Total variation-stokes strategy for sparse-view X-ray CT image reconstruction

Pure Vision Transformer (CT-ViT) with Noise2Neighbors Interpolation for Low-Dose CT Image Denoising

Convolutional neural networks (CNN) have been used for a wide variety of deep learning applications, especially in computer vision. For medical image processing, researchers have identified certain challenges associated with CNNs. These challenges encompass the generation of less informative features, limitations in capturing both high and low-frequency information within feature maps, and the computational cost incurred when enhancing receptive fields by deepening the network. Transformers have emerged as an approach aiming to address and overcome these specific limitations of CNNs in the context of medical image analysis. Preservation of all spatial details of medical images is necessary to ensure accurate patient diagnosis. Hence, this research introduced the use of a pure Vision Transformer (ViT) for a denoising artificial neural network for medical image processing specifically for low-dose computed tomography (LDCT) image denoising. The proposed model follows a U-Net framework that contains ViT modules with the integration of Noise2Neighbor (N2N) interpolation operation. Five different datasets containing LDCT and normal-dose CT (NDCT) image pairs were used to carry out this experiment. To test the efficacy of the proposed model, this experiment includes comparisons between the quantitative and visual results among CNN-based (BM3D, RED-CNN, DRL-E-MP), hybrid CNN-ViT-based (TED-Net), and the proposed pure ViT-based denoising model. The findings of this study showed that there is about 15-20% increase in SSIM and PSNR when using self-attention transformers than using the typical pure CNN. Visual results also showed improvements especially when it comes to showing fine structural details of CT images.

Robust residual-guided iterative reconstruction for sparse-view CT in small animal imaging

Objective. We introduce a robust image reconstruction algorithm named residual-guided Golub-Kahan iterative reconstruction technique (RGIRT) designed for sparse-view computed tomography (CT), which aims at high-fidelity image reconstruction from a limited number of projection views.Approach. RGIRT utilizes an inner-outer dual iteration framework, with a flexible least square QR (FLSQR) algorithm implemented in the inner iteration and a restarted iterative scheme applied in the outer iteration. The inner FLSQR employs a flexible Golub-Kahan bidiagonalization method to reduce the size of the inverse problem, and a weighted generalized cross-validation method to adaptively estimate the regularization hyper-parameter. The inner iteration efficiently yields the intermediate reconstruction result, while the outer iteration minimizes the residual and refines the solution by using the result obtained from the inner iteration.Main results. The reconstruction performance of RGIRT is evaluated and compared to other reference methods (FBPConvNet, SART-TV, and FLSQR) using projection data from both numerical phantoms and real experimental Micro-CT data. The experimental findings, from testing various numbers of projection views and different noise levels, underscore the robustness of RGIRT. Meanwhile, theoretical analysis confirms the convergence of residual for our approach.Significance. We propose a robust iterative reconstruction algorithm for x-ray CT scans with sparse views, thereby shortening scanning time and mitigating excessive ionizing radiation exposure to small animals.

Extreme Few-View Tomography without Training Data

There are fewer than 10 projection views in extreme few-view tomography. The state-of-the-art methods to reconstruct images with few-view data are compressed sensing based. Compressed sensing relies on a sparsification transformation and total variation (TV) norm minimization. However, for the extreme few-view tomography, the compressed sensing methods are not powerful enough. This paper seeks additional information as extra constraints so that extreme few-view tomography becomes possible. In transmission tomography, we roughly know the linear attenuation coefficients of the objects to be imaged. We can use these values as extra constraints. Computer simulations show that these extra constraints are helpful and improve the reconstruction quality.

Systematic Review on Learning-based Spectral CT

Spectral computed tomography (CT) has recently emerged as an advanced version of medical CT and significantly improves conventional (single-energy) CT. Spectral CT has two main forms: dual-energy computed tomography (DECT) and photon-counting computed tomography (PCCT), which offer image improvement, material decomposition, and feature quantification relative to conventional CT. However, the inherent challenges of spectral CT, evidenced by data and image artifacts, remain a bottleneck for clinical applications. To address these problems, machine learning techniques have been widely applied to spectral CT. In this review, we present the state-of-the-art data-driven techniques for spectral CT.

Fast Multi-Grid Methods for Minimizing Curvature Energies

The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners, and contrast. However, the dilemma between restoration quality and computational efficiency is an essential roadblock for high-order methods. In this paper, we propose fast multi-grid algorithms for minimizing both mean curvature and Gaussian curvature energy functionals without sacrificing accuracy for efficiency. Unlike the existing approaches based on operator splitting and the Augmented Lagrangian method (ALM), no artificial parameters are introduced in our formulation, which guarantees the robustness of the proposed algorithm. Meanwhile, we adopt the domain decomposition method to promote parallel computing and use the fine-to-coarse structure to accelerate convergence. Numerical experiments are presented on image denoising, CT, and MRI reconstruction problems to demonstrate the superiority of our method in preserving geometric structures and fine details. The proposed method is also shown effective in dealing with large-scale image processing problems by recovering an image of size $1024\times 1024$ within 40s, while the ALM-based method requires around 200s.

