Augmented Lagrangian with variable splitting for faster non-Cartesian L1-SPIRiT MR image reconstruction

A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI

Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers to describe the images of interest. The reconstruction process is equivalent to solving a composite optimization problem. Accelerated proximal methods (APMs) are very popular approaches for such problems. This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM). To make CQNPM more practical, we propose efficient methods to solve the related WPM. Numerical experiments on reconstructing non-Cartesian MRI data demonstrate the effectiveness and efficiency of CQNPM.

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.

DEep learning-based rapid Spiral Image REconstruction (DESIRE) for high-resolution spiral first-pass myocardial perfusion imaging

The objective of the current study was to develop and evaluate a DEep learning-based rapid Spiral Image REconstruction (DESIRE) technique for high-resolution spiral first-pass myocardial perfusion imaging with whole-heart coverage, to provide fast and accurate image reconstruction for both single-slice (SS) and simultaneous multislice (SMS) acquisitions. Three-dimensional U-Net-based image enhancement architectures were evaluated for high-resolution spiral perfusion imaging at 3 T. The SS and SMS MB = 2 networks were trained on SS perfusion images from 156 slices from 20 subjects. Structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), and normalized root mean square error (NRMSE) were assessed, and prospective images were blindly graded by two experienced cardiologists (5: excellent; 1: poor). Excellent performance was demonstrated for the proposed technique. For SS, SSIM, PSNR, and NRMSE were 0.977 [0.972, 0.982], 42.113 [40.174, 43.493] dB, and 0.102 [0.080, 0.125], respectively, for the best network. For SMS MB = 2 retrospective data, SSIM, PSNR, and NRMSE were 0.961 [0.950, 0.969], 40.834 [39.619, 42.004] dB, and 0.107 [0.086, 0.133], respectively, for the best network. The image quality scores were 4.5 [4.1, 4.8], 4.5 [4.3, 4.6], 3.5 [3.3, 4], and 3.5 [3.3, 3.8] for SS DESIRE, SS L1-SPIRiT, MB = 2 DESIRE, and MB = 2 SMS-slice-L1-SPIRiT, respectively, showing no statistically significant difference (p = 1 and p = 1 for SS and SMS, respectively) between L1-SPIRiT and the proposed DESIRE technique. The network inference time was ~100 ms per dynamic perfusion series with DESIRE, while the reconstruction time of L1-SPIRiT with GPU acceleration was ~ 30 min. It was concluded that DESIRE enabled fast and high-quality image reconstruction for both SS and SMS MB = 2 whole-heart high-resolution spiral perfusion imaging.

Systematic Analysis and Review of Magnetic Resonance Imaging (MRI) Reconstruction Techniques

BACKGROUND

Magnetic Resonance Imaging (MRI) plays an important role in the field of medical diagnostic imaging as it poses non-invasive acquisition and high soft-tissue contrast. However, a huge time is needed for the MRI scanning process that results in motion artifacts, degrades image quality, misinterprets the data, and may cause discomfort to the patient. Thus, the main goal of MRI research is to accelerate data acquisition processing without affecting the quality of the image.

INTRODUCTION

This paper presents a survey based on distinct conventional MRI reconstruction methodologies. In addition, a novel MRI reconstruction strategy is proposed based on weighted Compressive Sensing (CS), Penalty-aided minimization function, and Meta-heuristic optimization technique.

METHODS

An illustrative analysis is done concerning adapted methods, datasets used, execution tools, performance measures, and values of evaluation metrics. Moreover, the issues of existing methods and the research gaps considering conventional MRI reconstruction schemes are elaborated to obtain improved contribution for devising significant MRI reconstruction techniques.

RESULTS

The proposed method will reduce conventional aliasing artifact problems, may attain lower Mean Square Error (MSE), higher Peak Signal-to-Noise Ratio (PSNR), and Structural SIMilarity (SSIM) index.

CONCLUSION

The issues of existing methods and the research gaps considering conventional MRI reconstruction schemes are elaborated to devising an improved significant MRI reconstruction technique.

Accelerated radial echo-planar spectroscopic imaging using golden angle view-ordering and compressed-sensing reconstruction with total variation regularization

PURPOSE

To implement a novel, accelerated, 2D radial echo-planar spectroscopic imaging (REPSI) sequence using undersampled radial k-space trajectories and compressed-sensing reconstruction, and to compare results with those from an undersampled Cartesian spectroscopic sequence.

METHODS

The REPSI sequence was implemented using golden-angle view-ordering on a 3T MRI scanner. Radial and Cartesian echo-planar spectroscopic imaging (EPSI) data were acquired at six acceleration factors, each with time-equivalent scan durations, and reconstructed using compressed sensing with total variation regularization. Results from prospectively and retrospectively undersampled phantom and in vivo brain data were compared over estimated concentrations and Cramer-Rao lower-bound values, normalized RMS errors of reconstructed metabolite maps, and percent absolute differences between fully sampled and reconstructed spectroscopic images.

RESULTS

The REPSI method with compressed sensing is able to tolerate greater reductions in scan time compared with EPSI. The reconstruction and quantitation metrics (i.e., spectral normalized RMS error maps, metabolite map normalized RMS error values [e.g., for total N-acetyl asparate, REPSI = 9.4% vs EPSI = 16.3%; acceleration factor = 2.5], percent absolute difference maps, and concentration and Cramer-Rao lower-bound estimates) showed that accelerated REPSI can reduce the scan time by a factor of 2.5 while retaining image and quantitation quality.

CONCLUSION

Accelerated MRSI using undersampled radial echo-planar acquisitions provides greater reconstruction accuracy and more reliable quantitation for a range of acceleration factors compared with time-equivalent compressed-sensing reconstructions of undersampled Cartesian EPSI. Compared to the Cartesian approach, radial undersampling with compressed sensing could help reduce 2D spectroscopic imaging acquisition time, and offers a better trade-off between imaging speed and quality.

High spatial resolution spiral first-pass myocardial perfusion imaging with whole-heart coverage at 3 T

PURPOSE

To develop and evaluate a high spatial resolution (1.25 × 1.25 mm² ) spiral first-pass myocardial perfusion imaging technique with whole-heart coverage at 3T, to better assess transmural differences in perfusion between the endocardium and epicardium, to quantify the myocardial ischemic burden, and to improve the detection of obstructive coronary artery disease.

METHODS

Whole-heart high-resolution spiral perfusion pulse sequences and corresponding motion-compensated reconstruction techniques for both interleaved single-slice (SS) and simultaneous multi-slice (SMS) acquisition with or without outer-volume suppression (OVS) were developed. The proposed techniques were evaluated in 34 healthy volunteers and 8 patients (55 data sets). SS and SMS images were reconstructed using motion-compensated L1-SPIRiT and SMS-Slice-L1-SPIRiT, respectively. Images were blindly graded by 2 experienced cardiologists on a 5-point scale (5, excellent; 1, poor).

RESULTS

High-quality perfusion imaging was achieved for both SS and SMS acquisitions with or without OVS. The SS technique without OVS had the highest scores (4.5 [4, 5]), which were greater than scores for SS with OVS (3.5 [3.25, 3.75], P < .05), MB = 2 without OVS (3.75 [3.25, 4], P < .05), and MB = 2 with OVS (3.75 [2.75, 4], P < .05), but significantly higher than those for MB = 3 without OVS (4 [4, 4], P = .95). SMS image quality was improved using SMS-Slice-L1-SPIRiT as compared to SMS-L1-SPIRiT (P < .05 for both reviewers).

CONCLUSION

We demonstrated the successful implementation of whole-heart spiral perfusion imaging with high resolution at 3T. Good image quality was achieved, and the SS without OVS showed the best image quality. Evaluation in patients with expected ischemic heart disease is warranted.

