average CT number error from 51.76HU to 9.98HU on Shepp-Logan phantom and reduces the average CT number error from 50.13HU to 0.32HU on Catphan 600 phantom. On an anthropomorphic head phantom, the average CT number error is reduced from 84.21HU to 1.01HU in the central uniform area.

CONCLUSIONS

To the best of our knowledge this is the first work that apply the NESTA method into CT reconstruction based CS. Research shows that this method is of great potential, further studies and optimization are necessary.

Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction

Low-dose computed tomography (CT) reconstruction is a challenging problem in medical imaging. To complement the standard filtered back-projection (FBP) reconstruction, sparse regularization reconstruction gains more and more research attention, as it promises to reduce radiation dose, suppress artifacts, and improve noise properties. In this work, we present an iterative reconstruction approach using improved smoothed l₀ (SL0) norm regularization which is used to approximate l₀ norm by a family of continuous functions to fully exploit the sparseness of the image gradient. Due to the excellent sparse representation of the reconstruction signal, the desired tissue details are preserved in the resulting images. To evaluate the performance of the proposed SL0 regularization method, we reconstruct the simulated dataset acquired from the Shepp-Logan phantom and clinical head slice image. Additional experimental verification is also performed with two real datasets from scanned animal experiment. Compared to the referenced FBP reconstruction and the total variation (TV) regularization reconstruction, the results clearly reveal that the presented method has characteristic strengths. In particular, it improves reconstruction quality via reducing noise while preserving anatomical features.

A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom

Artifacts induced by respiratory motion during routine diagnosis severely degrades the image quality. The increase of scanning speed plays an important role to avoid motion artifacts. Limited to the mechanical structure of conventional CT, the increase of gantry rotational speed is unsustainable and a more feasible way is to increase the number of X-ray sources and detectors like the dual-source CT. This paper focuses on high-speed scanning CT and proposes a novel ultrafast micro-CT (UMCT) system based on carbon nanotube (CNT). At each exposure position, all of the X-ray sources are fast activated by turns and the flat-panel detectors collect the corresponding projection data. Then, the gantry will be contrarotated 40° to prepare for the next exposure until the rotation covers full 360°. Because each exposure is very fast, the organ motions of in vivo human body can be greatly reduced. This paper introduces the UMCT system design, image reconstruction algorithm and experimental results. Simulation experiment was also carried out on UMCT system. The result validated the feasibility of the UMCT system.

Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography

PURPOSE

This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing.

METHODS

The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ0 pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD.

RESULTS

The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks.

CONCLUSIONS

A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.

Total variation minimization filter for DBT imaging

PURPOSE

Compressed sensing (CS) is a new approach in medical imaging which allows a sparse image to be reconstructed from undersampled data. Total variation (TV) based minimization algorithms are the one CS technique that has achieved great success due to its virtue of preserving edges while reducing image noise. The purpose of this work is to implement and evaluate the performance of a TV minimization filter able to increase the signal difference to noise ratio (SDNR) of digital breast tomosynthesis (DBT) images.

METHODS

Assuming a Poisson noise model, the authors present a practical methodology, based on Rudin, Osher, and Fatemi model, which directly applies a TV minimization filter to real phantom and clinical DBT images. Different moments of filter application (before and after image reconstruction) and the suitable Lagrange multiplier (λ) to be used in filter equation are studied. Also, the relationship between background standard deviation (σB) of unfiltered images and optimal λ values is determined, in order to maximize the SDNR. Qualitative and quantitative analyses are conducted between unfiltered and filtered images and between the different moments of filter application. The proposed methodology is also tested with one clinical DBT data set.

RESULTS

Using phantom data, when the filter is applied to the projections, the authors observed a decrease of 31.34% in TV and an increase of 5.29% and 5.44% in SDNR and full width at half maximum (FWHM), respectively. When applied after reconstruction, a decrease of 35.48% and 2.59% was achieved for TV and FWHM, respectively, and an increase of 8.32% for SDNR. For each moment of filter application, the optimal λ value found through a comprehensive study was λ = 85 and λ = 60 when the filter is applied before and after reconstruction, respectively. The best fit found for the relationship between σB and the corresponding λ values that allowed the highest filtered SDNR was the logarithmic adjustment. The difference between the λ values obtained by the first approach and the logarithmic adjustment ranges from 0.11% (filter applied before reconstruction) to 2.54% (filter applied after reconstruction). On the other hand, a decrease of 37.63% and 2.42% in TV and FWHM, respectively, and an increase of 24.39% in SDNR were obtained when the filter is applied to clinical data. This great minimization is present through a visual inspection of unfiltered and filtered clinical images, where areas with higher noise level become smoother while preserving edges and details of the structures.

CONCLUSIONS

An optimized digital filter for TV minimization in DBT imaging has been presented. The reliability of a logarithmic relation found between σB and λ values was confirmed and can be used in future work. Both quantitative and qualitative analyses performed in a clinical DBT image confirmed the relevance of this approach in improving image quality in DBT imaging. The results obtained are very encouraging about increasing SDNR in a short time and preserving the principal variations in image, the structures' boundary.

Investigation of cone-beam CT image quality trade-off for image-guided radiation therapy

It is well-known that projections acquired over an angular range slightly over 180° (so-called short scan) are sufficient for fan-beam reconstruction. However, due to practical imaging conditions (projection data and reconstruction image discretization, physical factors, and data noise), the short-scan reconstructions may have different appearances and properties from the full-scan (scans over 360°) reconstructions. Nevertheless, short-scan configurations have been used in applications such as cone-beam CT (CBCT) for head-neck-cancer image-guided radiation therapy (IGRT) that only requires a small field of view due to the potential reduced imaging time and dose. In this work, we studied the image quality trade-off for full, short, and full/short scan configurations with both conventional filtered-backprojection (FBP) reconstruction and iterative reconstruction algorithms based on total-variation (TV) minimization for head-neck-cancer IGRT. Anthropomorphic and Catphan phantoms were scanned at different exposure levels with a clinical scanner used in IGRT. Both visualization- and numerical-metric-based evaluation studies were performed. The results indicate that the optimal exposure level and number of views are in the middle range for both FBP and TV-based iterative algorithms and the optimization is object-dependent and task-dependent. The optimal view numbers decrease with the total exposure levels for both FBP and TV-based algorithms. The results also indicate there are slight differences between FBP and TV-based iterative algorithms for the image quality trade-off: FBP seems to be more in favor of larger number of views while the TV-based algorithm is more robust to different data conditions (number of views and exposure levels) than the FBP algorithm. The studies can provide a general guideline for image-quality optimization for CBCT used in IGRT and other applications.

Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization

PURPOSE

The authors develop and investigate iterative image reconstruction algorithms based on data-discrepancy minimization with a total-variation (TV) constraint. The various algorithms are derived with different data-discrepancy measures reflecting the maximum likelihood (ML) principle. Simulations demonstrate the iterative algorithms and the resulting image statistical properties for low-dose CT data acquired with sparse projection view angle sampling. Of particular interest is to quantify improvement of image statistical properties by use of the ML data fidelity term.

METHODS

An incremental algorithm framework is developed for this purpose. The instances of the incremental algorithms are derived for solving optimization problems including a data fidelity objective function combined with a constraint on the image TV. For the data fidelity term the authors, compare application of the maximum likelihood principle, in the form of weighted least-squares (WLSQ) and Poisson-likelihood (PL), with the use of unweighted least-squares (LSQ).

RESULTS

The incremental algorithms are applied to projection data generated by a simulation modeling the breast computed tomography (bCT) imaging application. The only source of data inconsistency in the bCT projections is due to noise, and a Poisson distribution is assumed for the transmitted x-ray photon intensity. In the simulations involving the incremental algorithms an ensemble of images, reconstructed from 1000 noise realizations of the x-ray transmission data, is used to estimate the image statistical properties. The WLSQ and PL incremental algorithms are seen to reduce image variance as compared to that of LSQ without sacrificing image bias. The difference is also seen at few iterations--short of numerical convergence of the corresponding optimization problems.