Deep Learning Denoising of Low-Dose Computed Tomography Chest Images: A Quantitative and Qualitative Image Analysis

PURPOSE

To assess deep learning denoised (DLD) computed tomography (CT) chest images at various low doses by both quantitative and qualitative perceptual image analysis.

METHODS

Simulated noise was inserted into sinogram data from 32 chest CTs acquired at 100 mAs, generating anatomically registered images at 40, 20, 10, and 5 mAs. A DLD model was developed, with 23 scans selected for training, 5 for validation, and 4 for test.Quantitative analysis of perceptual image quality was assessed with Structural SIMilarity Index (SSIM) and Fréchet Inception Distance (FID). Four thoracic radiologists graded overall diagnostic image quality, image artifact, visibility of small structures, and lesion conspicuity. Noise-simulated and denoised image series were evaluated in comparison with one another, and in comparison with standard 100 mAs acquisition at the 4 mAs levels. Statistical tests were conducted at the 2-sided 5% significance level, with multiple comparison correction.

RESULTS

At the same mAs levels, SSIM and FID between noise-simulated and reconstructed DLD images indicated that images were closer to a perfect match with increasing mAs (closer to 1 for SSIM, and 0 for FID).In comparing noise-simulated and DLD images to standard-dose 100-mAs images, DLD improved SSIM and FID. Deep learning denoising improved SSIM of 40-, 20-, 10-, and 5-mAs simulations in comparison with standard-dose 100-mAs images, with change in SSIM from 0.91 to 0.94, 0.87 to 0.93, 0.67 to 0.87, and 0.54 to 0.84, respectively. Deep learning denoising improved FID of 40-, 20-, 10-, and 5-mAs simulations in comparison with standard-dose 100-mAs images, with change in FID from 20 to 13, 46 to 21, 104 to 41, and 148 to 69, respectively.Qualitative image analysis showed no significant difference in lesion conspicuity between DLD images at any mAs in comparison with 100-mAs images. Deep learning denoising images at 10 and 5 mAs were rated lower for overall diagnostic image quality ( P < 0.001), and at 5 mAs lower for overall image artifact and visibility of small structures ( P = 0.002), in comparison with 100 mAs.

CONCLUSIONS

Deep learning denoising resulted in quantitative improvements in image quality. Qualitative assessment demonstrated DLD images at or less than 10 mAs to be rated inferior to standard-dose images.

Iterative CT reconstruction based on ADMM using shearlet sparse regularization

The total variation (TV) method favors solutions with the piece-wise constant assumption of the desired image from sparse-view sampling, for example, simple geometric images with flat intensity. When the phantoms become more complex and contain complicated textures, for example, high-resolution phantom and lung CT images, the images reconstructed by TV regularization may lose their contrast and fine structures. One of the optimally sparse transforms for images, the shearlet transform, has C² without discontinuities on C² curves, giving excellent sensitive directional information as compared with other wavelet transform approaches. Here, we developed a Shearlet-Sparse Regularization (SSR) algorithm solved with the Alternating Direction Method of Multipliers (ADMM) to overcome this limitation. With the strengthened characteristics of SSR, we performed one simulation experiment and two real experiments using a NeuViz 64 X-ray CT scanning system to measure the performance and properties of proposed algorithm. The results demonstrate that the SSR method exhibits the advantage of providing high-quality directional information and contrast as compared with TV.

LRR-CED: low-resolution reconstruction-aware convolutional encoder–decoder network for direct sparse-view CT image reconstruction

Objective. Sparse-view computed tomography (CT) reconstruction has been at the forefront of research in medical imaging. Reducing the total x-ray radiation dose to the patient while preserving the reconstruction accuracy is a big challenge. The sparse-view approach is based on reducing the number of rotation angles, which leads to poor quality reconstructed images as it introduces several artifacts. These artifacts are more clearly visible in traditional reconstruction methods like the filtered-backprojection (FBP) algorithm. Approach. Over the years, several model-based iterative and more recently deep learning-based methods have been proposed to improve sparse-view CT reconstruction. Many deep learning-based methods improve FBP-reconstructed images as a post-processing step. In this work, we propose a direct deep learning-based reconstruction that exploits the information from low-dimensional scout images, to learn the projection-to-image mapping. This is done by concatenating FBP scout images at multiple resolutions in the decoder part of a convolutional encoder–decoder (CED). Main results. This approach is investigated on two different networks, based on Dense Blocks and U-Net to show that a direct mapping can be learned from a sinogram to an image. The results are compared to two post-processing deep learning methods (FBP-ConvNet and DD-Net) and an iterative method that uses a total variation (TV) regularization. Significance. This work presents a novel method that uses information from both sinogram and low-resolution scout images for sparse-view CT image reconstruction. We also generalize this idea by demonstrating results with two different neural networks. This work is in the direction of exploring deep learning across the various stages of the image reconstruction pipeline involving data correction, domain transfer and image improvement.

Dual-domain sparse-view CT reconstruction with Transformers

PURPOSE

Computed Tomography (CT) has been widely used in the medical field. Sparse-view CT is an effective and feasible method to reduce the radiation dose. However, the conventional filtered back projection (FBP) algorithm will suffer from severe artifacts in sparse-view CT. Iterative reconstruction algorithms have been adopted to remove artifacts, but they are time-consuming due to repeated projection and back projection and may cause blocky effects. To overcome the difficulty in sparse-view CT, we proposed a dual-domain sparse-view CT algorithm CT Transformer (CTTR) and paid attention to sinogram information.

METHODS

CTTR treats sinograms as sentences and enhances reconstructed images with sinogram's characteristics. We qualitatively evaluate the CTTR, an iterative method TVM-POCS, a convolutional neural network based method FBPConvNet in terms of a reduction in artifacts and a preservation of details. Besides, we also quantitatively evaluate these methods in terms of RMSE, PSNR and SSIM.

RESULTS

We evaluate our method on the Lung Image Database Consortium image collection with different numbers of projection views and noise levels. Experiment studies show that, compared with other methods, CTTR can reduce more artifacts and preserve more details on various scenarios. Specifically, CTTR improves the FBPConvNet performance of PSNR by 0.76dB with 30 projections.

CONCLUSIONS

The performance of our proposed CTTR is better than the method based on CNN in the case of extremely sparse views both on visual results and quantitative evaluation. Our proposed method provides a new idea for the application of Transformers to CT image processing.

Sparse Angle CBCT Reconstruction Based on Guided Image Filtering

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

A balanced total-variation-Chambolle-Pock algorithm for EPR imaging

Total variation (TV) minimization algorithm is an effective algorithm capable of accurately reconstructing images from sparse projection data in a variety of imaging modalities including computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). The data divergence constrained, TV minimization (DDcTV) model and its Chambolle-Pock (CP) solving algorithm have been proposed for CT. However, when the DDcTV-CP algorithm is applied to 3D EPRI, it suffers from slow convergence rate or divergence. We hypothesize that this is due to the magnitude imbalance between the data fidelity term and the TV regularization term. In this work, we propose a balanced TV (bTV) model incorporating a balance parameter and demonstrate its capability to avoid convergence issues for the 3D EPRI application. Simulation and real experiments show that the DDcTV-CP algorithm cannot guarantee convergence but the bTV-CP algorithm may guarantee convergence and achieve fast convergence by use of an appropriate balance parameter. Experiments also show that underweighting the balance parameter leads to slow convergence, whereas overweighting the balance parameter leads to divergence. The iteration-behavior change-law with the variation of the balance parameter is explained by use of the data tolerance ellipse and gradient descent principle. The findings and insights gained in this work may be applied to other imaging modalities and other constrained optimization problems.

The Reconstruction of Magnetic Particle Imaging: Current Approaches Based on the System Matrix

Magnetic particle imaging (MPI) is a novel non-invasive molecular imaging technology that images the distribution of superparamagnetic iron oxide nanoparticles (SPIONs). It is not affected by imaging depth, with high sensitivity, high resolution, and no radiation. The MPI reconstruction with high precision and high quality is of enormous practical importance, and many studies have been conducted to improve the reconstruction accuracy and quality. MPI reconstruction based on the system matrix (SM) is an important part of MPI reconstruction. In this review, the principle of MPI, current construction methods of SM and the theory of SM-based MPI are discussed. For SM-based approaches, MPI reconstruction mainly has the following problems: the reconstruction problem is an inverse and ill-posed problem, the complex background signals seriously affect the reconstruction results, the field of view cannot cover the entire object, and the available 3D datasets are of relatively large volume. In this review, we compared and grouped different studies on the above issues, including SM-based MPI reconstruction based on the state-of-the-art Tikhonov regularization, SM-based MPI reconstruction based on the improved methods, SM-based MPI reconstruction methods to subtract the background signal, SM-based MPI reconstruction approaches to expand the spatial coverage, and matrix transformations to accelerate SM-based MPI reconstruction. In addition, the current phantoms and performance indicators used for SM-based reconstruction are listed. Finally, certain research suggestions for MPI reconstruction are proposed, expecting that this review will provide a certain reference for researchers in MPI reconstruction and will promote the future applications of MPI in clinical medicine.

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

BACKGROUND AND OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Characterization of tissue-specific pre-log Bayesian CT reconstruction by texture-dose relationship

PURPOSE

Tissue textures have been recognized as biomarkers for various clinical tasks. In computed tomography (CT) image reconstruction, it is important but challenging to preserve the texture when lowering x-ray exposure from full- toward low-/ultra-low dose level. Therefore, this paper aims to explore the texture-dose relationship within one tissue-specific pre-log Bayesian CT reconstruction algorithm.

METHODS

To enhance the texture in ultra-low dose CT (ULdCT) reconstruction, this paper presents a Bayesian type algorithm. A shifted Poisson model is adapted to describe the statistical properties of pre-log data, and a tissue-specific Markov random field prior (MRFt) is used to incorporate tissue texture from previous full-dose CT, thus called SP-MRFt algorithm. Utilizing the SP-MRFt algorithm, we investigated tissue texture degradation as a function of x-ray dose levels from full dose (100 mAs/120 kVp) to ultralow dose (1 mAs/120 kVp) by using quantitative texture-based evaluation metrics.

