Projected Iterative Soft-Thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

ISRSL0: compressed sensing MRI with image smoothness regularized-smoothed [Formula: see text] norm

The reconstruction of MR images has always been a challenging inverse problem in medical imaging. Acceleration of MR scanning is of great importance for clinical research and cutting-edge applications. One of the primary efforts to achieve this is using compressed sensing (CS) theory. The CS aims to reconstruct MR images using a small number of sampled data in k-space. The CS-MRI techniques face challenges, including the potential loss of fine structure and increased computational complexity. We introduce a novel framework based on a regularized sparse recovery problem and a sharpening step to improve the CS-MRI approaches regarding fine structure loss under high acceleration factors. This problem is solved via the Half Quadratic Splitting (HQS) approach. The inverse problem for reconstructing MR images is converted into two distinct sub-problems, each of which can be solved separately. One key feature of the proposed approach is the replacement of one sub-problem with a denoiser. This regularization assists the optimization of the Smoothed [Formula: see text] (SL0) norm in escaping local minimums and enhances its precision. The proposed method consists of smoothing, feature modification, and Smoothed [Formula: see text] cost function optimization. The proposed approach improves the SL0 algorithm for MRI reconstruction without complicating it. The convergence of the proposed approach is illustrated analytically. The experimental results show an acceptable performance of the proposed method compared to the network-based approaches.

Distortionless, free-breathing, and respiratory resolved 3D diffusion weighted imaging of the abdomen

PURPOSE

Abdominal imaging is frequently performed with breath holds or respiratory triggering to reduce the effects of respiratory motion. Diffusion weighted sequences provide a useful clinical contrast but have prolonged scan times due to low signal-to-noise ratio (SNR), and cannot be completed in a single breath hold. Echo-planar imaging (EPI) is the most commonly used trajectory for diffusion weighted imaging but it is susceptible to off-resonance artifacts. A respiratory resolved, three-dimensional (3D) diffusion prepared sequence that obtains distortionless diffusion weighted images during free-breathing is presented. Techniques to address the myriad of challenges including: 3D shot-to-shot phase correction, respiratory binning, diffusion encoding during free-breathing, and robustness to off-resonance are described.

METHODS

A twice-refocused, M1-nulled diffusion preparation was combined with an RF-spoiled gradient echo readout and respiratory resolved reconstruction to obtain free-breathing diffusion weighted images in the abdomen. Cartesian sampling permits a sampling density that enables 3D shot-to-shot phase navigation and reduction of transient fat artifacts. Theoretical properties of a region-based shot rejection are described. The region-based shot rejection method was evaluated with free-breathing (normal and exaggerated breathing), and respiratory triggering. The proposed sequence was compared in vivo with multishot DW-EPI.

RESULTS

The proposed sequence exhibits no evident distortion in vivo when compared to multishot DW-EPI, robustness to B0 and B1 field inhomogeneities, and robustness to motion from different respiratory patterns.

CONCLUSION

Acquisition of distortionless, diffusion weighted images is feasible during free-breathing with a b-value of 500 s/mm2, scan time of 6 min, and a clinically viable reconstruction time.

Magnetic resonance image reconstruction based on image decomposition constrained by total variation and tight frame

OBJECTIVES

Magnetic resonance imaging (MRI) is a commonly used tool in clinical medicine, but it suffers from the disadvantage of slow imaging speed. To address this, we propose a novel MRI reconstruction algorithm based on image decomposition to realize accurate image reconstruction with undersampled k-space data.

METHODS

In our algorithm, the MR images to be recovered are split into cartoon and texture components utilizing image decomposition theory. Different sparse transform constraints are applied to each component based on their morphological structure characteristics. The total variation transform constraint is used for the smooth cartoon component, while the L0 norm constraint of tight frame redundant transform is used for the oscillatory texture component. Finally, an alternating iterative minimization approach is adopted to complete the reconstruction.

RESULTS

Numerous numerical experiments are conducted on several MR images and the results consistently show that, compared with the existing classical compressed sensing algorithm, our algorithm significantly improves the peak signal-to-noise ratio of the reconstructed images and preserves more image details.

CONCLUSIONS

Our algorithm harnesses the sparse characteristics of different image components to reconstruct MR images accurately with highly undersampled data. It can greatly accelerate MRI speed and be extended to other imaging reconstruction fields.

A fused LASSO operator for fast 3D magnetic particle imaging reconstruction

Objective.Magnetic particle imaging (MPI) is a promising imaging modality that leverages the nonlinear magnetization behavior of superparamagnetic iron oxide nanoparticles to determine their concentration distribution. Previous optimization models with multiple regularization terms have been proposed to achieve high-quality MPI reconstruction, but these models often result in increased computational burden, particularly for dense gridding 3D fields of view. In order to achieve faster reconstruction speeds without compromising reconstruction quality, we have developed a novel fused LASSO operator, total sum-difference (TSD), which effectively captures the sparse and smooth priors of MPI images.Methods.Through an analysis-synthesis equivalence strategy and a constraint smoothing strategy, the TSD regularized model was solved using the fast iterative soft-thresholding algorithm (FISTA). The resulting reconstruction method, TSD-FISTA, boasts low computational complexity and quadratic convergence rate over iterations.Results.Experimental results demonstrated that TSD-FISTA required only 10% and 37% of the time to achieve comparable or superior reconstruction quality compared to commonly used fused LASSO-based alternating direction method of multipliers and Tikhonov-based algebraic reconstruction techniques, respectively.Significance.TSD-FISTA shows promise for enabling real-time 3D MPI reconstruction at high frame rates for large fields of view.