CONCLUSIONS

The proposed incremental algorithms prove effective and efficient for iterative image reconstruction in low-dose CT applications particularly with sparse-view projection data.

Low-dose CT statistical iterative reconstruction via modified MRF regularization

It is desirable to reduce the excessive radiation exposure to patients in repeated medical CT applications. One of the most effective ways is to reduce the X-ray tube current (mAs) or tube voltage (kVp). However, it is difficult to achieve accurate reconstruction from the noisy measurements. Compared with the conventional filtered back-projection (FBP) algorithm leading to the excessive noise in the reconstructed images, the approaches using statistical iterative reconstruction (SIR) with low mAs show greater image quality. To eliminate the undesired artifacts and improve reconstruction quality, we proposed, in this work, an improved SIR algorithm for low-dose CT reconstruction, constrained by a modified Markov random field (MRF) regularization. Specifically, the edge-preserving total generalized variation (TGV), which is a generalization of total variation (TV) and can measure image characteristics up to a certain degree of differentiation, was introduced to modify the MRF regularization. In addition, a modified alternating iterative algorithm was utilized to optimize the cost function. Experimental results demonstrated that images reconstructed by the proposed method could not only generate high accuracy and resolution properties, but also ensure a higher peak signal-to-noise ratio (PSNR) in comparison with those using existing methods.

Iterative image reconstruction for limited-angle inverse helical cone-beam computed tomography

Helical trajectory satisfying the condition of exact reconstruction, has been widely utilized in the commercial computed tomography (CT). While limited by the scanning environment in some practical applications, the conventional helical cone-beam CT imaging is hard to complete, thus, developing an imaging system suited for long-object may be valuable. Three-dimensional C-arm CT is an innovative imaging technique which has been greatly concerned. Since there is a high degree of freedom of C-arm, more flexible image acquisition trajectories for 3D imaging can be achieved. In this work, a fast iterative reconstruction algorithm based on total variation minimization is developed for a trajectory of limited-angle inverse helical cone-beam CT, which can be applied to detect long-object without slip-ring technology. The experimental results show that the developed algorithm can yield reconstructed images of low noise level and high image quality.

Adaptively Tuned Iterative Low Dose CT Image Denoising

Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction.

3D fluoroscopic image estimation using patient-specific 4DCBCT-based motion models

3D fluoroscopic images represent volumetric patient anatomy during treatment with high spatial and temporal resolution. 3D fluoroscopic images estimated using motion models built using 4DCT images, taken days or weeks prior to treatment, do not reliably represent patient anatomy during treatment. In this study we developed and performed initial evaluation of techniques to develop patient-specific motion models from 4D cone-beam CT (4DCBCT) images, taken immediately before treatment, and used these models to estimate 3D fluoroscopic images based on 2D kV projections captured during treatment. We evaluate the accuracy of 3D fluoroscopic images by comparison to ground truth digital and physical phantom images. The performance of 4DCBCT-based and 4DCT-based motion models are compared in simulated clinical situations representing tumor baseline shift or initial patient positioning errors. The results of this study demonstrate the ability for 4DCBCT imaging to generate motion models that can account for changes that cannot be accounted for with 4DCT-based motion models. When simulating tumor baseline shift and patient positioning errors of up to 5 mm, the average tumor localization error and the 95th percentile error in six datasets were 1.20 and 2.2 mm, respectively, for 4DCBCT-based motion models. 4DCT-based motion models applied to the same six datasets resulted in average tumor localization error and the 95th percentile error of 4.18 and 5.4 mm, respectively. Analysis of voxel-wise intensity differences was also conducted for all experiments. In summary, this study demonstrates the feasibility of 4DCBCT-based 3D fluoroscopic image generation in digital and physical phantoms and shows the potential advantage of 4DCBCT-based 3D fluoroscopic image estimation when there are changes in anatomy between the time of 4DCT imaging and the time of treatment delivery.