RESULTS

Experimental results show the SP-MRFt algorithm outperforms conventional filtered back projection (FBP) and post-log domain penalized weighted least square MRFt (PWLS-MRFt) in terms of noise suppression and texture preservation. Comparable results are also obtained with shifted Poisson model with 7 × 7 Huber MRF weights (SP-Huber7). The investigation on texture-dose relationship shows that the quantified texture measures drop monotonically as dose level decreases, and interestingly a turning point is observed on the texture-dose response curve.

CONCLUSIONS

This important observation implies that there exists a minimum dose level, at which a given CT scanner (hardware configuration and image reconstruction software) can achieve without compromising clinical tasks. Moreover, the experiment results show that the variance of electronic noise has higher impact than the mean to the texture-dose relationship.

Deformable registration and region-of-interest image reconstruction in sparse repeat CT scanning

BACKGROUND

Repeat CT scanning is ubiquitous in many clinical situations, e.g. to follow disease progression, to evaluate treatment efficacy, and to monitor interventional CT procedures. However, it incurs in cumulative radiation to the patient which can be significantly reduced by using a region of interest (ROI) and the existing baseline scan.

OBJECTIVE

To obtain a high-quality reconstruction of a ROI with a significantly reduced X-ray radiation dosage that accounts for deformations.

METHODS

We present a new method for deformable registration and image reconstruction inside an ROI in repeat CT scans with a highly reduced X-ray radiation dose based on sparse scanning. Our method uses the existing baseline scan data, a user-defined ROI, and a new sparse repeat scan to compute a high-quality repeat scan ROI image with a significantly reduced radiation dose. Our method first performs rigid registration between the densely scanned baseline and the sparsely scanned repeat CT scans followed by deformable registration with a low-order parametric model, both in 3D Radon space and without reconstructing the repeat scan image. It then reconstructs the repeat scan ROI without computing the entire repeat scan image.

RESULTS

Our experimental results on clinical lung and liver CT scans yield a mean × 14 computation speedup and a × 7.6-12.5 radiation dose reduction, with a minor image quality loss of 0.0157 in the NRMSE metric.

CONCLUSION

Our method is considerably faster than existing methods, thereby enabling intraoperative online repeat scanning that it is accurate and accounts for position, deformation, and structure changes at a fraction of the radiation dose required by existing methods.

Automatic Change Detection in Sparse Repeat CT Scanning

We describe a new method for the automatic detection of changes in repeat CT scanning with a reduced X-ray radiation dose. We present a theoretical formulation of the automatic change detection problem based on the on-line sparse-view repeat CT scanning dose optimization framework. We prove that the change detection problem is NP-hard and therefore cannot be efficiently solved exactly. We describe a new greedy change detection algorithm that is simple and robust and relies on only two key parameters. We demonstrate that the greedy algorithm accurately detects small, low contrast changes with only 12 scan angles. Our experimental results show that the new algorithm yields a mean changed region recall rate >89% and a mean precision rate >76%. It outperforms both our previous heuristic approach and a thresholding method using a low-dose prior image-constrained compressed sensing (PICCS) reconstruction of the repeat scan. The resulting changed region map may obviate the need for a high-quality repeat scan image when no major changes are detected and may streamline the radiologist's workflow by highlighting the regions of interest.

Accelerating Neutron Tomography experiments through Artificial Neural Network based reconstruction

Neutron Tomography (NT) is a non-destructive technique to investigate the inner structure of a wide range of objects and, in some cases, provides valuable results in comparison to the more common X-ray imaging techniques. However, NT is time consuming and scanning a set of similar objects during a beamtime leads to data redundancy and long acquisition times. Nowadays NT is unfeasible for quality checking study of large quantities of similar objects. One way to decrease the total scan time is to reduce the number of projections. Analytical reconstruction methods are very fast but under this condition generate streaking artifacts in the reconstructed images. Iterative algorithms generally provide better reconstruction for limited data problems, but at the expense of longer reconstruction time. In this study, we propose the recently introduced Neural Network Filtered Back-Projection (NN-FBP) method to optimize the time usage in NT experiments. Simulated and real neutron data were used to assess the performance of the NN-FBP method as a function of the number of projections. For the first time a machine learning based algorithm is applied and tested for NT image reconstruction problem. We demonstrate that the NN-FBP method can reliably reduce acquisition and reconstruction times and it outperforms conventional reconstruction methods used in NT, providing high image quality for limited datasets.

Performance of sparse-view CT reconstruction with multi-directional gradient operators

To further reduce the noise and artifacts in the reconstructed image of sparse-view CT, we have modified the traditional total variation (TV) methods, which only calculate the gradient variations in x and y directions, and have proposed 8- and 26-directional (the multi-directional) gradient operators for TV calculation to improve the quality of reconstructed images. Different from traditional TV methods, the proposed 8- and 26-directional gradient operators additionally consider the diagonal directions in TV calculation. The proposed method preserves more information from original tomographic data in the step of gradient transform to obtain better reconstruction image qualities. Our algorithms were tested using two-dimensional Shepp–Logan phantom and three-dimensional clinical CT images. Results were evaluated using the root-mean-square error (RMSE), peak signal-to-noise ratio (PSNR), and universal quality index (UQI). All the experiment results show that the sparse-view CT images reconstructed using the proposed 8- and 26-directional gradient operators are superior to those reconstructed by traditional TV methods. Qualitative and quantitative analyses indicate that the more number of directions that the gradient operator has, the better images can be reconstructed. The 8- and 26-directional gradient operators we proposed have better capability to reduce noise and artifacts than traditional TV methods, and they are applicable to be applied to and combined with existing CT reconstruction algorithms derived from CS theory to produce better image quality in sparse-view reconstruction.