Radial magnetic resonance image reconstruction with a deep unrolled projected fast iterative soft-thresholding network

Radially sampling of magnetic resonance imaging (MRI) is an effective way to accelerate the imaging. How to preserve the image details in reconstruction is always challenging. In this work, a deep unrolled neural network is designed to emulate the iterative sparse image reconstruction process of a projected fast soft-threshold algorithm (pFISTA). The proposed method, an unrolled pFISTA network for Deep Radial MRI (pFISTA-DR), include the preprocessing module to refine coil sensitivity maps and initial reconstructed image, the learnable convolution filters to extract image feature maps, and adaptive threshold to robustly remove image artifacts. Experimental results show that, among the compared methods, pFISTA-DR provides the best reconstruction and achieved the highest PSNR, the highest SSIM and the lowest reconstruction errors.

A Sparse Model-Inspired Deep Thresholding Network for Exponential Signal Reconstruction-Application in Fast Biological Spectroscopy

The nonuniform sampling (NUS) is a powerful approach to enable fast acquisition but requires sophisticated reconstruction algorithms. Faithful reconstruction from partially sampled exponentials is highly expected in general signal processing and many applications. Deep learning (DL) has shown astonishing potential in this field, but many existing problems, such as lack of robustness and explainability, greatly limit its applications. In this work, by combining the merits of the sparse model-based optimization method and data-driven DL, we propose a DL architecture for spectra reconstruction from undersampled data, called MoDern. It follows the iterative reconstruction in solving a sparse model to build the neural network, and we elaborately design a learnable soft-thresholding to adaptively eliminate the spectrum artifacts introduced by undersampling. Extensive results on both synthetic and biological data show that MoDern enables more robust, high-fidelity, and ultrafast reconstruction than the state-of-the-art methods. Remarkably, MoDern has a small number of network parameters and is trained on solely synthetic data while generalizing well to biological data in various scenarios. Furthermore, we extend it to an open-access and easy-to-use cloud computing platform (XCloud-MoDern), contributing a promising strategy for further development of biological applications.

GRIN-toolbox: A versatile and light toolbox for NMR inversion

NMR technique serves as a powerful analytical tool with diverse applications in fields such as chemistry, biology, and material science. However, the effectiveness of NMR heavily relies on data post-processing which is often modeled as regularized inverse problem. Recently, we proposed the Generally Regularized INversion (GRIN) algorithm and demonstrated its effectiveness in NMR data processing. GRIN has been integrated as a friendly graphic user interface-based toolbox which was not detailed in the original paper. In this paper, to make GRIN more practically accessible to NMR practitioners, we focus on introducing the usage of GRIN-Toolbox with processing examples and the corresponding processing graphic interfaces, and the user manual is attached as Supplementary Material. GRIN-Toolbox is versatile and lightweight, where various kinds of data processing tasks can be completed with one click, including but not limited to diffusion-ordered spectroscopy processing, magnetic resonance imaging under-sampling reconstruction, Laplace (diffusion or relaxation) NMR inversion, spectrum denoising, etc. In addition, GRIN-Toolbox could be extended to more applications with user-designed inversion models and freely available at https://github.com/EricLin1993/GRIN.

Pilot Lightweight Denoising Algorithm for Multiple Sclerosis on Spine MRI

Multiple sclerosis (MS) is a severely debilitating disease which requires accurate and timely diagnosis. MRI is the primary diagnostic vehicle; however, it is susceptible to noise and artifact which can limit diagnostic accuracy. A myriad of denoising algorithms have been developed over the years for medical imaging yet the models continue to become more complex. We developed a lightweight algorithm which utilizes the image's inherent noise via dictionary learning to improve image quality without high computational complexity or pretraining through a process known as orthogonal matching pursuit (OMP). Our algorithm is compared to existing traditional denoising algorithms to evaluate performance on real noise that would commonly be encountered in a clinical setting. Fifty patients with a history of MS who received 1.5 T MRI of the spine between the years of 2018 and 2022 were retrospectively identified in accordance with local IRB policies. Native resolution 5 mm sagittal images were selected from T2 weighted sequences for evaluation using various denoising techniques including our proposed OMP denoising algorithm. Peak signal to noise ratio (PSNR) and structural similarity index (SSIM) were measured. While wavelet denoising demonstrated an expected higher PSNR than other models, its SSIM was variable and consistently underperformed its comparators (0.94 ± 0.10). Our pilot OMP denoising algorithm provided superior performance with greater consistency in terms of SSIM (0.99 ± 0.01) with similar PSNR to non-local means filtering (NLM), both of which were superior to other comparators (OMP 37.6 ± 2.2, NLM 38.0 ± 1.8). The superior performance of our OMP denoising algorithm in comparison to traditional models is promising for clinical utility. Given its individualized and lightweight approach, implementation into PACS may be more easily incorporated. It is our hope that this technology will provide improved diagnostic accuracy and workflow optimization for Neurologists and Radiologists, as well as improved patient outcomes.