Accelerating Non-Cartesian MRI Reconstruction Convergence Using k-Space Preconditioning

We propose a k-space preconditioning formulation for accelerating the convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from non-uniformly sampled k-space data. Existing methods either use sampling density compensations which sacrifice reconstruction accuracy, or circulant preconditioners which increase per-iteration computation. Our approach overcomes both shortcomings. Concretely, we show that viewing the reconstruction problem in the dual formulation allows us to precondition in k-space using density-compensation-like operations. Using the primal-dual hybrid gradient method, the proposed preconditioning method does not have inner loops and are competitive in accelerating convergence compared to existing algorithms. We derive l2 -optimized preconditioners, and demonstrate through experiments that the proposed method converges in about ten iterations in practice.

Minimal Linear Networks for Magnetic Resonance Image Reconstruction

Modern sequences for Magnetic Resonance Imaging (MRI) trade off scan time with computational challenges, resulting in ill-posed inverse problems and the requirement to account for more elaborated signal models. Various deep learning techniques have shown potential for image reconstruction from reduced data, outperforming compressed sensing, dictionary learning and other advanced techniques based on regularization, by characterization of the image manifold. In this work we suggest a framework for reducing a “neural” network to the bare minimum required by the MR physics, reducing the network depth and removing all non-linearities. The networks performed well both on benchmark simulated data and on arterial spin labeling perfusion imaging, showing clear images while preserving sensitivity to the minute signal changes. The results indicate that the deep learning framework plays a major role in MR image reconstruction, and suggest a concrete approach for probing into the contribution of additional elements.

Undersampled MR image reconstruction using an enhanced recursive residual network

When using aggressive undersampling, it is difficult to recover the high quality image with reliably fine features. In this paper, we propose an enhanced recursive residual network (ERRN) that improves the basic recursive residual network with a high-frequency feature guidance, an error-correction unit and dense connections. The feature guidance is designed to predict the underlying anatomy based on image a priori learned from the label data, playing a complementary role to the residual learning. The ERRN is adapted for two important applications: compressed sensing (CS) MRI and super resolution (SR) MRI, while an application-specific error-correction unit is added into the framework, i.e. data consistency for CS-MRI and back projection for SR-MRI due to their different sampling schemes. Our proposed network was evaluated using a real-valued brain dataset, a complex-valued knee dataset, pathological brain data and in vivo rat brain data with different undersampling masks and rates. Experimental results demonstrated that ERRN presented superior reconstructions at all cases with distinctly restored structural features and highest image quality metrics compared to both the state-of-the-art convolutional neural networks and the conventional optimization-based methods, particularly for the undersampling rate over 5-fold. Thus, an excellent framework design can endow the network with a flexible architecture, fewer parameters, outstanding performances for various undersampling schemes, and reduced overfitting in generalization, which will facilitate real-time reconstruction on MRI scanners.

Real-Time Filtering with Sparse Variations for Head Motion in Magnetic Resonance Imaging

Estimating a time-varying signal, such as head motion from magnetic resonance imaging data, becomes particularly challenging in the face of other temporal dynamics such as functional activation. This paper describes a new Kalman filter-like framework that includes a sparse residual term in the measurement model. This additional term allows the extended Kalman filter to generate real-time motion estimates suitable for prospective motion correction when such dynamics occur. An iterative augmented Lagrangian algorithm similar to the alterating direction method of multipliers implements the update step for this Kalman filter. This paper evaluates the accuracy and convergence rate of this iterative method for small and large motion in terms of its sensitivity to parameter selection. The included experiment on a simulated functional magnetic resonance imaging acquisition demonstrates that the resulting method improves the maximum Youden's J index of the time series analysis by 2-3% versus retrospective motion correction, while the sensitivity index increases from 4.3 to 5.4 when combining prospective and retrospective correction.

