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

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.

Signal intensity informed multi-coil encoding operator for physics-guided deep learning reconstruction of highly accelerated myocardial perfusion CMR

PURPOSE

To develop a physics-guided deep learning (PG-DL) reconstruction strategy based on a signal intensity informed multi-coil (SIIM) encoding operator for highly-accelerated simultaneous multislice (SMS) myocardial perfusion cardiac MRI (CMR).

METHODS

First-pass perfusion CMR acquires highly-accelerated images with dynamically varying signal intensity/SNR following the administration of a gadolinium-based contrast agent. Thus, using PG-DL reconstruction with a conventional multi-coil encoding operator leads to analogous signal intensity variations across different time-frames at the network output, creating difficulties in generalization for varying SNR levels. We propose to use a SIIM encoding operator to capture the signal intensity/SNR variations across time-frames in a reformulated encoding operator. This leads to a more uniform/flat contrast at the output of the PG-DL network, facilitating generalizability across time-frames. PG-DL reconstruction with the proposed SIIM encoding operator is compared to PG-DL with conventional encoding operator, split slice-GRAPPA, locally low-rank (LLR) regularized reconstruction, low-rank plus sparse (L + S) reconstruction, and regularized ROCK-SPIRiT.

RESULTS

Results on highly accelerated free-breathing first pass myocardial perfusion CMR at three-fold SMS and four-fold in-plane acceleration show that the proposed method improves upon the reconstruction methods use for comparison. Substantial noise reduction is achieved compared to split slice-GRAPPA, and aliasing artifacts reduction compared to LLR regularized reconstruction, L + S reconstruction and PG-DL with conventional encoding. Furthermore, a qualitative reader study indicated that proposed method outperformed all methods.

CONCLUSION

PG-DL reconstruction with the proposed SIIM encoding operator improves generalization across different time-frames /SNRs in highly accelerated perfusion CMR.

Signal-Intensity Informed Multi-Coil MRI Encoding Operator for Improved Physics-Guided Deep Learning Reconstruction of Dynamic Contrast-Enhanced MRI

Dynamic contrast enhanced (DCE) MRI acquires a series of images following the administration of a contrast agent, and plays an important clinical role in diagnosing various diseases. DCE MRI typically necessitates rapid imaging to provide sufficient spatio-temporal resolution and coverage. Conventional MRI acceleration techniques exhibit limited image quality at such high acceleration rates. Recently, deep learning (DL) methods have gained interest for improving highly-accelerated MRI. However, DCE MRI series show substantial variations in SNR and contrast across images. This hinders the quality and generalizability of DL methods, when applied across time frames. In this study, we propose signal intensity informed multi-coil MRI encoding operator for improved DL reconstruction of DCE MRI. The output of the corresponding inverse problem for this forward operator leads to more uniform contrast across time frames, since the proposed operator captures signal intensity variations across time frames while not altering the coil sensitivities. Our results in perfusion cardiac MRI show that high-quality images are reconstructed at very high acceleration rates, with substantial improvement over existing methods.

Learning a preconditioner to accelerate compressed sensing reconstructions in MRI

Purpose

To learn a preconditioner that accelerates parallel imaging (PI) and compressed sensing (CS) reconstructions.

Methods

A convolutional neural network (CNN) with residual connections was used to train a preconditioning operator. Training and validation data were simulated using 50% brain images and 50% white Gaussian noise images. Each multichannel training example contains a simulated sampling mask, complex coil sensitivity maps, and two regularization parameter maps. The trained model was integrated in the preconditioned conjugate gradient (PCG) method as part of the split Bregman CS method. The acceleration performance was compared with that of a circulant PI‐CS preconditioner for varying undersampling factors, number of coil elements and anatomies.

Results

The learned preconditioner reduces the number of PCG iterations by a factor of 4, yielding a similar acceleration as an efficient circulant preconditioner. The method generalizes well to different sampling schemes, coil configurations and anatomies.

Conclusion

It is possible to learn adaptable preconditioners for PI and CS reconstructions that meet the performance of state‐of‐the‐art preconditioners. Further acceleration could be achieved by optimizing the network architecture and the training set. Such a preconditioner could also be integrated in fully learned reconstruction methods to accelerate the training process of unrolled networks.

Parallel magnetic resonance imaging acceleration with a hybrid sensing approach

In magnetic resonance imaging (MRI), the scan time for acquiring an image is relatively long, resulting in patient uncomfortable and error artifacts. Fortunately, the compressed sensing (CS) and parallel magnetic resonance imaging (pMRI) can reduce the scan time of the MRI without significantly compromising the quality of the images. It has been found that the combination of pMRI and CS can better improve the image reconstruction, which will accelerate the speed of MRI acquisition because the number of measurements is much smaller than that by pMRI. In this paper, we propose combining a combined CS method and pMRI for better accelerating the MRI acquisition. In the combined CS method, the under-sampled data of the K-space is performed by taking both regular sampling and traditional random under-sampling approaches. MRI image reconstruction is then performed by using nonlinear conjugate gradient optimization. The performance of the proposed method is simulated and evaluated using the reconstruction error measure, the universal image quality Q-index, and the peak signal-to-noise ratio (PSNR). The numerical simulations confirmed that, the average error, the Q index, and the PSNR ratio of the appointed scheme are remarkably improved up to 59, 63, and 39% respectively as compared to the traditional scheme. For the first time, instead of using highly computational approaches, a simple and efficient combination of CS and pMRI is proposed for the better MRI reconstruction. These findings are very meaningful for reducing the imaging time of MRI systems.