A new difference of anisotropic and isotropic total variation regularization method for image restoration

Total variation (TV) regularizer has diffusely emerged in image processing. In this paper, we propose a new nonconvex total variation regularization method based on the generalized Fischer-Burmeister function for image restoration. Since our model is nonconvex and nonsmooth, the specific difference of convex algorithms (DCA) are presented, in which the subproblem can be minimized by the alternating direction method of multipliers (ADMM). The algorithms have a low computational complexity in each iteration. Experiment results including image denoising and magnetic resonance imaging demonstrate that the proposed models produce more preferable results compared with state-of-the-art methods.

A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI

Radial sampling is a fast magnetic resonance imaging technique. Further imaging acceleration can be achieved with undersampling but how to reconstruct a clear image with fast algorithm is still challenging. Previous work has shown the advantage of removing undersampling image artifacts using the tight-frame sparse reconstruction model. This model was further solved with a projected fast iterative soft-thresholding algorithm (pFISTA). However, the convergence of this algorithm under radial sampling has not been clearly set up. In this work, the authors derived a theoretical convergence condition for this algorithm. This condition was approximated by estimating the maximal eigenvalue of reconstruction operators through the power iteration. Based on the condition, an optimal step size was further suggested to allow the fastest convergence. Verifications were made on the prospective in vivo data of static brain imaging and dynamic contrast-enhanced liver imaging, demonstrating that the recommended parameter allowed fast convergence in radial MRI.

Undersampled MRI reconstruction based on spectral graph wavelet transform

Compressed sensing magnetic resonance imaging (CS-MRI) has exhibited great potential to accelerate magnetic resonance imaging if an image can be sparsely represented. How to sparsify the image significantly affects the reconstruction quality of images. In this paper, a spectral graph wavelet transform (SGWT) is introduced to sparsely represent magnetic resonance images in iterative image reconstructions. The SGWT is achieved by extending the traditional wavelets transform to the signal defined on the vertices of the weighted graph, i.e. the spectral graph domain. This SGWT uses only the connectivity information encoded in the edge weights, and does not rely on any other attributes of the vertices. Therefore, SGWT can be defined and calculated for any domain where the underlying relations between data locations can be represented by a weighted graph. Furthermore, we present a Chebyshev polynomial approximation algorithm for fast computing this SGWT transform. The l₁ norm regularized CS-MRI reconstruction model is introduced and solved by the projected iterative soft-thresholding algorithm to verify its feasibility. Numerical experiment results demonstrate that our proposed method outperforms several state-of-the-art sparsify transforms in terms of suppressing artifacts and achieving lower reconstruction errors on the tested datasets.

Deep compressed sensing MRI via a gradient-enhanced fusion model

BACKGROUND

Compressed sensing has been employed to accelerate magnetic resonance imaging by sampling fewer measurements. However, conventional iterative optimization-based CS-MRI are time-consuming for iterative calculations and often share poor generalization ability on multicontrast datasets. Most deep-learning-based CS-MRI focus on learning an end-to-end mapping while ignoring some prior knowledge existed in MR images.

PURPOSE

We propose an iterative fusion model to integrate the image and gradient-based priors into reconstruction via convolutional neural network models while maintaining high quality and preserving the detailed information as well.

METHODS

We propose a gradient-enhanced fusion network (GFN) for fast and accurate MRI reconstruction, in which dense blocks with dilated convolution and dense residual learnings are used to capture abundant features with fewer parameters. Meanwhile, decomposed gradient maps containing obvious structural information are introduced into the network to enhance the reconstructed images. Besides this, gradient-based priors along directions X and Y are exploited to learn adaptive tight frames for reconstructing the desired image contrast and edges by respective gradient fusion networks. After that, both image and gradient priors are fused in the proposed optimization model, in which we employ the l₂ -norm to promote the sparsity of gradient priors. The proposed fusion model can effectively help to capture edge structures in the gradient images and to preserve more detailed information of MR images.

RESULTS

Experimental results demonstrate that the proposed method outperforms several CS-MRI methods in terms of peak signal-to-noise (PSNR), the structural similarity index (SSIM), and visualizations on three sampling masks with different rates. Noteworthy, to evaluate the generalization ability, the proposed model conducts cross-center training and testing experiments for all three modalities and shares more stable performance compared than other approaches. In addition, the proposed fusion model is applied to other comparable deep learning methods. The quantitative results show that the reconstruction results of these methods are obviously improved.

CONCLUSIONS

The gradient-based priors reconstructed from GFNs can effectively enhance the edges and details of under-sampled data. The proposed fusion model integrates image and gradient priors using l₂ -norm can effectively improve the generalization ability on multicontrast datasets reconstruction.

A Joint Group Sparsity-based deep learning for multi-contrast MRI reconstruction

Multi-contrast magnetic resonance imaging (MRI) can provide richer diagnosis information. The data acquisition time, however, is increased than single-contrast imaging. To reduce this time, k-space undersampling is an effective way but a smart reconstruction algorithm is required to remove undersampling image artifacts. Traditional algorithms commonly explore the similarity of multi-contrast images through joint sparsity. However, these algorithms are time-consuming due to the iterative process and require adjusting hyperparameters manually. Recently, data-driven deep learning successfully overcome these limitations but the reconstruction error still needs to be further reduced. Here, we propose a Joint Group Sparsity-based Network (JGSN) for multi-contrast MRI reconstruction, which unrolls the iterative process of the joint sparsity algorithm. The designed network includes data consistency modules, learnable sparse transform modules, and joint group sparsity constraint modules. In particular, weights of different contrasts in the transform module are shared to reduce network parameters without sacrificing the quality of reconstruction. The experiments were performed on the retrospective undersampled brain and knee data. Experimental results on in vivo brain data and knee data show that our method consistently outperforms the state-of-the-art methods under different sampling patterns.