Few-view CT image reconstruction using improved total variation regularization

X-ray radiation is harmful to human health. Thus, obtaining a better reconstructed image with few projection view constraints is a major challenge in the computed tomography (CT) field to reduce radiation dose. In this study, we proposed and tested a new algorithm that combines penalized weighted least-squares using total generalized variation (PWLS-TGV) and dictionary learning (DL), named PWLS-TGV-DL to address this challenge. We first presented and tested this new algorithm and evaluated it through both data simulation and physical experiments. We then analyzed experimental data in terms of image qualitative and quantitative measures, such as the structural similarity index (SSIM) and the root mean square error (RMSE). The experiments and data analysis indicated that applying the new algorithm to CT data recovered images more efficiently and yielded better results than the traditional CT image reconstruction approaches.

Noise-robust Mojette reconstruction using sparse-view CT projections

Sparse-view Computed Tomography (CT) has important significance in industrial inspection and medical diagnosis. Mojette transform is a kind of discrete Radon transform that can yield exact reconstructions instead of an approximate solution due to finite Radon sampling. However, the image is iteratively reconstructed pixel by pixel from corner to center, and the image error is proportional to the number of iterations. In this paper, we propose that there exist different sets of projection combinations to recover the original image within the close-to-minimal iterations. And a scheme is given to obtain multiple projection sets, each of which has the same number of minimum iterations and can recover a CT image with a similar level of small noise but different distributions. These images can be used further to restore the final CT image by counteracting noise with each other. The accuracy and validity of the proposed algorithm are verified by comparison with both other Mojette inversion algorithms and the classical SART algorithm.

Multiple limited-angles computed tomography reconstruction based on multi-direction total variation minimization

Accurate computed tomography (CT) reconstruction from incomplete projections is an important research topic. Sparse sampling and limited-angle sampling are two effective ways to reduce the X-ray radiation dose or the scanning time. However, it is technically complicated to realize sparse sampling in medical CT since the tube power or the pre-patient collimator is difficult to be switched frequently. Limited-angle sampling makes it difficult to reconstruct an accurate image. The developed multiple limited-angles (MLA) sampling scheme could well balance the technical implementation complexity and the CT reconstruction difficulty. It does not require frequent switching of the tube power or the pre-patient collimator. The data correlation of the acquired projections is lower than that in limited-angle sampling. Using the projections acquired by MLA sampling, CT images reconstructed by the total variation minimization (TVM) method suffer from shading artifacts. Because the artifacts are distributed in several fixed directions, the artifact-suppression reconstruction model based on multi-direction total variation was designed for MLA CT reconstruction in this work. The multi-direction total variation minimization (MDTVM) was utilized to solve the optimization model. Experiments on digital phantoms and real projections indicated that MDTVM can better suppress the shading artifacts than TVM.

Statistical CT reconstruction using region-aware texture preserving regularization learning from prior normal-dose CT image

In some clinical applications, prior normal-dose CT (NdCT) images are available, and the valuable textures and structure features in them may be used to promote follow-up low-dose CT (LdCT) reconstruction. This study aims to learn texture information from the NdCT images and leverage it for follow-up LdCT image reconstruction to preserve textures and structure features. Specifically, the proposed reconstruction method first learns the texture information from those patches with similar structures in NdCT image, and the similar patches can be clustered by searching context features efficiently from the surroundings of the current patch. Then it utilizes redundant texture information from the similar patches as a priori knowledge to describe specific regions in the LdCT image. The advanced region-aware texture preserving prior is termed as 'RATP'. The main advantage of the PATP prior is that it can properly learn the texture features from available NdCT images and adaptively characterize the region-specific structures in the LdCT image. The experiments using patient data were performed to evaluate the performance of the proposed method. The proposed RATP method demonstrated superior performance in LdCT imaging compared to the filtered back projection (FBP) and statistical iterative reconstruction (SIR) methods using Gaussian regularization, Huber regularization and the original texture preserving regularization.

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.

Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects

The purpose of this paper is to design and simulate a new computed tomography (CT) system with a high temporal resolution for dynamic objects. We propose a multisource cubical CT (MCCT) system with X-ray tubes and detectors installed on a cube. Carbon nanotube- (CNT-) based X-ray focal spots are distributed on the twelve edges of the cube. The distribution of X-ray focal spots and detectors completely avoids mechanical movements to scan an object under inspection. CNTs are excellent electron field emitters because the use of a "cold" cathode makes it possible to fabricate a cathode with multiple electron emission points, and the CNT-based X-ray focal spots possess little response time and programmable emission. The proposed rotation-free MCCT system can acquire a high scanning speed when using a high frame rate detector. A three-dimensional (3D) reconstruction algorithm with tensor framelet-based L0-norm (TF-L0) minimization is developed for the simulation study of the MCCT. Simulation experiment results demonstrate the feasibility of the MCCT system.

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.

4D cone-beam computed tomography (CBCT) using a moving blocker for simultaneous radiation dose reduction and scatter correction

Four-dimensional (4D) x-ray cone-beam computed tomography (CBCT) is important for a precise radiation therapy for lung cancer. Due to the repeated use and 4D acquisition over a course of radiotherapy, the radiation dose becomes a concern. Meanwhile, the scatter contamination in CBCT deteriorates image quality for treatment tasks. In this work, we propose the use of a moving blocker (MB) during the 4D CBCT acquisition ('4D MB') and to combine motion-compensated reconstruction to address these two issues simultaneously. In 4D MB CBCT, the moving blocker reduces the x-ray flux passing through the patient and collects the scatter information in the blocked region at the same time. The scatter signal is estimated from the blocked region for correction. Even though the number of projection views and projection data in each view are not complete for conventional reconstruction, 4D reconstruction with a total-variation (TV) constraint and a motion-compensated temporal constraint can utilize both spatial gradient sparsity and temporal correlations among different phases to overcome the missing data problem. The feasibility simulation studies using the 4D NCAT phantom showed that 4D MB with motion-compensated reconstruction with 1/3 imaging dose reduction could produce satisfactory images and achieve 37% improvement on structural similarity (SSIM) index and 55% improvement on root mean square error (RMSE), compared to 4D reconstruction at the regular imaging dose without scatter correction. For the same 4D MB data, 4D reconstruction outperformed 3D TV reconstruction by 28% on SSIM and 34% on RMSE. A study of synthetic patient data also demonstrated the potential of 4D MB to reduce the radiation dose by 1/3 without compromising the image quality. This work paves the way for more comprehensive studies to investigate the dose reduction limit offered by this novel 4D MB method using physical phantom experiments and real patient data based on clinical relevant metrics.

Artifact Removal using Improved GoogLeNet for Sparse-view CT Reconstruction

Sparse-view Reconstruction can be used to provide accelerated low dose CT imaging with both accelerated scan and reduced projection/back-projection calculation. Despite the rapid developments, image noise and artifacts still remain a major issue in the low dose protocol. In this paper, a deep learning based method named Improved GoogLeNet is proposed to remove streak artifacts due to projection missing in sparse-view CT reconstruction. Residual learning is used in GoogLeNet to study the artifacts of sparse-view CT reconstruction, and then subtracts the artifacts obtained by learning from the sparse reconstructed images, finally recovers a clear correction image. The intensity of reconstruction using the proposed method is very close to the full-view projective reconstructed image. The results indicate that the proposed method is practical and effective for reducing the artifacts and preserving the quality of the reconstructed image.

A new Mumford-Shah total variation minimization based model for sparse-view x-ray computed tomography image reconstruction

Total variation (TV) minimization for the sparse-view x-ray computer tomography (CT) reconstruction has been widely explored to reduce radiation dose. However, due to the piecewise constant assumption for the TV model, the reconstructed images often suffer from over-smoothness on the image edges. To mitigate this drawback of TV minimization, we present a Mumford-Shah total variation (MSTV) minimization algorithm in this paper. The presented MSTV model is derived by integrating TV minimization and Mumford-Shah segmentation. Subsequently, a penalized weighted least-squares (PWLS) scheme with MSTV is developed for the sparse-view CT reconstruction. For simplicity, the proposed algorithm is named as 'PWLS-MSTV.' To evaluate the performance of the present PWLS-MSTV algorithm, both qualitative and quantitative studies were conducted by using a digital XCAT phantom and a physical phantom. Experimental results show that the present PWLS-MSTV algorithm has noticeable gains over the existing algorithms in terms of noise reduction, contrast-to-ratio measure and edge-preservation.

Frame-Based CT Image Reconstruction via the Balanced Approach

Frame-based regularization method as one kind of sparsity representation method has been developed in recent years and has been proved to be an efficient method for CT image reconstruction. However, most of the developed CT image reconstruction methods are analysis-based frame methods. This paper proposes a novel frame-based balanced hybrid model with two sparse regularization terms for CT image reconstruction. We generalize the fast alternating direction method to solve the proposed model so that every subproblem can be easily solved. The numerical experiments suggest that the proposed hybrid balanced-based wavelet regularization scheme is efficient in terms of reducing the defined reconstruction root mean squared error and improving the signal to noise ratio in CT image reconstruction.

Discriminative Feature Representation to Improve Projection Data Inconsistency for Low Dose CT Imaging

In low dose computed tomography (LDCT) imaging, the data inconsistency of measured noisy projections can significantly deteriorate reconstruction images. To deal with this problem, we propose here a new sinogram restoration approach, the sinogram- discriminative feature representation (S-DFR) method. Different from other sinogram restoration methods, the proposed method works through a 3-D representation-based feature decomposition of the projected attenuation component and the noise component using a well-designed composite dictionary containing atoms with discriminative features. This method can be easily implemented with good robustness in parameter setting. Its comparison to other competing methods through experiments on simulated and real data demonstrated that the S-DFR method offers a sound alternative in LDCT.