Image distortion correction for MRI in low field permanent magnet systems with strong B0 inhomogeneity and gradient field nonlinearities

Objective

To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneity and gradient field nonlinearities.

Materials and methods

Conventional image distortion correction algorithms require accurate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta B}_{0}$$\end{document}ΔB0 maps which are not possible to acquire directly when the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities also produce significant image distortions. Here we use a readout gradient time-shift in a TSE sequence to encode the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 field inhomogeneities in the k-space signals. Using a non-shifted and a shifted acquisition as input, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images were reconstructed in an iterative manner. In each iteration, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps were reconstructed from the phase difference using Tikhonov regularization, while images were reconstructed using either conjugate phase reconstruction (CPR) or model-based (MB) image reconstruction, taking the reconstructed field map into account. MB reconstructions were, furthermore, combined with compressed sensing (CS) to show the flexibility of this approach towards undersampling. These methods were compared to the standard fast Fourier transform (FFT) image reconstruction approach in simulations and measurements. Distortions due to gradient nonlinearities were corrected in CPR and MB using simulated gradient maps.

Results

Simulation results show that for moderate field inhomogeneities and gradient nonlinearities, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images reconstructed using iterative CPR result in comparable quality to that for iterative MB reconstructions. However, for stronger inhomogeneities, iterative MB reconstruction outperforms iterative CPR in terms of signal intensity correction. Combining MB with CS, similar image and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map quality can be obtained without a scan time penalty. These findings were confirmed by experimental results.

Discussion

In case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities in the order of kHz, iterative MB reconstructions can help to improve both image quality and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map estimation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00907-2.

Low-field magnetic resonance imaging using multiplicative regularization

In this paper we present a magnetic resonance imaging (MRI) technique that is based on multiplicative regularization. Instead of adding a regularizing objective function to a data fidelity term, we multiply by such a regularizing function. By following this approach, no regularization parameter needs to be determined for each new data set that is acquired. Reconstructions are obtained by iteratively updating the images using short-term conjugate gradient-type update formulas and Polak-Ribière update directions. We show that the algorithm can be used as an image reconstruction algorithm and as a denoising algorithm. We illustrate the performance of the algorithm on two-dimensional simulated low-field MR data that is corrupted by noise and on three-dimensional measured data obtained from a low-field MR scanner. Our reconstruction results show that the algorithm effectively suppresses noise and produces accurate reconstructions even for low-field MR signals with a low signal-to-noise ratio.

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.

Optimization Methods for Magnetic Resonance Image Reconstruction: Key Models and Optimization Algorithms

The development of compressed sensing methods for magnetic resonance (MR) image reconstruction led to an explosion of research on models and optimization algorithms for MR imaging (MRI). Roughly 10 years after such methods first appeared in the MRI literature, the U.S. Food and Drug Administration (FDA) approved certain compressed sensing methods for commercial use, making compressed sensing a clinical success story for MRI. This review paper summarizes several key models and optimization algorithms for MR image reconstruction, including both the type of methods that have FDA approval for clinical use, as well as more recent methods being considered in the research community that use data-adaptive regularizers. Many algorithms have been devised that exploit the structure of the system model and regularizers used in MRI; this paper strives to collect such algorithms in a single survey.

Compressed Sensing: From Research to Clinical Practice with Deep Neural Networks

Compressed sensing (CS) reconstruction methods leverage sparse structure in underlying signals to recover high-resolution images from highly undersampled measurements. When applied to magnetic resonance imaging (MRI), CS has the potential to dramatically shorten MRI scan times, increase diagnostic value, and improve overall patient experience. However, CS has several shortcomings which limit its clinical translation such as: 1) artifacts arising from inaccurate sparse modelling assumptions, 2) extensive parameter tuning required for each clinical application, and 3) clinically infeasible reconstruction times. Recently, CS has been extended to incorporate deep neural networks as a way of learning complex image priors from historical exam data. Commonly referred to as unrolled neural networks, these techniques have proven to be a compelling and practical approach to address the challenges of sparse CS. In this tutorial, we will review the classical compressed sensing formulation and outline steps needed to transform this formulation into a deep learning-based reconstruction framework. Supplementary open source code in Python will be used to demonstrate this approach with open databases. Further, we will discuss considerations in applying unrolled neural networks in the clinical setting.

[Elimination of Gibbs artifact based on local subpixel shift and interlaced local variation]

OBJECTIVE

To extend the application of Gibbs artifact reduction method that exploits local subvoxel- shifts (LSS) to zero- padded k-space magnetic resonance imaging (MRI) data.

METHODS

We investigated two approaches to extending the application of LSS-based method to under-sampled data. The first approach, namely LSS+ interpolation, utilized the original LSS-based method to minimize the local variation on nonzero-padding reconstructed images, followed by image interpolation to obtain the final images. The second approach, interlaced local variation, used zero-padded Fourier transformation followed by elimination of Gibbs artifacts by minimizing a novel interlaced local variations (iLV) term. We compared the two methods with the original LSS and Hamming window filter algorithms, and verified their feasibility and robustness in phantom and in vivo data.

RESULTS

The two methods proposed showed better performance than the original LSS and Hamming window filters and effectively eliminated Gibbs artifacts while preserving the image details. Compared to LSS + interpolation method, iLV method better preserved the details of the images.

CONCLUSIONS

The iLV and LSS+interpolation methods proposed herein both extend the application of the original LSS method and can eliminate Gibbs artifacts in zero-filled k-space data reconstruction images, and iLV method shows a more prominent advantage in retaining the image details.

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.