Iterative projection onto convex sets for quantitative susceptibility mapping

PURPOSE

Quantitative susceptibility map (QSM) reconstruction is ill posed due to the zero values on the "magic angle cone" that make the maps prone to streaking artifacts. We propose projection onto convex sets (POCS) in the method of steepest descent (SD) for QSM reconstruction.

METHODS

Two convex projections, an object-support projection in the image domain and a projection in k-space were used. QSM reconstruction using the proposed SD-POCS method was compared with SD and POCS alone as well as with truncated k-space division (TKD) for numerically simulated and 7 Tesla (T) human brain phase data.

RESULTS

The QSM reconstruction error from noise-free simulated phase data using SD-POCS is at least two orders of magnitude lower than using SD, POCS, or TKD and has reduced streaking artifacts. Using the l1 -TV reconstructed susceptibility as a gold standard for 7T in vivo imaging, SD-POCS showed better image quality comparing to SD, POCS, or TKD from visual inspection.

CONCLUSION

POCS is an alternative method for regularization that can be used in an iterative minimization method such as SD for QSM reconstruction.

Analysis of iterative region-of-interest image reconstruction for x-ray computed tomography

One of the challenges for iterative image reconstruction (IIR) is that such algorithms solve an imaging model implicitly, requiring a complete representation of the scanned subject within the viewing domain of the scanner. This requirement can place a prohibitively high computational burden for IIR applied to x-ray computed tomography (CT), especially when high-resolution tomographic volumes are required. In this work, we aim to develop an IIR algorithm for direct region-of-interest (ROI) image reconstruction. The proposed class of IIR algorithms is based on an optimization problem that incorporates a data fidelity term, which compares a derivative of the estimated data with the available projection data. In order to characterize this optimization problem, we apply it to computer-simulated two-dimensional fan-beam CT data, using both ideal noiseless data and realistic data containing a level of noise comparable to that of the breast CT application. The proposed method is demonstrated for both complete field-of-view and ROI imaging. To demonstrate the potential utility of the proposed ROI imaging method, it is applied to actual CT scanner data.

Investigation of iterative image reconstruction in low-dose breast CT

There is interest in developing computed tomography (CT) dedicated to breast-cancer imaging. Because breast tissues are radiation-sensitive, the total radiation exposure in a breast-CT scan is kept low, often comparable to a typical two-view mammography exam, thus resulting in a challenging low-dose-data-reconstruction problem. In recent years, evidence has been found that suggests that iterative reconstruction may yield images of improved quality from low-dose data. In this work, based upon the constrained image total-variation minimization program and its numerical solver, i.e., the adaptive steepest descent-projection onto the convex set (ASD-POCS), we investigate and evaluate iterative image reconstructions from low-dose breast-CT data of patients, with a focus on identifying and determining key reconstruction parameters, devising surrogate utility metrics for characterizing reconstruction quality, and tailoring the program and ASD-POCS to the specific reconstruction task under consideration. The ASD-POCS reconstructions appear to outperform the corresponding clinical FDK reconstructions, in terms of subjective visualization and surrogate utility metrics.

Accelerated barrier optimization compressed sensing (ABOCS) for CT reconstruction with improved convergence