Eigenvector-based SPIRiT Parallel MR Imaging Reconstruction based on ℓp pseudo-norm Joint Total Variation

Parallel Magnetic Resonance (MR) imaging is a well-established acceleration technique based on the spatial sensitivities of array receivers. Eigenvector-based SPIRiT (ESPIRiT) is a new parallel MR imaging reconstruction method that combines the advantages of the SENSE and GRAPPA methods. It estimates multiple sets of the sensitivity maps from the calibration matrix that is constructed from the auto-calibration data. To improve the quality of the reconstructed image, we introduced the Total Variation (TV) and ℓ_p pseudo-norm Joint TV (ℓ_pJTV) regularization terms to the ESPIRiT model for parallel MR imaging reconstruction, which were solved by using the Operator Splitting (OS) method. The resulting denoising problems with the TV and ℓ_pJTV regularization terms were solved by exploiting the Majorization Minimization method. Simulation experiments on two in vivo data sets demonstrated that the proposed OS algorithm with the TV regularization term (OSTV) and OS algorithm with the ℓ_pJTV regularization term (OSℓ_pJTV) outperformed the conventional method with the ℓ₁ regularization term in terms of SNR and NRMSE. And the OSℓ_pJTV algorithm was slightly superior to the OSTV algorithm with the TV regularization term.

Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories

PURPOSE

Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories.

THEORY

PI and CS reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved inℓ 1 andℓ 2 -norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques.

METHODS

In this article we construct such a preconditioner by approximating the system matrix of the linear system, which comprises the data fidelity and includes total variation and wavelet regularization, by a matrix that is block circulant with circulant blocks. Due to this structure, the preconditioner can be constructed quickly and its inverse can be evaluated fast using only two fast Fourier transformations. We test the performance of the preconditioner for the conjugate gradient method as the linear solver, integrated into the well-established Split Bregman algorithm.

RESULTS

The designed circulant preconditioner reduces the number of iterations required in the conjugate gradient method by almost a factor of 5. The speed up results in a total acceleration factor of approximately 2.5 for the entire reconstruction algorithm when implemented in MATLAB, while the initialization time of the preconditioner is negligible.

CONCLUSION

The proposed preconditioner reduces the reconstruction time for PI and CS in a Split Bregman implementation without compromising reconstruction stability and can easily handle large systems since it is Fourier-based, allowing for efficient computations.

Content-aware compressive magnetic resonance image reconstruction

This paper describes an adaptive approach to regularizing model-based reconstructions in magnetic resonance imaging to account for local structure or image content. In conjunction with common models like wavelet and total variation sparsity, this content-aware regularization avoids oversmoothing or compromising image features while suppressing noise and incoherent aliasing from accelerated imaging. To evaluate this regularization approach, the experiments reconstruct images from single- and multi-channel, Cartesian and non-Cartesian, brain and cardiac data. These reconstructions combine common analysis-form regularizers and autocalibrating parallel imaging (when applicable). In most cases, the results show widespread improvement in structural similarity and peak-signal-to-error ratio relative to the fully sampled images. These results suggest that this content-aware regularization can preserve local image structures such as edges while providing denoising power superior to sparsity-promoting or sparsity-reweighted regularization.

Image reconstruction by domain-transform manifold learning

Image reconstruction is essential for imaging applications across the physical and life sciences, including optical and radar systems, magnetic resonance imaging, X-ray computed tomography, positron emission tomography, ultrasound imaging and radio astronomy. During image acquisition, the sensor encodes an intermediate representation of an object in the sensor domain, which is subsequently reconstructed into an image by an inversion of the encoding function. Image reconstruction is challenging because analytic knowledge of the exact inverse transform may not exist a priori, especially in the presence of sensor non-idealities and noise. Thus, the standard reconstruction approach involves approximating the inverse function with multiple ad hoc stages in a signal processing chain, the composition of which depends on the details of each acquisition strategy, and often requires expert parameter tuning to optimize reconstruction performance. Here we present a unified framework for image reconstruction-automated transform by manifold approximation (AUTOMAP)-which recasts image reconstruction as a data-driven supervised learning task that allows a mapping between the sensor and the image domain to emerge from an appropriate corpus of training data. We implement AUTOMAP with a deep neural network and exhibit its flexibility in learning reconstruction transforms for various magnetic resonance imaging acquisition strategies, using the same network architecture and hyperparameters. We further demonstrate that manifold learning during training results in sparse representations of domain transforms along low-dimensional data manifolds, and observe superior immunity to noise and a reduction in reconstruction artefacts compared with conventional handcrafted reconstruction methods. In addition to improving the reconstruction performance of existing acquisition methodologies, we anticipate that AUTOMAP and other learned reconstruction approaches will accelerate the development of new acquisition strategies across imaging modalities.