Robust Low-Dose CT Sinogram Preprocessing via Exploiting Noise-Generating Mechanism

Computed tomography (CT) image recovery from low-mAs acquisitions without adequate treatment is always severely degraded due to a number of physical factors. In this paper, we formulate the low-dose CT sinogram preprocessing as a standard maximum a posteriori (MAP) estimation, which takes full consideration of the statistical properties of the two intrinsic noise sources in low-dose CT, i.e., the X-ray photon statistics and the electronic noise background. In addition, instead of using a general image prior as found in the traditional sinogram recovery models, we design a new prior formulation to more rationally encode the piecewise-linear configurations underlying a sinogram than previously used ones, like the TV prior term. As compared with the previous methods, especially the MAP-based ones, both the likelihood/loss and prior/regularization terms in the proposed model are ameliorated in a more accurate manner and better comply with the statistical essence of the generation mechanism of a practical sinogram. We further construct an efficient alternating direction method of multipliers algorithm to solve the proposed MAP framework. Experiments on simulated and real low-dose CT data demonstrate the superiority of the proposed method according to both visual inspection and comprehensive quantitative performance evaluation.

Iterative metal artifact reduction for x-ray computed tomography using unmatched projector/backprojector pairs

PURPOSE

Metal artifact reduction (MAR) is a major problem and a challenging issue in x-ray computed tomography (CT) examinations. Iterative reconstruction from sinograms unaffected by metals shows promising potential in detail recovery. This reconstruction has been the subject of much research in recent years. However, conventional iterative reconstruction methods easily introduce new artifacts around metal implants because of incomplete data reconstruction and inconsistencies in practical data acquisition. Hence, this work aims at developing a method to suppress newly introduced artifacts and improve the image quality around metal implants for the iterative MAR scheme.

METHODS

The proposed method consists of two steps based on the general iterative MAR framework. An uncorrected image is initially reconstructed, and the corresponding metal trace is obtained. The iterative reconstruction method is then used to reconstruct images from the unaffected sinogram. In the reconstruction step of this work, an iterative strategy utilizing unmatched projector/backprojector pairs is used. A ramp filter is introduced into the back-projection procedure to restrain the inconsistency components in low frequencies and generate more reliable images of the regions around metals. Furthermore, a constrained total variation (TV) minimization model is also incorporated to enhance efficiency. The proposed strategy is implemented based on an iterative FBP and an alternating direction minimization (ADM) scheme, respectively. The developed algorithms are referred to as "iFBP-TV" and "TV-FADM," respectively. Two projection-completion-based MAR methods and three iterative MAR methods are performed simultaneously for comparison.

RESULTS

The proposed method performs reasonably on both simulation and real CT-scanned datasets. This approach could reduce streak metal artifacts effectively and avoid the mentioned effects in the vicinity of the metals. The improvements are evaluated by inspecting regions of interest and by comparing the root-mean-square errors, normalized mean absolute distance, and universal quality index metrics of the images. Both iFBP-TV and TV-FADM methods outperform other counterparts in all cases. Unlike the conventional iterative methods, the proposed strategy utilizing unmatched projector/backprojector pairs shows excellent performance in detail preservation and prevention of the introduction of new artifacts.

CONCLUSIONS

Qualitative and quantitative evaluations of experimental results indicate that the developed method outperforms classical MAR algorithms in suppressing streak artifacts and preserving the edge structural information of the object. In particular, structures lying close to metals can be gradually recovered because of the reduction of artifacts caused by inconsistency effects.

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.

Discriminative feature representation: an effective postprocessing solution to low dose CT imaging

This paper proposes a concise and effective approach termed discriminative feature representation (DFR) for low dose computerized tomography (LDCT) image processing, which is currently a challenging problem in medical imaging field. This DFR method assumes LDCT images as the superposition of desirable high dose CT (HDCT) 3D features and undesirable noise-artifact 3D features (the combined term of noise and artifact features induced by low dose scan protocols), and the decomposed HDCT features are used to provide the processed LDCT images with higher quality. The target HDCT features are solved via the DFR algorithm using a featured dictionary composed by atoms representing HDCT features and noise-artifact features. In this study, the featured dictionary is efficiently built using physical phantom images collected from the same CT scanner as the target clinical LDCT images to process. The proposed DFR method also has good robustness in parameter setting for different CT scanner types. This DFR method can be directly applied to process DICOM formatted LDCT images, and has good applicability to current CT systems. Comparative experiments with abdomen LDCT data validate the good performance of the proposed approach.