Recently, we proposed a new algorithm of accelerated barrier optimization compressed sensing (ABOCS) for iterative CT reconstruction. The previous implementation of ABOCS uses gradient projection (GP) with a Barzilai-Borwein (BB) step-size selection scheme (GP-BB) to search for the optimal solution. The algorithm does not converge stably due to its non-monotonic behavior. In this paper, we further improve the convergence of ABOCS using the unknown-parameter Nesterov (UPN) method and investigate the ABOCS reconstruction performance on clinical patient data. Comparison studies are carried out on reconstructions of computer simulation, a physical phantom and a head-and-neck patient. In all of these studies, the ABOCS results using UPN show more stable and faster convergence than those of the GP-BB method and a state-of-the-art Bregman-type method. As shown in the simulation study of the Shepp-Logan phantom, UPN achieves the same image quality as those of GP-BB and the Bregman-type methods, but reduces the iteration numbers by up to 50% and 90%, respectively. In the Catphan©600 phantom study, a high-quality image with relative reconstruction error (RRE) less than 3% compared to the full-view result is obtained using UPN with 17% projections (60 views). In the conventional filtered-backprojection reconstruction, the corresponding RRE is more than 15% on the same projection data. The superior performance of ABOCS with the UPN implementation is further demonstrated on the head-and-neck patient. Using 25% projections (91 views), the proposed method reduces the RRE from 21% as in the filtered backprojection (FBP) results to 7.3%. In conclusion, we propose UPN for ABOCS implementation. As compared to GP-BB and the Bregman-type methods, the new method significantly improves the convergence with higher stability and fewer iterations.

Super-resolution for computed tomography based on discrete tomography

In computed tomography (CT), partial volume effects impede accurate segmentation of structures that are small with respect to the pixel size. In this paper, it is shown that for objects consisting of a small number of homogeneous materials, the reconstruction resolution can be substantially increased without altering the acquisition process. A super-resolution reconstruction approach is introduced that is based on discrete tomography, in which prior knowledge about the materials in the object is assumed. Discrete tomography has already been used to create reconstructions from a low number of projection angles, but in this paper, it is demonstrated that it can also be applied to increase the reconstruction resolution. Experiments on simulated and real μCT data of bone and foam structures show that the proposed method indeed leads to significantly improved structure segmentation and quantification compared with what can be achieved from conventional reconstructions.

Non-local total variation based low-dose Computed Tomography denoising

Radiation dose of X-ray Computed Tomography (CT) imaging has raised a worldwide health concern. Therefore, low-dose CT imaging has been of a huge interest in the last decade. However, lowering the radiation dose degrades the image quality by increasing the noise level, which may reduce the diagnostic performance of the images. As a result, image denoising is one of the fundamental tasks in low-dose CT imaging. One of the state of art denoising methods, which has been successfully used in this area, is Total Variation (TV) denoising. Nevertheless, if the parameters of the TV denoising are not optimally adjusted or the algorithm is not stopped in an appropriate point, some of the small structures will be removed by this method. Here, we provide a solution to this problem by proposing a modified nonlocal TV method, called probabilistic NLTV (PNLTV). Denoising performance of PNLTV is improved by using better weights and an appropriate stopping criterion based on statistics of image wavelet coefficients. Non-locality allows the algorithm to preserve the image texture, which combined with the proposed stopping criterion enables PNLTV to keep fine details unchanged.

Single shot high resolution digital holography

We demonstrate a novel computational method for high resolution image recovery from a single digital hologram frame. The complex object field is obtained from the recorded hologram by solving a constrained optimization problem. This approach which is unlike the physical hologram replay process is shown to provide high quality image recovery even when the dc and the cross terms in the hologram overlap in the Fourier domain. Experimental results are shown for a Fresnel zone hologram of a resolution chart, intentionally recorded with a small off-axis reference beam angle. Excellent image recovery is observed without the presence of dc or twin image terms and with minimal speckle noise.

Optimization-based reconstruction of sparse images from few-view projections

In this work, we investigate optimization-based image reconstruction from few-view (i.e. less than ten views) projections of sparse objects such as coronary-artery specimens. Using optimization programs as a guide, we formulate constraint programs as reconstruction programs and develop algorithms to reconstruct images through solving the reconstruction programs. Characterization studies are carried out for elucidating the algorithm properties of 'convergence' (relative to designed solutions) and 'utility' (relative to desired solutions) by using simulated few-view data calculated from a discrete FORBILD coronary-artery phantom, and real few-view data acquired from a human coronary-artery specimen. Study results suggest that carefully designed reconstruction programs and algorithms can yield accurate reconstructions of sparse images from few-view projections.