Learning Joint-Sparse Codes for Calibration-Free Parallel MR Imaging

The integration of compressed sensing and parallel imaging (CS-PI) has shown an increased popularity in recent years to accelerate magnetic resonance (MR) imaging. Among them, calibration-free techniques have presented encouraging performances due to its capability in robustly handling the sensitivity information. Unfortunately, existing calibration-free methods have only explored joint-sparsity with direct analysis transform projections. To further exploit joint-sparsity and improve reconstruction accuracy, this paper proposes to Learn joINt-sparse coDes for caliBration-free parallEl mR imaGing (LINDBERG) by modeling the parallel MR imaging problem as an - - minimization objective with an norm constraining data fidelity, Frobenius norm enforcing sparse representation error and the mixed norm triggering joint sparsity across multichannels. A corresponding algorithm has been developed to alternatively update the sparse representation, sensitivity encoded images and K-space data. Then, the final image is produced as the square root of sum of squares of all channel images. Experimental results on both physical phantom and in vivo data sets show that the proposed method is comparable and even superior to state-of-the-art CS-PI reconstruction approaches. Specifically, LINDBERG has presented strong capability in suppressing noise and artifacts while reconstructing MR images from highly undersampled multichannel measurements.

Efficient operator splitting algorithm for joint sparsity-regularized SPIRiT-based parallel MR imaging reconstruction

Self-consistent parallel imaging (SPIRiT) is an auto-calibrating model for the reconstruction of parallel magnetic resonance imaging, which can be formulated as a regularized SPIRiT problem. The Projection Over Convex Sets (POCS) method was used to solve the formulated regularized SPIRiT problem. However, the quality of the reconstructed image still needs to be improved. Though methods such as NonLinear Conjugate Gradients (NLCG) can achieve higher spatial resolution, these methods always demand very complex computation and converge slowly. In this paper, we propose a new algorithm to solve the formulated Cartesian SPIRiT problem with the JTV and JL1 regularization terms. The proposed algorithm uses the operator splitting (OS) technique to decompose the problem into a gradient problem and a denoising problem with two regularization terms, which is solved by our proposed split Bregman based denoising algorithm, and adopts the Barzilai and Borwein method to update step size. Simulation experiments on two in vivo data sets demonstrate that the proposed algorithm is 1.3 times faster than ADMM for datasets with 8 channels. Especially, our proposal is 2 times faster than ADMM for the dataset with 32 channels.

Rapid compressed sensing reconstruction of 3D non-Cartesian MRI

PURPOSE

Conventional non-Cartesian compressed sensing requires multiple nonuniform Fourier transforms every iteration, which is computationally expensive. Accordingly, time-consuming reconstructions have slowed the adoption of undersampled 3D non-Cartesian acquisitions into clinical protocols. In this work we investigate several approaches to minimize reconstruction times without sacrificing accuracy.

METHODS

The reconstruction problem can be reformatted to exploit the Toeplitz structure of matrices that are evaluated every iteration, but it requires larger oversampling than what is strictly required by nonuniform Fourier transforms. Accordingly, we investigate relative speeds of the two approaches for various nonuniform Fourier transform kernel sizes and oversampling for both GPU and CPU implementations. Second, we introduce a method to minimize matrix sizes by estimating the image support. Finally, density compensation weights have been used as a preconditioning matrix to improve convergence, but this increases noise. We propose a more general approach to preconditioning that allows a trade-off between accuracy and convergence speed.

RESULTS

When using a GPU, the Toeplitz approach was faster for all practical parameters. Second, it was found that properly accounting for image support can prevent aliasing errors with minimal impact on reconstruction time. Third, the proposed preconditioning scheme improved convergence rates by an order of magnitude with negligible impact on noise.

