Parallel MR image reconstruction using augmented Lagrangian methods

DONet: Dual-Octave Network for Fast MR Image Reconstruction

Magnetic resonance (MR) image acquisition is an inherently prolonged process, whose acceleration has long been the subject of research. This is commonly achieved by obtaining multiple undersampled images, simultaneously, through parallel imaging. In this article, we propose the dual-octave network (DONet), which is capable of learning multiscale spatial-frequency features from both the real and imaginary components of MR data, for parallel fast MR image reconstruction. More specifically, our DONet consists of a series of dual-octave convolutions (Dual-OctConvs), which are connected in a dense manner for better reuse of features. In each Dual-OctConv, the input feature maps and convolutional kernels are first split into two components (i.e., real and imaginary) and then divided into four groups according to their spatial frequencies. Then, our Dual-OctConv conducts intragroup information updating and intergroup information exchange to aggregate the contextual information across different groups. Our framework provides three appealing benefits: 1) it encourages information interaction and fusion between the real and imaginary components at various spatial frequencies to achieve richer representational capacity; 2) the dense connections between the real and imaginary groups in each Dual-OctConv make the propagation of features more efficient by feature reuse; and 3) DONet enlarges the receptive field by learning multiple spatial-frequency features of both the real and imaginary components. Extensive experiments on two popular datasets (i.e., clinical knee and fastMRI), under different undersampling patterns and acceleration factors, demonstrate the superiority of our model in accelerated parallel MR image reconstruction.

An accelerated alternating direction method of multiplier for MRI with TV regularisation

Compressed Sensing (CS) is important in the field of image processing and signal processing, and CS-Magnetic Resonance Imaging (MRI) is used to reconstruct image from undersampled k-space data. Total Variation (TV) regularisation is a common technique to improve the sparsity of image, and the Alternating Direction Multiplier Method (ADMM) plays a key role in the variational image processing problem. This paper aims to improve the quality of MRI and shorten the reconstruction time. We consider MRI to solve a linear inverse problem, we convert it into a constrained optimization problem based on TV regularisation, then an accelerated ADMM is established. Through a series of theoretical derivations, we verify that the algorithm satisfies the convergence rate of O1/k2 under the condition that one objective function is quadratically convex and the other is strongly convex. We select five undersampled templates for testing in MRI experiment and compare it with other algorithms, experimental results show that our proposed method not only improves the running speed but also gives better reconstruction results.

Highly accelerated parameter mapping using model-based alternating reconstruction coupling fitting

Objective.A model-based alternating reconstruction coupling fitting, termed Model-based Alternating Reconstruction COupling fitting (MARCO), is proposed for accurate and fast magnetic resonance parameter mapping.Approach.MARCO utilizes the signal model as a regularization by minimizing the bias between the image series and the signal produced by the suitable signal model based on iteratively updated parameter maps when reconstructing. The technique can incorporate prior knowledge of both image series and parameters by adding sparsity constraints. The optimization problem is decomposed into three subproblems and solved through three alternating steps involving reconstruction and nonlinear least-square fitting, which can produce both contrast-weighted images and parameter maps simultaneously.Main results.The algorithm is applied toT2mapping with extended phase graph algorithm integrated and validated on undersampled multi-echo spin-echo data from both phantom and in vivo sources. Compared with traditional compressed sensing and model-based methods, the proposed approach yields more accurateT2maps with more details at high acceleration factors.Significance.The proposed method provides a basic framework for quantitative MR relaxometry, theoretically applicable to all quantitative MR relaxometry. It has the potential to improve the diagnostic utility of quantitative imaging techniques.

Constrained alternating minimization for parameter mapping (CAMP)

OBJECTIVE

To improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images.

APPROACH

In multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps. In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12.

MAIN RESULTS

CAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias.

SIGNIFICANCE

For a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

Model-based iterative reconstruction for direct imaging with point spread function encoded echo planar MRI

BACKGROUND

Echo planar imaging (EPI) is a fast measurement technique commonly used in magnetic resonance imaging (MRI), but is highly sensitive to measurement non-idealities in reconstruction. Point spread function (PSF)-encoded EPI is a multi-shot strategy which alleviates distortion, but acquisition of encodings suitable for direct distortion-free imaging prolongs scan time. In this work, a model-based iterative reconstruction (MBIR) framework is introduced for direct imaging with PSF-EPI to improve image quality and acceleration potential.

METHODS

An MBIR platform was developed for accelerated PSF-EPI. The reconstruction utilizes a subspace representation, is regularized to promote local low-rankedness (LLR), and uses variable splitting for efficient iteration. Comparisons were made against standard reconstructions from prospectively accelerated PSF-EPI data and with retrospective subsampling. Exploring aggressive partial Fourier acceleration of the PSF-encoding dimension, additional comparisons were made against an extension of Homodyne to direct PSF-EPI in numerical experiments. A neuroradiologists' assessment was completed comparing images reconstructed with MBIR from retrospectively truncated data directly against images obtained with standard reconstructions from non-truncated datasets.

RESULTS

Image quality results were consistently superior for MBIR relative to standard and Homodyne reconstructions. As the MBIR signal model and reconstruction allow for arbitrary sampling of the PSF space, random sampling of the PSF-encoding dimension was also demonstrated, with quantitative assessments indicating best performance achieved through nonuniform PSF sampling combined with partial Fourier. With retrospective subsampling, MBIR reconstructs high-quality images from sub-minute scan datasets. MBIR was shown to be superior in a neuroradiologists' assessment with respect to three of five performance criteria, with equivalence for the remaining two.

CONCLUSIONS

A novel image reconstruction framework is introduced for direct imaging with PSF-EPI, enabling arbitrary PSF space sampling and reconstruction of diagnostic-quality images from highly accelerated PSF-encoded EPI data.

NON-CARTESIAN SELF-SUPERVISED PHYSICS-DRIVEN DEEP LEARNING RECONSTRUCTION FOR HIGHLY-ACCELERATED MULTI-ECHO SPIRAL FMRI

Functional MRI (fMRI) is an important tool for non-invasive studies of brain function. Over the past decade, multi-echo fMRI methods that sample multiple echo times has become popular with potential to improve quantification. While these acquisitions are typically performed with Cartesian trajectories, non-Cartesian trajectories, in particular spiral acquisitions, hold promise for denser sampling of echo times. However, such acquisitions require very high acceleration rates for sufficient spatiotemporal resolutions. In this work, we propose to use a physics-driven deep learning (PD-DL) reconstruction to accelerate multi-echo spiral fMRI by 10-fold. We modify a self-supervised learning algorithm for optimized training with non-Cartesian trajectories and use it to train the PD-DL network. Results show that the proposed self-supervised PD-DL reconstruction achieves high spatio-temporal resolution with meaningful BOLD analysis.

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.

AliasNet: Alias artefact suppression network for accelerated phase-encode MRI

Sparse reconstruction is an important aspect of MRI, helping to reduce acquisition time and improve spatial-temporal resolution. Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of k-space to produce incoherent (noise-like) artefacts. Due to hardware constraints, 1D Cartesian phase-encode under-sampling schemes are popular for 2D CS-MRI. However, 1D under-sampling limits 2D incoherence between measurements, yielding structured aliasing artefacts (ghosts) that may be difficult to remove assuming a 2D sparsity model. Reconstruction algorithms typically deploy direction-insensitive 2D regularisation for these direction-associated artefacts. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation and leverage the excellent 1D incoherence characteristics. We also derive a combined 1D + 2D reconstruction technique that takes advantage of spatial relationships within the image. Experiments conducted on retrospectively under-sampled brain and knee data demonstrate that combination of the proposed 1D AliasNet modules with existing 2D deep learned (DL) recovery techniques leads to an improvement in image quality. We also find AliasNet enables a superior scaling of performance compared to increasing the size of the original 2D network layers. AliasNet therefore improves the regularisation of aliasing artefacts arising from phase-encode under-sampling, by tailoring the network architecture to account for their expected appearance. The proposed 1D + 2D approach is compatible with any existing 2D DL recovery technique deployed for this application.

Frequency Learning via Multi-Scale Fourier Transformer for MRI Reconstruction

Since Magnetic Resonance Imaging (MRI) requires a long acquisition time, various methods were proposed to reduce the time, but they ignored the frequency information and non-local similarity, so that they failed to reconstruct images with a clear structure. In this article, we propose Frequency Learning via Multi-scale Fourier Transformer for MRI Reconstruction (FMTNet), which focuses on repairing the low-frequency and high-frequency information. Specifically, FMTNet is composed of a high-frequency learning branch (HFLB) and a low-frequency learning branch (LFLB). Meanwhile, we propose a Multi-scale Fourier Transformer (MFT) as the basic module to learn the non-local information. Unlike normal Transformers, MFT adopts Fourier convolution to replace self-attention to efficiently learn global information. Moreover, we further introduce a multi-scale learning and cross-scale linear fusion strategy in MFT to interact information between features of different scales and strengthen the representation of features. Compared with normal Transformers, the proposed MFT occupies fewer computing resources. Based on MFT, we design a Residual Multi-scale Fourier Transformer module as the main component of HFLB and LFLB. We conduct several experiments under different acceleration rates and different sampling patterns on different datasets, and the experiment results show that our method is superior to the previous state-of-the-art method.

MEDL-Net: A model-based neural network for MRI reconstruction with enhanced deep learned regularizers

PURPOSE

To improve the MRI reconstruction performance of model-based networks and to alleviate their large demand for GPU memory.

METHODS

A model-based neural network with enhanced deep learned regularizers (MEDL-Net) was proposed. The MEDL-Net is separated into several submodules, each of which consists of several cascades to mimic the optimization steps in conventional MRI reconstruction algorithms. Information from shallow cascades is densely connected to latter ones to enrich their inputs in each submodule, and additional revising blocks (RB) are stacked at the end of the submodules to bring more flexibility. Moreover, a composition loss function was designed to explicitly supervise RBs.

RESULTS

Network performance was evaluated on a publicly available dataset. The MEDL-Net quantitatively outperforms the state-of-the-art methods on different MR image sequences with different acceleration rates (four-fold and six-fold). Moreover, the reconstructed images showed that the detailed textures are better preserved. In addition, fewer cascades are required when achieving the same reconstruction results compared with other model-based networks.

CONCLUSION

In this study, a more efficient model-based deep network was proposed to reconstruct MR images. The experimental results indicate that the proposed method improves reconstruction performance with fewer cascades, which alleviates the large demand for GPU memory.

Efficient Approximation of Jacobian Matrices Involving a Non-Uniform Fast Fourier Transform (NUFFT)

There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling, the system models typically involve non-uniform fast Fourier transform (NUFFT) operations. Commonly used NUFFT algorithms contain frequency domain interpolation, which is not differentiable with respect to the sampling pattern, complicating the use of gradient methods. This paper describes an efficient and accurate approach for computing approximate gradients involving NUFFTs. Multiple numerical experiments validate the improved accuracy and efficiency of the proposed approximation. As an application to computational imaging, the NUFFT Jacobians were used to optimize non-Cartesian MRI sampling trajectories via data-driven stochastic optimization. Specifically, the sampling patterns were learned with respect to various model-based image reconstruction (MBIR) algorithms. The proposed approach enables sampling optimization for image sizes that are infeasible with standard auto-differentiation methods due to memory limits. The synergistic acquisition and reconstruction design leads to remarkably improved image quality. In fact, we show that model-based image reconstruction methods with suitably optimized imaging parameters can perform nearly as well as CNN-based methods.

Pyramid Convolutional RNN for MRI Image Reconstruction

Fast and accurate MRI image reconstruction from undersampled data is crucial in clinical practice. Deep learning based reconstruction methods have shown promising advances in recent years. However, recovering fine details from undersampled data is still challenging. In this paper, we introduce a novel deep learning based method, Pyramid Convolutional RNN (PC-RNN), to reconstruct images from multiple scales. Based on the formulation of MRI reconstruction as an inverse problem, we design the PC-RNN model with three convolutional RNN (ConvRNN) modules to iteratively learn the features in multiple scales. Each ConvRNN module reconstructs images at different scales and the reconstructed images are combined by a final CNN module in a pyramid fashion. The multi-scale ConvRNN modules learn a coarse-to-fine image reconstruction. Unlike other common reconstruction methods for parallel imaging, PC-RNN does not employ coil sensitive maps for multi-coil data and directly model the multiple coils as multi-channel inputs. The coil compression technique is applied to standardize data with various coil numbers, leading to more efficient training. We evaluate our model on the fastMRI knee and brain datasets and the results show that the proposed model outperforms other methods and can recover more details. The proposed method is one of the winner solutions in the 2019 fastMRI competition.

Splitting proximate algorithm for deformable image registration based on functions of bounded deformation

BACKGROUND

Deformable image registration is a crucial task in the field of medical image analysis. Functions of bounded deformation (BD) have been proved effective for modeling the displacement fields between medical images since they can capture the discontinuity of displacement fields along edges of organs and tissues.

PURPOSE

However, we find that at the same time, BD functions-based models tend to obtain discontinuous displacement fields inside the regions of organs and tissues due to image noises in some cases and the presented gradient descent algorithm is time-consuming. To alleviate these problems, we propose a faster algorithm named SPA: splitting proximate algorithm.

METHODS

In the framework of variable-splitting scheme, we incorporate a proximal term in the deformable registration energy based on functions of BD.

RESULTS

The proposed algorithm can efficiently solve the original model and obtain displacement fields, which look more natural and plausible. Numerical experiments show the effectiveness and stability of the proposed algorithm.

CONCLUSIONS

The proposed SPA is able to drastically register the images with a plausible deformation field and not sensitive to noise.

Joint Reconstruction of Vascular Structure and Function Maps in Dynamic Contrast Enhanced MRI Using Vascular Heterogeneity Priors

This work introduces a novel, joint reconstruction of vascular structure and microvascular function maps directly from highly undersampled data in k - t space using vascular heterogeneity priors for high-definition, dynamic contrast-enhanced (DCE) MRI. In DCE MRI, arteries and veins are characterized by rapid, high uptake and wash-out of contrast agents (CA). On the other hand, depending on CA uptake and wash-out signal patterns, capillary tissues can be categorized into highly perfused, moderately perfused, and necrotic regions. Given the above considerations, macrovascular maps are generated as a prior to differentiate penalties on arteries relative to capillary tissues during image reconstruction. Furthermore, as a microvascular prior, contrast dynamics in capillary regions are represented in a low dimensional space using a finite number of basic vectors that reflect actual tissue-specific signal patterns. Both vascular structure and microvascular function maps are jointly estimated by solving a constrained optimization problem in which the above vascular heterogeneity priors are represented by spatially weighted nonnegative matrix factorization. Retrospective and prospective experiments are performed to validate the effectiveness of the proposed method in generating well-defined vascular structure and microvascular function maps for patients with brain tumor at high reduction factors.

Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM)

PURPOSE

The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts.

METHODS

QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages.

RESULTS

The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups.

CONCLUSION

The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers.

Dynamic MRI Reconstruction via Weighted Tensor Nuclear Norm Regularizer

In this paper, we propose a novel multi-dimensional reconstruction method based on the low-rank plus sparse tensor (L+S) decomposition model to reconstruct dynamic magnetic resonance imaging (dMRI). The multi-dimensional reconstruction method is formulated using a non-convex alternating direction method of multipliers (ADMM), where the weighted tensor nuclear norm (WTNN) and l₁-norm are used to enforce the low-rank in L and the sparsity in S, respectively. In particular, the weights used in the WTNN are sorted in a non-descending order, and we obtain a closed-form optimal solution of the WTNN minimization problem. The theoretical properties provided guarantee the weak convergence of our reconstruction method. In addition, a fast inexact reconstruction method is proposed to increase imaging speed and efficiency. Experimental results demonstrate that both of our reconstruction methods can achieve higher reconstruction quality than the state-of-the-art reconstruction methods.

Complementary time-frequency domain networks for dynamic parallel MR image reconstruction

PURPOSE

To introduce a novel deep learning-based approach for fast and high-quality dynamic multicoil MR reconstruction by learning a complementary time-frequency domain network that exploits spatiotemporal correlations simultaneously from complementary domains.

THEORY AND METHODS

Dynamic parallel MR image reconstruction is formulated as a multivariable minimization problem, where the data are regularized in combined temporal Fourier and spatial (x-f) domain as well as in spatiotemporal image (x-t) domain. An iterative algorithm based on variable splitting technique is derived, which alternates among signal de-aliasing steps in x-f and x-t spaces, a closed-form point-wise data consistency step and a weighted coupling step. The iterative model is embedded into a deep recurrent neural network which learns to recover the image via exploiting spatiotemporal redundancies in complementary domains.

RESULTS

Experiments were performed on two datasets of highly undersampled multicoil short-axis cardiac cine MRI scans. Results demonstrate that our proposed method outperforms the current state-of-the-art approaches both quantitatively and qualitatively. The proposed model can also generalize well to data acquired from a different scanner and data with pathologies that were not seen in the training set.

CONCLUSION

The work shows the benefit of reconstructing dynamic parallel MRI in complementary time-frequency domains with deep neural networks. The method can effectively and robustly reconstruct high-quality images from highly undersampled dynamic multicoil data ( 16 × and 24 × yielding 15 s and 10 s scan times respectively) with fast reconstruction speed (2.8 seconds). This could potentially facilitate achieving fast single-breath-hold clinical 2D cardiac cine imaging.

Deep learning in magnetic resonance image reconstruction

Magnetic resonance (MR) imaging visualises soft tissue contrast in exquisite detail without harmful ionising radiation. In this work, we provide a state-of-the-art review on the use of deep learning in MR image reconstruction from different image acquisition types involving compressed sensing techniques, parallel image acquisition and multi-contrast imaging. Publications with deep learning-based image reconstruction for MR imaging were identified from the literature (PubMed and Google Scholar), and a comprehensive description of each of the works was provided. A detailed comparison that highlights the differences, the data used and the performance of each of these works were also made. A discussion of the potential use cases for each of these methods is provided. The sparse image reconstruction methods were found to be most popular in using deep learning for improved performance, accelerating acquisitions by around 4-8 times. Multi-contrast image reconstruction methods rely on at least one pre-acquired image, but can achieve 16-fold, and even up to 32- to 50-fold acceleration depending on the set-up. Parallel imaging provides frameworks to be integrated in many of these methods for additional speed-up potential. The successful use of compressed sensing techniques and multi-contrast imaging with deep learning and parallel acquisition methods could yield significant MR acquisition speed-ups within clinical routines in the near future.

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.

Calibration-Less Multi-Coil Compressed Sensing Magnetic Resonance Image Reconstruction Based on OSCAR Regularization

Over the last decade, the combination of compressed sensing (CS) with acquisition over multiple receiver coils in magnetic resonance imaging (MRI) has allowed the emergence of faster scans while maintaining a good signal-to-noise ratio (SNR). Self-calibrating techniques, such as ESPiRIT, have become the standard approach to estimating the coil sensitivity maps prior to the reconstruction stage. In this work, we proceed differently and introduce a new calibration-less multi-coil CS reconstruction method. Calibration-less techniques no longer require the prior extraction of sensitivity maps to perform multi-coil image reconstruction but usually alternate estimation sensitivity map estimation and image reconstruction. Here, to get rid of the nonconvexity of the latter approach we reconstruct as many MR images as the number of coils. To compensate for the ill-posedness of this inverse problem, we leverage structured sparsity of the multi-coil images in a wavelet transform domain while adapting to variations in SNR across coils owing to the OSCAR (octagonal shrinkage and clustering algorithm for regression) regularization. Coil-specific complex-valued MR images are thus obtained by minimizing a convex but nonsmooth objective function using the proximal primal-dual Condat-Vù algorithm. Comparison and validation on retrospective Cartesian and non-Cartesian studies based on the Brain fastMRI data set demonstrate that the proposed reconstruction method outperforms the state-of-the-art (ℓ1-ESPIRiT, calibration-less AC-LORAKS and CaLM methods) significantly on magnitude images for the T1 and FLAIR contrasts. Additionally, further validation operated on 8 to 20-fold prospectively accelerated high-resolution ex vivo human brain MRI data collected at 7 Tesla confirms the retrospective results. Overall, OSCAR-based regularization preserves phase information more accurately (both visually and quantitatively) compared to other approaches, an asset that can only be assessed on real prospective experiments.

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.

Dense Recurrent Neural Networks for Accelerated MRI: History-Cognizant Unrolling of Optimization Algorithms

Inverse problems for accelerated MRI typically incorporate domain-specific knowledge about the forward encoding operator in a regularized reconstruction framework. Recently physics-driven deep learning (DL) methods have been proposed to use neural networks for data-driven regularization. These methods unroll iterative optimization algorithms to solve the inverse problem objective function, by alternating between domain-specific data consistency and data-driven regularization via neural networks. The whole unrolled network is then trained end-to-end to learn the parameters of the network. Due to simplicity of data consistency updates with gradient descent steps, proximal gradient descent (PGD) is a common approach to unroll physics-driven DL reconstruction methods. However, PGD methods have slow convergence rates, necessitating a higher number of unrolled iterations, leading to memory issues in training and slower reconstruction times in testing. Inspired by efficient variants of PGD methods that use a history of the previous iterates, we propose a history-cognizant unrolling of the optimization algorithm with dense connections across iterations for improved performance. In our approach, the gradient descent steps are calculated at a trainable combination of the outputs of all the previous regularization units. We also apply this idea to unrolling variable splitting methods with quadratic relaxation. