Improved compressed sensing-based algorithm for sparse-view CT image reconstruction

DuDoCFNet: Dual-Domain Coarse-to-Fine Progressive Network for Simultaneous Denoising, Limited-View Reconstruction, and Attenuation Correction of Cardiac SPECT

Single-Photon Emission Computed Tomography (SPECT) is widely applied for the diagnosis of coronary artery diseases. Low-dose (LD) SPECT aims to minimize radiation exposure but leads to increased image noise. Limited-view (LV) SPECT, such as the latest GE MyoSPECT ES system, enables accelerated scanning and reduces hardware expenses but degrades reconstruction accuracy. Additionally, Computed Tomography (CT) is commonly used to derive attenuation maps ( μ -maps) for attenuation correction (AC) of cardiac SPECT, but it will introduce additional radiation exposure and SPECT-CT misalignments. Although various methods have been developed to solely focus on LD denoising, LV reconstruction, or CT-free AC in SPECT, the solution for simultaneously addressing these tasks remains challenging and under-explored. Furthermore, it is essential to explore the potential of fusing cross-domain and cross-modality information across these interrelated tasks to further enhance the accuracy of each task. Thus, we propose a Dual-Domain Coarse-to-Fine Progressive Network (DuDoCFNet), a multi-task learning method for simultaneous LD denoising, LV reconstruction, and CT-free μ -map generation of cardiac SPECT. Paired dual-domain networks in DuDoCFNet are cascaded using a multi-layer fusion mechanism for cross-domain and cross-modality feature fusion. Two-stage progressive learning strategies are applied in both projection and image domains to achieve coarse-to-fine estimations of SPECT projections and CT-derived μ -maps. Our experiments demonstrate DuDoCFNet's superior accuracy in estimating projections, generating μ -maps, and AC reconstructions compared to existing single- or multi-task learning methods, under various iterations and LD levels. The source code of this work is available at https://github.com/XiongchaoChen/DuDoCFNet-MultiTask.

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

BACKGROUND

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

METHODS

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

RESULTS

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

DISCUSSION

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

Reconstruction of Sparse-View X-ray Computed Tomography Based on Adaptive Total Variation Minimization

Sparse-view reconstruction has garnered significant interest in X-ray computed tomography (CT) imaging owing to its ability to lower radiation doses and enhance detection efficiency. Among current methods for sparse-view CT reconstruction, an algorithm utilizing iterative reconstruction based on full variational regularization demonstrates good performance. The optimized direction and number of computations for the gradient operator of the regularization term play a crucial role in determining not only the reconstructed image quality but also the convergence speed of the iteration process. The conventional TV approach solely accounts for the vertical and horizontal directions of the two-dimensional plane in the gradient direction. When projection data decrease, the edges of the reconstructed image become blurred. Exploring too many gradient directions for TV terms often comes at the expense of more computational costs. To enhance the balance of computational cost and reconstruction quality, this study suggests a novel TV computation model that is founded on a four-direction gradient operator. In addition, selecting appropriate iteration parameters significantly impacts the quality of the reconstructed image. We propose a nonparametric control method utilizing the improved TV approach as a solution to the tedious manual parameter optimization issue. The relaxation parameters of projection onto convex sets (POCS) are determined according to the scanning number and numerical proportion of the projection data; according to the image error before and after iterations, the gradient descent step of the TV item is adaptively adjusted. Compared with several representative iterative reconstruction algorithms, the experimental results show that the algorithm can effectively preserve edges and suppress noise in sparse-view CT reconstruction.

Cone-Beam Angle Dependency of 3D Models Computed from Cone-Beam CT Images

Cone-beam dental CT can provide high-precision 3D images of the teeth and surrounding bones. From the 3D CT images, 3D models, also called digital impressions, can be computed for CAD/CAM-based fabrication of dental restorations or orthodontic devices. However, the cone-beam angle-dependent artifacts, mostly caused by the incompleteness of the projection data acquired in the circular cone-beam scan geometry, can induce significant errors in the 3D models. Using a micro-CT, we acquired CT projection data of plaster cast models at several different cone-beam angles, and we investigated the dependency of the model errors on the cone-beam angle in comparison with the reference models obtained from the optical scanning of the plaster models. For the 3D CT image reconstruction, we used the conventional Feldkamp algorithm and the combined half-scan image reconstruction algorithm to investigate the dependency of the model errors on the image reconstruction algorithm. We analyzed the mean of positive deviations and the mean of negative deviations of the surface points on the CT-image-derived 3D models from the reference model, and we compared them between the two image reconstruction algorithms. It has been found that the model error increases as the cone-beam angle increases in both algorithms. However, the model errors are smaller in the combined half-scan image reconstruction when the cone-beam angle is as large as 10 degrees.

Compressed sensing two-dimensional Bragg scatter imaging

Here we introduce a new reconstruction technique for two-dimensional Bragg scattering tomography (BST), based on the Radon transform models of Webber and Miller [Inverse Probl. Imaging15, 683 (2021).10.3934/ipi.2021010]. Our method uses a combination of ideas from multibang control and microlocal analysis to construct an objective function which can regularize the BST artifacts; specifically the boundary artifacts due to sharp cutoff in sinogram space (as observed in [arXiv preprint, arXiv:2007.00208 (2020)]), and artifacts arising from approximations made in constructing the model used for inversion. We then test our algorithm in a variety of Monte Carlo (MC) simulated examples of practical interest in airport baggage screening and threat detection. The data used in our studies is generated with a novel Monte-Carlo code presented here. The model, which is available from the authors upon request, captures both the Bragg scatter effects described by BST as well as beam attenuation and Compton scatter.

Compressed medical imaging based on average sparsity model and reweighted analysis of multiple basis pursuit

In medical imaging and applications, efficient image sampling and transfer are some of the key fields of research. The compressed sensing (CS) theory has shown that such compression can be performed during the data retrieval process and that the uncompressed image can be retrieved using a computationally flexible optimization method. The objective of this study is to propose compressed medical imaging for a different type of medical images, based on the combination of the average sparsity model and reweighted analysis of multiple basis pursuit (M-BP) reconstruction methods, referred to as multiple basis reweighted analysis (M-BRA). The proposed algorithm includes the joint multiple sparsity averaging to improves the signal sparsity in M-BP. In this study, four types of medical images are opted to fill the gap of lacking a detailed analysis of M-BRA in medical images. The medical dataset consists of magnetic resonance imaging (MRI) data, computed tomography (CT) data, colonoscopy data, and endoscopy data. Employing the proposed approach, a signal-to-noise ratio (SNR) of 30 dB was achieved for MRI data on a sampling ratio of M/N=0.3. SNR of 34, 30, and 34 dB are corresponding to CT, colonoscopy, and endoscopy data on the same sampling ratio of M/N=0.15. The proposed M-BRA performance indicates the potential for compressed medical imaging analysis with high reconstruction image quality.

Deep learning-based solvability of underdetermined inverse problems in medical imaging

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain, where underdetermined problems are motivated by the willingness to provide high resolution medical images with as little data as possible, by optimizing data collection in terms of minimal acquisition time, cost-effectiveness, and low invasiveness. Typical examples include undersampled magnetic resonance imaging(MRI), interior tomography, and sparse-view computed tomography(CT), where deep learning techniques have achieved excellent performances. However, there is a lack of mathematical analysis of why the deep learning method is performing well. This study aims to explain about learning the causal relationship regarding the structure of the training data suitable for deep learning, to solve highly underdetermined problems. We present a particular low-dimensional solution model to highlight the advantage of deep learning methods over conventional methods, where two approaches use the prior information of the solution in a completely different way. We also analyze whether deep learning methods can learn the desired reconstruction map from training data in the three models (undersampled MRI, sparse-view CT, interior tomography). This paper also discusses the nonlinearity structure of underdetermined linear systems and conditions of learning (called M-RIP condition).

Generative Noise Reduction in Dental Cone-Beam CT by a Selective Anatomy Analytic Iteration Reconstruction Algorithm

Dental cone-beam computed tomography (CBCT) is a powerful tool in clinical treatment planning, especially in a digital dentistry platform. Currently, the “as low as diagnostically acceptable” (ALADA) principle and diagnostic ability are a trade-off in most of the 3D integrated applications, especially in the low radio-opaque densified tissue structure. The CBCT benefits in comprehensive diagnosis and its treatment prognosis for post-operation predictability are clinically known in modern dentistry. In this paper, we propose a new algorithm called the selective anatomy analytic iteration reconstruction (SA2IR) algorithm for the sparse-projection set. The algorithm was simulated on a phantom structure analogous to a patient’s head for geometric similarity. The proposed algorithm is projection-based. Interpolated set enrichment and trio-subset enhancement were used to reduce the generative noise and maintain the scan’s clinical diagnostic ability. The results show that proposed method was highly applicable in medico-dental imaging diagnostics fusion for the computer-aided treatment planning, because it had significant generative noise reduction and lowered computational cost when compared to the other common contemporary algorithms for sparse projection, which generate a low-dosed CBCT reconstruction.

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.

Subspace-based resolution-enhancing image reconstruction method for few-view differential phase-contrast tomography

It is well known that properly designed image reconstruction methods can facilitate reductions in imaging doses and data-acquisition times in tomographic imaging. The ability to do so is particularly important for emerging modalities, such as differential x-ray phase-contrast tomography (D-XPCT), which are currently limited by these factors. An important application of D-XPCT is high-resolution imaging of biomedical samples. However, reconstructing high-resolution images from few-view tomographic measurements remains a challenging task due to the high-frequency information loss caused by data incompleteness. In this work, a subspace-based reconstruction strategy is proposed and investigated for use in few-view D-XPCT image reconstruction. By adopting a two-step approach, the proposed method can simultaneously recover high-frequency details within a certain region of interest while suppressing noise and/or artifacts globally. The proposed method is investigated by the use of few-view experimental data acquired by an edge-illumination D-XPCT scanner.

Radon Space Dose Optimization in Repeat CT Scanning

We present a new method for on-line radiation dose optimization in repeat computer tomography (CT) scanning. Our method uses the information of the baseline scan during the repeat scanning to significantly reduce the radiation dose without compromising the repeat scan quality. It automatically registers the patient to the baseline scan using fractional scanning and detects in sinogram space the patient regions where changes have occurred without having to reconstruct the repeat scan image. It scans only these regions in the patient, thereby considerably reducing the necessary radiation dose. It then completes the missing values of the sparsely sampled repeat scan sinogram with those of the fully sampled baseline sinogram in regions where no changes were detected and computes the repeat scan image by standard filtered backprojection reconstruction. Experiments on a patient scan with simulated changes yield a mean recall of 98% using <19% of a full dose. Experiments on real CT scans of an abdomen phantom produce similar results, with a mean recall of 94.5% and only 14.4% of a full dose more than the theoretical optimum. As hardly any changed rays are missed, the reconstructed images are practically indistinguishable from a full dose scan. Our method successfully detects small, low contrast changes and produces an accurate repeat scan reconstruction using three times less radiation than an image space baseline method.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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.

Interior tomographic imaging of mouse heart in a carbon nanotube micro-CT

BACKGROUND

The relatively high radiation dose from micro-CT is a cause for concern in preclinical research involving animal subjects. Interior region-of-interest (ROI) imaging was proposed for dose reduction, but has not been experimentally applied in micro-CT.

OBJECTIVE

Our aim is to implement interior ROI imaging in a carbon nanotube (CNT) x-ray source based micro-CT, and present the ROI image quality and radiation dose reduction for interior cardiac micro-CT imaging of a mouse heart in situ.

METHODS

An aperture collimator was mounted at the source-side to induce a small-sized cone beam (10 mm width) at the isocenter. Interior in situ micro-CT scans were conducted on a mouse carcass and several micro-CT phantoms. A GPU-accelerated hybrid iterative reconstruction algorithm was employed for volumetric image reconstruction. Radiation dose was measured for the same system operated at the interior and global micro-CT modes.

RESULTS

Visual inspection demonstrated comparable image quality between two scan modes. Quantitative evaluation demonstrated high structural similarity index (up to 0.9614) with improved contrast-noise-ratio (CNR) on interior micro-CT mode. Interior micro-CT mode yielded significant reduction (up to 83.9%) for dose length product (DLP).

CONCLUSIONS

This work demonstrates the applicability of using CNT x-ray source based interior micro-CT for preclinical imaging with significantly reduced radiation dose.

Accelerated Compressed Sensing Based CT Image Reconstruction

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

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.

Sparsity-regularized image reconstruction of decomposed K-edge data in spectral CT

The development of spectral computed tomography (CT) using binned photon-counting detectors has garnered great interest in recent years and has enabled selective imaging of K-edge materials. A practical challenge in CT image reconstruction of K-edge materials is the mitigation of image artifacts that arise from reduced-view and/or noisy decomposed sinogram data. In this note, we describe and investigate sparsity-regularized penalized weighted least squares-based image reconstruction algorithms for reconstructing K-edge images from few-view decomposed K-edge sinogram data. To exploit the inherent sparseness of typical K-edge images, we investigate use of a total variation (TV) penalty and a weighted sum of a TV penalty and an ℓ1-norm with a wavelet sparsifying transform. Computer-simulation and experimental phantom studies are conducted to quantitatively demonstrate the effectiveness of the proposed reconstruction algorithms.