CONCLUSION

With the proposed methods, 3D non-Cartesian compressed sensing with clinically relevant reconstruction times (<2 min) is feasible using practical computer resources. Magn Reson Med 79:2685-2692, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Single-step quantitative susceptibility mapping with variational penalties

Quantitative susceptibility mapping (QSM) estimates the underlying tissue magnetic susceptibility from the gradient echo (GRE) phase signal through background phase removal and dipole inversion steps. Each of these steps typically requires the solution of an ill-posed inverse problem and thus necessitates additional regularization. Recently developed single-step QSM algorithms directly relate the unprocessed GRE phase to the unknown susceptibility distribution, thereby requiring the solution of a single inverse problem. In this work, we show that such a holistic approach provides susceptibility estimation with artifact mitigation and develop efficient algorithms that involve simple analytical solutions for all of the optimization steps. Our methods employ total variation (TV) and total generalized variation (TGV) to jointly perform the background removal and dipole inversion in a single step. Using multiple spherical mean value (SMV) kernels of varying radii permits high-fidelity background removal whilst retaining the phase information in the cortex. Using numerical simulations, we demonstrate that the proposed single-step methods reduce the reconstruction error by up to 66% relative to the multi-step methods that involve SMV background filtering with the same number of SMV kernels, followed by TV- or TGV-regularized dipole inversion. In vivo single-step experiments demonstrate a dramatic reduction in dipole streaking artifacts and improved homogeneity of image contrast. These acquisitions employ the rapid three-dimensional echo planar imaging (3D EPI) and Wave-CAIPI (controlled aliasing in parallel imaging) trajectories for signal-to-noise ratio-efficient whole-brain imaging. Herein, we also demonstrate the multi-echo capability of the Wave-CAIPI sequence for the first time, and introduce an automated, phase-sensitive coil sensitivity estimation scheme based on a 4-s calibration acquisition. Copyright © 2016 John Wiley & Sons, Ltd.

Comparison-Based Image Quality Assessment for Selecting Image Restoration Parameters

Image quality assessment (IQA) is traditionally classified into full-reference (FR) IQA, reduced-reference (RR) IQA, and no-reference (NR) IQA according to the amount of information required from the original image. Although NR-IQA and RR-IQA are widely used in practical applications, room for improvement still remains because of the lack of the reference image. Inspired by the fact that in many applications, such as parameter selection for image restoration algorithms, a series of distorted images are available, the authors propose a novel comparison-based IQA (C-IQA) framework. The new comparison-based framework parallels FR-IQA by requiring two input images and resembles NR-IQA by not using the original image. As a result, the new comparison-based approach has more application scenarios than FR-IQA does, and takes greater advantage of the accessible information than the traditional single-input NR-IQA does. Further, C-IQA is compared with other state-of-the-art NR-IQA methods and another RR-IQA method on two widely used IQA databases. Experimental results show that C-IQA outperforms the other methods for parameter selection, and the parameter trimming framework combined with C-IQA saves the computation of iterative image reconstruction up to 80%.

Sparse Parallel MRI Based on Accelerated Operator Splitting Schemes

Recently, the sparsity which is implicit in MR images has been successfully exploited for fast MR imaging with incomplete acquisitions. In this paper, two novel algorithms are proposed to solve the sparse parallel MR imaging problem, which consists of l₁ regularization and fidelity terms. The two algorithms combine forward-backward operator splitting and Barzilai-Borwein schemes. Theoretically, the presented algorithms overcome the nondifferentiable property in l₁ regularization term. Meanwhile, they are able to treat a general matrix operator that may not be diagonalized by fast Fourier transform and to ensure that a well-conditioned optimization system of equations is simply solved. In addition, we build connections between the proposed algorithms and the state-of-the-art existing methods and prove their convergence with a constant stepsize in Appendix. Numerical results and comparisons with the advanced methods demonstrate the efficiency of proposed algorithms.