Edge Preserving and Noise Reducing Reconstruction for Magnetic Particle Imaging

Magnetic particle imaging (MPI) is an emerging medical imaging modality which is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. It is an important feature of MPI that even fast dynamic processes can be captured for 3D volumes. The high temporal resolution in turn leads to large amounts of data which have to be handled efficiently. But as the system matrix of MPI is non-sparse, the image reconstruction gets computationally demanding. Therefore, currently only basic image reconstruction methods such as Tikhonov regularization are used. However, Tikhonov regularization is known to oversmooth edges in the reconstructed image and to have only a limited noise reducing effect. In this work, we develop an efficient edge preserving and noise reducing reconstruction method for MPI. As regularization model, we propose to use the nonnegative fused lasso model, and we devise a discretization that is adapted to the acquisition geometry of the preclinical MPI scanner considered in this work. We develop a customized solver based on a generalized forward-backward scheme which is particularly suitable for the dense and not well-structured system matrices in MPI. Already a non-optimized prototype implementation processes a 3D volume within a few seconds so that processing several frames per second seems amenable. We demonstrate the improvement in reconstruction quality over the state-of-the-art method in an experimental medical setup for an in-vitro angioplasty of a stenosis.

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.

Dual energy CT with one full scan and a second sparse-view scan using structure preserving iterative reconstruction (SPIR)

Conventional dual-energy CT (DECT) reconstruction requires two full-size projection datasets with two different energy spectra. In this study, we propose an iterative algorithm to enable a new data acquisition scheme which requires one full scan and a second sparse-view scan for potential reduction in imaging dose and engineering cost of DECT. A bilateral filter is calculated as a similarity matrix from the first full-scan CT image to quantify the similarity between any two pixels, which is assumed unchanged on a second CT image since DECT scans are performed on the same object. The second CT image from reduced projections is reconstructed by an iterative algorithm which updates the image by minimizing the total variation of the difference between the image and its filtered image by the similarity matrix under data fidelity constraint. As the redundant structural information of the two CT images is contained in the similarity matrix for CT reconstruction, we refer to the algorithm as structure preserving iterative reconstruction (SPIR). The proposed method is evaluated on both digital and physical phantoms, and is compared with the filtered-backprojection (FBP) method, the conventional total-variation-regularization-based algorithm (TVR) and prior-image-constrained-compressed-sensing (PICCS). SPIR with a second 10-view scan reduces the image noise STD by a factor of one order of magnitude with same spatial resolution as full-view FBP image. SPIR substantially improves over TVR on the reconstruction accuracy of a 10-view scan by decreasing the reconstruction error from 6.18% to 1.33%, and outperforms TVR at 50 and 20-view scans on spatial resolution with a higher frequency at the modulation transfer function value of 10% by an average factor of 4. Compared with the 20-view scan PICCS result, the SPIR image has 7 times lower noise STD with similar spatial resolution. The electron density map obtained from the SPIR-based DECT images with a second 10-view scan has an average error of less than 1%.

Extracting Information From Previous Full-Dose CT Scan for Knowledge-Based Bayesian Reconstruction of Current Low-Dose CT Images

Markov random field (MRF) model has been widely employed in edge-preserving regional noise smoothing penalty to reconstruct piece-wise smooth images in the presence of noise, such as in low-dose computed tomography (LdCT). While it preserves edge sharpness, its regional smoothing may sacrifice tissue image textures, which have been recognized as useful imaging biomarkers, and thus it may compromise clinical tasks such as differentiating malignant vs. benign lesions, e.g., lung nodules or colon polyps. This study aims to shift the edge-preserving regional noise smoothing paradigm to texture-preserving framework for LdCT image reconstruction while retaining the advantage of MRF's neighborhood system on edge preservation. Specifically, we adapted the MRF model to incorporate the image textures of muscle, fat, bone, lung, etc. from previous full-dose CT (FdCT) scan as a priori knowledge for texture-preserving Bayesian reconstruction of current LdCT images. To show the feasibility of the proposed reconstruction framework, experiments using clinical patient scans were conducted. The experimental outcomes showed a dramatic gain by the a priori knowledge for LdCT image reconstruction using the commonly-used Haralick texture measures. Thus, it is conjectured that the texture-preserving LdCT reconstruction has advantages over the edge-preserving regional smoothing paradigm for texture-specific clinical applications.

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l1-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.

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.

Gamma regularization based reconstruction for low dose CT

Reducing the radiation in computerized tomography is today a major concern in radiology. Low dose computerized tomography (LDCT) offers a sound way to deal with this problem. However, more severe noise in the reconstructed CT images is observed under low dose scan protocols (e.g. lowered tube current or voltage values). In this paper we propose a Gamma regularization based algorithm for LDCT image reconstruction. This solution is flexible and provides a good balance between the regularizations based on l0-norm and l1-norm. We evaluate the proposed approach using the projection data from simulated phantoms and scanned Catphan phantoms. Qualitative and quantitative results show that the Gamma regularization based reconstruction can perform better in both edge-preserving and noise suppression when compared with other norms.

On Few-View Tomography and Staircase Artifacts

This paper investigates some potential methods for few-view tomography, and investigates the cause and remedy of the staircase artifacts. This paper also discusses whether there is any benefit to use edge-preserving filters in emission tomography. We formulate a general Green's one-step-late algorithm, so that it can incorporate any linear or non-linear filters. We argue that the derivative of the penalty function can be "artificially" created, not naturally derived from a penalty function. We have gained more insight into constrained image reconstruction especially with edge-preserving constraints. Our numerical results show that the bilateral method can have better performance than the TV method, and higher order methods may not be necessary for non-piecewise-constant objects.