Data-driven optimization of sampling patterns for MR brain T1ρ mapping

PURPOSE

The goal of this study was to apply a fast data-driven optimization algorithm, called bias-accelerated subset selection, for MR brain T1ρ mapping to generate optimized sampling patterns (SPs) for compressed sensing reconstruction of brain 3D-T1ρ MRI.

METHODS

Five healthy volunteers were recruited, and fully sampled Cartesian 3D-T1ρ MRIs were obtained. Variable density (VD) and Poisson disc (PD) undersampling was used as the input to SP optimization process. The reconstruction used 3 compressed sensing methods: spatiotemporal finite differences, low-rank plus sparse with spatial finite differences, and low rank. The performance of images and T1ρ maps using PD-SP and VD-SP and their optimized sampling patterns (PD-OSP and VD-OSP) were compared to the fully sampled reference using normalized root mean square error (NRMSE).

RESULTS

The VD-OSP with spatiotemporal finite differences reconstruction (NRMSE = 0.078) and the PD-OSP with spatiotemporal finite differences reconstruction (NRMSE = 0.079) at the highest acceleration factors (AF = 30) showed the largest improvement compared to the respective nonoptimized SPs (VD NRMSE = 0.087 and PD NRMSE = 0.149). Prospective undersampling was tested at AF = 4, with VD-OSP NRMSE = 0.057 versus PD-OSP NRMSE = 0.060, with optimized sampling performing better that input PD or VD sampling. For brain T1ρ mapping, the VD-OSP with low rank reconstruction for AFs <10 and VD-OSP with spatiotemporal finite differences for AFs >10 perform better.

CONCLUSIONS

The study demonstrated that the appropriate use of data-driven optimized sampling and suitable compressed sensing reconstruction technique can be employed to potentially accelerate 3D T1ρ mapping for brain imaging applications.

One-Dimensional Deep Low-Rank and Sparse Network for Accelerated MRI

Deep learning has shown astonishing performance in accelerated magnetic resonance imaging (MRI). Most state-of-the-art deep learning reconstructions adopt the powerful convolutional neural network and perform 2D convolution since many magnetic resonance images or their corresponding k-space are in 2D. In this work, we present a new approach that explores the 1D convolution, making the deep network much easier to be trained and generalized. We further integrate the 1D convolution into the proposed deep network, named as One-dimensional Deep Low-rank and Sparse network (ODLS), which unrolls the iteration procedure of a low-rank and sparse reconstruction model. Extensive results on in vivo knee and brain datasets demonstrate that, the proposed ODLS is very suitable for the case of limited training subjects and provides improved reconstruction performance than state-of-the-art methods both visually and quantitatively. Additionally, ODLS also shows nice robustness to different undersampling scenarios and some mismatches between the training and test data. In summary, our work demonstrates that the 1D deep learning scheme is memory-efficient and robust in fast MRI.

Joint optimization of Cartesian sampling patterns and reconstruction for single-contrast and multi-contrast fast magnetic resonance imaging

BACKGROUND AND OBJECTIVE

Compressed sensing (CS) has gained increased attention in magnetic resonance imaging (MRI), leveraging its efficacy to accelerate image acquisition. Incoherence measurement and non-linear reconstruction are the most crucial guarantees of accurate restoration. However, the loose link between measurement and reconstruction hinders the further improvement of reconstruction quality, i.e., the default sampling pattern is not adaptively tailored to the downstream reconstruction method. When single-contrast reconstruction (SCR) has been upgraded to its multi-contrast reconstruction (MCR) variant, the identical morphologic information as a priori source could be integrated into the reconstruction procedure. How to measure less and reconstruct effectively by using the shareable morphologic information of various contrast images is an attractive topic.

METHODS

An adaptive sampling (AS) based end-to-end framework (ASSCR or ASMCR) is proposed to address this issue, which simultaneously optimizes sampling patterns and reconstruction from under-sampled data in SCR or MCR scenarios. Several deep probabilistic subsampling (DPS) modules are used in AS network to construct a sampling pattern generator. In SCR and MCR, a convolution block and a data consistency layer are iteratively applied in the reconstruction network. Specifically, the learned optimal sampling pattern output from the trained AS sub-net is used for under-sampling. Incoherence measurement for single-contrast images and the combination of sampling patterns for multi-contrast data are guided by the SCR/MCR sub-net.

RESULTS

Experiments were conducted on two single-contrast and one multi-contrast public MRI datasets. Compared with several state-of-the-art reconstruction methods, SCR results show that a learned sampling pattern brings the quality of the reconstructed image closer to the fully-sampled reference. With the addition of different contrast images, under-sampled images with higher acceleration factors could be well recovered.

CONCLUSION

The proposed method could improve the reconstruction quality of under-sampled images by using adaptive sampling patterns and learning-based reconstruction.

Accelerated MRI Reconstruction With Separable and Enhanced Low-Rank Hankel Regularization

Magnetic resonance imaging serves as an essential tool for clinical diagnosis, however, suffers from a long acquisition time. Sparse sampling effectively saves this time but images need to be faithfully reconstructed from undersampled data. Among the existing reconstruction methods, the structured low-rank methods have advantages in robustness to the sampling patterns and lower error. However, the structured low-rank methods use the 2D or higher dimension k-space data to build a huge block Hankel matrix, leading to considerable time and memory consumption. To reduce the size of the Hankel matrix, we proposed to separably construct multiple small Hankel matrices from rows and columns of the k-space and then constrain the low-rankness on these small matrices. This separable model can significantly reduce the computational time but ignores the correlation existed in inter- and intra-row or column, resulting in increased reconstruction error. To improve the reconstructed image without obviously increasing the computation, we further introduced the self-consistency of k-space and virtual coil prior. Besides, the proposed separable model can be extended into other imaging scenarios which hold exponential characteristics in the parameter dimension. The in vivo experimental results demonstrated that the proposed method permits the lowest reconstruction error with a fast reconstruction. The proposed approach requires only 4% of the state-of-the-art STDLR-SPIRiT runtime for parallel imaging reconstruction, and achieves the fastest computational speed in parameter imaging reconstruction.

MRI Reconstruction with Separate Magnitude and Phase Priors Based on Dual-Tree Complex Wavelet Transform

The methods of compressed sensing magnetic resonance imaging (CS-MRI) can be divided into two categories roughly based on the number of target variables. One group devotes to estimating the complex-valued MRI image. And the other calculates the magnitude and phase parts of the complex-valued MRI image, respectively, by enforcing separate penalties on them. We propose a new CS-based method based on dual-tree complex wavelet (DT CWT) sparsity, which is under the frame of the second class of CS-MRI. Owing to the separate regularization frame, this method reduces the impact of the phase jumps (that means the jumps or discontinuities of phase values) on magnitude reconstruction. Moreover, by virtue of the excellent features of DT CWT, such as nonoscillating envelope of coefficients and multidirectional selectivity, the proposed method is capable of capturing more details in the magnitude and phase images. The experimental results show that the proposed method recovers the image contour and edges information well and can eliminate the artifacts in magnitude results caused by phase jumps.

A review on deep learning MRI reconstruction without fully sampled k-space

BACKGROUND

Magnetic resonance imaging (MRI) is an effective auxiliary diagnostic method in clinical medicine, but it has always suffered from the problem of long acquisition time. Compressed sensing and parallel imaging are two common techniques to accelerate MRI reconstruction. Recently, deep learning provides a new direction for MRI, while most of them require a large number of data pairs for training. However, there are many scenarios where fully sampled k-space data cannot be obtained, which will seriously hinder the application of supervised learning. Therefore, deep learning without fully sampled data is indispensable.

MAIN TEXT

In this review, we first introduce the forward model of MRI as a classic inverse problem, and briefly discuss the connection of traditional iterative methods to deep learning. Next, we will explain how to train reconstruction network without fully sampled data from the perspective of obtaining prior information.

CONCLUSION

Although the reviewed methods are used for MRI reconstruction, they can also be extended to other areas where ground-truth is not available. Furthermore, we may anticipate that the combination of traditional methods and deep learning will produce better reconstruction results.

Adjustable shrinkage-thresholding projection algorithm for compressed sensing magnetic resonance imaging

Compressed sensing (CS) aims to reconstruct a high quality images with as little sample data as possible. Magnetic resonance imaging (MRI) plays an important role in medical imaging tools but has a slower data acquisition process. Applying CS to MRI offers significant scan time reductions. In this paper, we proposed a fast and efficient algorithm for compressed sensing magnetic resonance imaging (CS-MRI) reconstruction, denoted as adjustable shrinkage-thresholding projection algorithm (ASTP). It is designed to use adjustable shrinkage rules for l_p-norm based CS-MRI model. This algorithm is established by using an iterative projection and acceleration scheme. In each iteration, the proposed adjustable shrinkage-thresholding rules are employed to ensure global convergence to accurate solution. Furthermore, the parameter p can be selected flexibly according to different practical application situations, and the orthogonal projection operation is used to reduce the dimension of the solution space to accelerate the convergence speed and improve the reconstruction quality. Numerical experiments show that proposed ASTP algorithm provides a higher accuracy, convergence speed and ability to suppress noise compared with some certain state-of-the-art algorithms.

Accelerated image reconstruction with separable Hankel regularization in parallel MRI

Magnetic resonance imaging has been widely adopted in clinical diagnose, however, it suffers from relatively long data acquisition time. Sparse sampling with reconstruction can speed up the data acquisition duration. As the state-of-the-art magnetic resonance imaging methods, the structured low rank reconstruction approaches embrace the advantage of holding low reconstruction errors and permit flexible undersampling patterns. However, this type of method demands intensive computations and high memory consumptions, thereby resulting in a lengthy reconstruction time. In this work, we proposed a separable Hankel low rank reconstruction method to explore the low rankness of each row and each column. Furthermore, we utilized the self-consistence and conjugate symmetry property of k-space data. The experimental results demonstrated that the proposed method outperforms the state-of-the-art approaches in terms of lower reconstruction errors and better detail preservation. Besides, the proposed method requires much less computation and memory consumption.Clinical Relevance- Parallel imaging, image reconstruction, Hankel low-rank.

XCloud-pFISTA: A Medical Intelligence Cloud for Accelerated MRI

Machine learning and artificial intelligence have shown remarkable performance in accelerated magnetic resonance imaging (MRI). Cloud computing technologies have great advantages in building an easily accessible platform to deploy advanced algorithms. In this work, we develop an open-access, easy-to-use and high-performance medical intelligence cloud computing platform (XCloud-pFISTA) to reconstruct MRI images from undersampled k-space data. Two state-of-the-art approaches of the Projected Fast Iterative Soft-Thresholding Algorithm (pFISTA) family have been successfully implemented on the cloud. This work can be considered as a good example of cloud-based medical image reconstruction and may benefit the future development of integrated reconstruction and online diagnosis system.

Optimizing multicontrast MRI reconstruction with shareable feature aggregation and selection

This paper proposes a new method for optimizing feature sharing in deep neural network-based, rapid, multicontrast magnetic resonance imaging (MC-MRI). Using the shareable information of MC images for accelerated MC-MRI reconstruction, current algorithms stack the MC images or features without optimizing the sharing protocols, leading to suboptimal reconstruction results. In this paper, we propose a novel feature aggregation and selection scheme in a deep neural network to better leverage the MC features and improve the reconstruction results. First, we propose to extract and use the shareable information by mapping the MC images into multiresolution feature maps with multilevel layers of the neural network. In this way, the extracted features capture complementary image properties, including local patterns from the shallow layers and semantic information from the deep layers. Then, an explicit selection module is designed to compile the extracted features optimally. That is, larger weights are learned to incorporate the constructive, shareable features; and smaller weights are assigned to the unshareable information. We conduct comparative studies on publicly available T2-weighted and T2-weighted fluid attenuated inversion recovery brain images, and the results show that the proposed network consistently outperforms existing algorithms. In addition, the proposed method can recover the images with high fidelity under 16 times acceleration. The ablation studies are conducted to evaluate the effectiveness of the proposed feature aggregation and selection mechanism. The results and the visualization of the weighted features show that the proposed method does effectively improve the usage of the useful features and suppress useless information, leading to overall enhanced reconstruction results. Additionally, the selection module can zero-out repeated and redundant features and improve network efficiency.

Deep Learning-Based Denoised MRI Images for Correlation Analysis between Lumbar Facet Joint and Lumbar Disc Herniation in Spine Surgery

This work aimed to explore the relationship between spine surgery lumbar facet joint (LFJ) and lumbar disc herniation (LDH) via compressed sensing algorithm-based MRI images to analyze the clinical symptoms of patients with residual neurological symptoms after LDH. Under weighted BM3D denoising, Epigraph method was introduced to establish the novel CSMRI reconstruction algorithm (BEMRI). 127 patients with LDH were taken as the research objects. The BEMRI algorithm was compared with others regarding peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM). Patients' bilateral LFJ angles were compared. The relationships between LFJ angles, lumbar disc degeneration, and LFJ degeneration were analyzed. It turned out that the PSNR and SSIM of BEMRI algorithm were evidently superior to those of other algorithms. The proportion of patients with grade IV degeneration was at most 31.76%. Lumbar disc grading was positively correlated with change grading of LFJ degeneration (P < 0.001). LFJ asymmetry was positively correlated with LFJ degeneration grade and LDH (P < 0.001). Incidence of residual neurological symptoms in patients aged 61–70 years was as high as 63.77%. The proportion of patients with severe urinary excretion disorders was 71.96%. Therefore, the BEMRI algorithm improved the quality of MRI images. Degeneration of LDH was positively correlated with degeneration of LFJ. Asymmetry of LFJ was notably positively correlated with the degeneration of LFJ and LDH. Patients aged 61–70 years had a high incidence of residual neurological symptoms after surgery, most of which were manifested as urinary excretion disorders.

Spatiotemporal Flexible Sparse Reconstruction for Rapid Dynamic Contrast-enhanced MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a tissue perfusion imaging technique. Some versatile free-breathing DCE-MRI techniques combining compressed sensing (CS) and parallel imaging with golden-angle radial sampling have been developed to improve motion robustness with high spatial and temporal resolution. These methods have demonstrated good diagnostic performance in clinical setting, but the reconstruction quality will degrade at high acceleration rates and overall reconstruction time remains long. In this paper, we proposed a new parallel CS reconstruction model for DCE-MRI that enforces flexible weighted sparse constraint along both spatial and temporal dimensions. Weights were introduced to flexibly adjust the importance of time and space sparsity, and we derived a fast-thresholding algorithm which was proven to be simple and efficient for solving the proposed reconstruction model. Results on both the brain tumor DCE and liver DCE show that, at relatively high acceleration factor of fast sampling, lowest reconstruction error and highest image structural similarity are obtained by the proposed method. Besides, the proposed method achieves faster reconstruction for liver datasets and better physiological measures are also obtained on tumor images.

Blind Deconvolution Based on Compressed Sensing with bi-l0-l2-norm Regularization in Light Microscopy Image

Blind deconvolution of light microscopy images could improve the ability of distinguishing cell-level substances. In this study, we investigated the blind deconvolution framework for a light microscope image, which combines the benefits of bi-l₀-l₂-norm regularization with compressed sensing and conjugated gradient algorithms. Several existing regularization approaches were limited by staircase artifacts (or cartooned artifacts) and noise amplification. Thus, we implemented our strategy to overcome these problems using the bi-l₀-l₂-norm regularization proposed. It was investigated through simulations and experiments using optical microscopy images including the background noise. The sharpness was improved through the successful image restoration while minimizing the noise amplification. In addition, quantitative factors of the restored images, including the intensity profile, root-mean-square error (RMSE), edge preservation index (EPI), structural similarity index measure (SSIM), and normalized noise power spectrum, were improved compared to those of existing or comparative images. In particular, the results of using the proposed method showed RMSE, EPI, and SSIM values of approximately 0.12, 0.81, and 0.88 when compared with the reference. In addition, RMSE, EPI, and SSIM values in the restored image were proven to be improved by about 5.97, 1.26, and 1.61 times compared with the degraded image. Consequently, the proposed method is expected to be effective for image restoration and to reduce the cost of a high-performance light microscope.