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

Compressed sensing (CS) has exhibited great potential for accelerating magnetic resonance imaging (MRI). In CS-MRI, we want to reconstruct a high-quality image from very few samples in a short time. In this paper, we propose a fast algorithm, called projected iterative soft-thresholding algorithm (pISTA), and its acceleration pFISTA for CS-MRI image reconstruction. The proposed algorithms exploit sparsity of the magnetic resonance (MR) images under the redundant representation of tight frames. We prove that pISTA and pFISTA converge to a minimizer of a convex function with a balanced tight frame sparsity formulation. The pFISTA introduces only one adjustable parameter, the step size, and we provide an explicit rule to set this parameter. Numerical experiment results demonstrate that pFISTA leads to faster convergence speeds than the state-of-art counterpart does, while achieving comparable reconstruction errors. Moreover, reconstruction errors incurred by pFISTA appear insensitive to the step size.

High-resolution intracranial vessel wall imaging: imaging beyond the lumen

Accurate and timely diagnosis of intracranial vasculopathies is important due to significant risk of morbidity with delayed and/or incorrect diagnosis both from the disease process as well as inappropriate therapies. Conventional vascular imaging techniques for analysis of intracranial vascular disease provide limited information since they only identify changes to the vessel lumen. New advanced MR intracranial vessel wall imaging (IVW) techniques can allow direct characterisation of the vessel wall. These techniques can advance diagnostic accuracy and may potentially improve patient outcomes by better guided treatment decisions in comparison to previously available invasive and non-invasive techniques. While neuroradiological expertise is invaluable in accurate examination interpretation, clinician familiarity with the application and findings of the various vasculopathies on IVW can help guide diagnostic and therapeutic decision-making. This review article provides a brief overview of the technical aspects of IVW and discusses the IVW findings of various intracranial vasculopathies, differentiating characteristics and indications for when this technique can be beneficial in patient management.

Efficient Compressed Sensing SENSE pMRI Reconstruction With Joint Sparsity Promotion

The theory and techniques of compressed sensing (CS) have shown their potential as a breakthrough in accelerating k-space data acquisition for parallel magnetic resonance imaging (pMRI). However, the performance of CS reconstruction models in pMRI has not been fully maximized, and CS recovery guarantees for pMRI are largely absent. To improve reconstruction accuracy from parsimonious amounts of k-space data while maintaining flexibility, a new CS SENSitivity Encoding (SENSE) pMRI reconstruction framework promoting joint sparsity (JS) across channels (JS CS SENSE) is proposed in this paper. The recovery guarantee derived for the proposed JS CS SENSE model is demonstrated to be better than that of the conventional CS SENSE model and similar to that of the coil-by-coil CS model. The flexibility of the new model is better than the coil-by-coil CS model and the same as that of CS SENSE. For fast image reconstruction and fair comparisons, all the introduced CS-based constrained optimization problems are solved with split Bregman, variable splitting, and combined-variable splitting techniques. For the JS CS SENSE model in particular, these techniques lead to an efficient algorithm. Numerical experiments show that the reconstruction accuracy is significantly improved by JS CS SENSE compared with the conventional CS SENSE. In addition, an accurate residual-JS regularized sensitivity estimation model is also proposed and extended to calibration-less (CaL) JS CS SENSE. Numerical results show that CaL JS CS SENSE outperforms other state-of-the-art CS-based calibration-less methods in particular for reconstructing non-piecewise constant images.

Forward Looking Radar Imaging by Truncated Singular Value Decomposition and Its Application for Adverse Weather Aircraft Landing

The forward looking radar imaging task is a practical and challenging problem for adverse weather aircraft landing industry. Deconvolution method can realize the forward looking imaging but it often leads to the noise amplification in the radar image. In this paper, a forward looking radar imaging based on deconvolution method is presented for adverse weather aircraft landing. We first present the theoretical background of forward looking radar imaging task and its application for aircraft landing. Then, we convert the forward looking radar imaging task into a corresponding deconvolution problem, which is solved in the framework of algebraic theory using truncated singular decomposition method. The key issue regarding the selecting of the truncated parameter is addressed using generalized cross validation approach. Simulation and experimental results demonstrate that the proposed method is effective in achieving angular resolution enhancement with suppressing the noise amplification in forward looking radar imaging.