A guaranteed convergence analysis for the projected fast iterative soft-thresholding algorithm in parallel MRI

Sparse sampling and parallel imaging techniques are two effective approaches to alleviate the lengthy magnetic resonance imaging (MRI) data acquisition problem. Promising data recoveries can be obtained from a few MRI samples with the help of sparse reconstruction models. To solve the optimization models, proper algorithms are indispensable. The pFISTA, a simple and efficient algorithm, has been successfully extended to parallel imaging. However, its convergence criterion is still an open question. Besides, the existing convergence criterion of single-coil pFISTA cannot be applied to the parallel imaging pFISTA, which, therefore, imposes confusions and difficulties on users about determining the only parameter - step size. In this work, we provide the guaranteed convergence analysis of the parallel imaging version pFISTA to solve the two well-known parallel imaging reconstruction models, SENSE and SPIRiT. Along with the convergence analysis, we provide recommended step size values for SENSE and SPIRiT reconstructions to obtain fast and promising reconstructions. Experiments on in vivo brain images demonstrate the validity of the convergence criterion.

On the regularization of feature fusion and mapping for fast MR multi-contrast imaging via iterative networks

Multi-contrast (MC) Magnetic Resonance Imaging (MRI) of the same patient usually requires long scanning times, despite the images sharing redundant information. In this work, we propose a new iterative network that utilizes the sharable information among MC images for MRI acceleration. The proposed network has reinforced data fidelity control and anatomy guidance through an iterative optimization procedure of Gradient Descent, leading to reduced uncertainties and improved reconstruction results. Through a convolutional network, the new method incorporates a learnable regularization unit that is capable of extracting, fusing, and mapping shareable information among different contrasts. Specifically, a dilated inception block is proposed to promote multi-scale feature extractions and increase the receptive field diversity for contextual information incorporation. Lastly, an optimal MC information feeding protocol is built through the design of a complementary feature extractor block. Comprehensive experiments demonstrated the superiority of the proposed network, both qualitatively and quantitatively.

pFISTA-SENSE-ResNet for parallel MRI reconstruction

Magnetic resonance imaging has been widely applied in clinical diagnosis. However, it is limited by its long data acquisition time. Although the imaging can be accelerated by sparse sampling and parallel imaging, achieving promising reconstructed images with a fast computation speed remains a challenge. Recently, deep learning methods have attracted a lot of attention for encouraging reconstruction results, but they are lack of proper interpretability for neural networks. In this work, in order to enable high-quality image reconstruction for the parallel magnetic resonance imaging, we design the network structure from the perspective of sparse iterative reconstruction and enhance it with the residual structure. Experimental results on a public knee dataset indicate that, as compared with the state-of-the-art deep learning-based and optimization-based methods, the proposed network achieves lower error in reconstruction and is more robust under different samplings.

Nonbifurcating Phylogenetic Tree Inference via the Adaptive LASSO

Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including sampled ancestors in which we sequence a genotype along with its direct descendants, and polytomies in which multiple descendants arise simultaneously. These features are apparent after identifying zero-length branches in the tree. However, current maximum-likelihood based approaches are not capable of revealing such zero-length branches. In this paper, we find these zero-length branches by introducing adaptive-LASSO-type regularization estimators for the branch lengths of phylogenetic trees, deriving their properties, and showing regularization to be a practically useful approach for phylogenetics.

MRI Reconstruction Using Markov Random Field and Total Variation as Composite Prior

Reconstruction of magnetic resonance images (MRI) benefits from incorporating a priori knowledge about statistical dependencies among the representation coefficients. Recent results demonstrate that modeling intraband dependencies with Markov Random Field (MRF) models enable superior reconstructions compared to inter-scale models. In this paper, we develop a novel reconstruction method, which includes a composite prior based on an MRF model and Total Variation (TV). We use an anisotropic MRF model and propose an original data-driven method for the adaptive estimation of its parameters. From a Bayesian perspective, we define a new position-dependent type of regularization and derive a compact reconstruction algorithm with a novel soft-thresholding rule. Experimental results show the effectiveness of this method compared to the state of the art in the field.

Compressed MRI reconstruction exploiting a rotation-invariant total variation discretization

Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration.

Coupled Dictionary Learning for Multi-Contrast MRI Reconstruction

Magnetic resonance (MR) imaging tasks often involve multiple contrasts, such as T1-weighted, T2-weighted and fluid-attenuated inversion recovery (FLAIR) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities in either structure level or gray level. In this paper, we propose a coupled dictionary learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage the dependency correlation between different contrasts for guided or joint reconstruction from their under-sampled k -space data. Our approach iterates between three stages: coupled dictionary learning, coupled sparse denoising, and enforcing k -space consistency. The first stage learns a set of dictionaries that not only are adaptive to the contrasts, but also capture correlations among multiple contrasts in a sparse transform domain. By capitalizing on the learned dictionaries, the second stage performs coupled sparse coding to remove the aliasing and noise in the corrupted contrasts. The third stage enforces consistency between the denoised contrasts and the measurements in the k -space domain. Numerical experiments, consisting of retrospective under-sampling of various MRI contrasts with a variety of sampling schemes, demonstrate that CDLMRI is capable of capturing structural dependencies between different contrasts. The learned priors indicate notable advantages in multi-contrast MR imaging and promising applications in quantitative MR imaging such as MR fingerprinting.

Plug-and-Play Methods for Magnetic Resonance Imaging: Using Denoisers for Image Recovery

Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then we review several PnP methods, where the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from the equilibrium perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

CS-MRI reconstruction based on analysis dictionary learning and manifold structure regularization

Compressed sensing (CS) significantly accelerates magnetic resonance imaging (MRI) by allowing the exact reconstruction of image from highly undersampling k-space data. In this process, the high sparsity obtained by the learned dictionary and exploitation of correlation among patches are essential to the reconstructed image quality. In this paper, by a use of these two aspects, we propose a novel CS-MRI model based on analysis dictionary learning and manifold structure regularization (ADMS). Furthermore, a proper tight frame constraint is used to obtain an effective overcomplete analysis dictionary with a high sparsifying capacity. The constructed manifold structure regularization nonuniformly enforces the correlation of each group formed by similar patches, which is more consistent with the diverse nonlocal similarity in realistic images. The proposed model is efficiently solved by the alternating direction method of multipliers (ADMM), in which the fast algorithm for each sub-problem is separately developed. The experimental results demonstrate that main components in the proposed method contribute to the final reconstruction performance and the effectiveness of the proposed model.

A cosparse analysis model with combined redundant systems for MRI reconstruction

PURPOSE

Magnetic resonance imaging (MRI) is widely used due to its noninvasive and nonionizing properties. However, MRI requires a long scanning time. In this paper, our goal is to reconstruct a high-quality MR image from its sampled k-space data to accelerate the data acquisition in MRI.

METHODS

We propose a cosparse analysis model with combined redundant systems to fully exploit the sparsity of MR images. Two fixed redundant systems are used to characterize different structures, namely, the wavelet tight frame and Gabor frame. An alternating iteration scheme is used for reconstruction with simple implementation and good performance.

RESULTS

The proposed method is tested on two MR images under three sampling patterns with sampling ratios ranging from 10% to 60%. The results show that the proposed method outperforms other state-of-the-art MRI reconstruction methods in terms of both subjective visual quality and objective quantitative measurement. For instance, for brain images under random sampling with a ratio of 10%, compared to the other three methods, the proposed method improves the peak signal-to-noise ratio (PSNR) by more than 9 dB.

CONCLUSIONS

To better characterize different sparsities of different structures of MRI, a cosparse analysis model combining the wavelet tight frame and Gabor frame is proposed. A partial ℓ 2 norm regularization is leveraged to obtain the optimal solution in a lower dimension. Compared to other state-of-the-art MRI reconstruction methods, the proposed method improves the reconstruction quality of MRI, especially highly undersampled MRI.

Compressed sensing MRI based on image decomposition model and group sparsity

The image representation plays an important role in compressed sensing magnetic resonance imaging (CSMRI). However, how to adaptive sparsely represent images is a challenge for accurately reconstructing magnetic resonance (MR) images from highly undersampled data with noise. In order to further improve the reconstruction quality of the MR image, this paper first proposes tight frame-based group sparsity (TFGS) regularization that can capture the structure information of images appropriately, then TFGS regularization is employed to the image cartoon-texture decomposition model to construct CSMRI algorithm, termed cartoon-texture decomposition CSMRI algorithm (CD-MRI). CD-MRI effectively integrates the total variation and TFGS regularization into the image cartoon-texture decomposition framework, and utilizes the sparse priors of image cartoon and texture components to reconstruct MR images. Virtually, CD-MRI exploits the global sparse representations of image cartoon components by the total variation regularization, and explores group sparse representations of image texture components via the adaptive tight frame learning technique and group sparsity regularization. The alternating iterative method combining with the majorization-minimization algorithm is applied to solve the formulated optimization problem. Finally, simulation experiments demonstrate that the proposed algorithm can achieve high-quality MR image reconstruction from undersampled K-space data, and can remove noise in different sampling schemes. Compared to the previous CSMRI algorithms, the proposed approach can lead to better image reconstruction performance and better robustness to noise.

Salt and Pepper Noise Removal with Multi-Class Dictionary Learning and L0 Norm Regularizations

Images may be corrupted by salt and pepper impulse noise during image acquisitions or transmissions. Although promising denoising performances have been recently obtained with sparse representations, how to restore high-quality images remains challenging and open. In this work, image sparsity is enhanced with a fast multiclass dictionary learning, and then both the sparsity regularization and robust data fidelity are formulated as minimizations of L0-L0 norms for salt and pepper impulse noise removal. Additionally, a numerical algorithm of modified alternating direction minimization is derived to solve the proposed denoising model. Experimental results demonstrate that the proposed method outperforms the compared state-of-the-art ones on preserving image details and achieving higher objective evaluation criteria.

A Regularized Weighted Smoothed L₀ Norm Minimization Method for Underdetermined Blind Source Separation

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed L 0 -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L p -RLSand achieves better performances when it is used for UBSS.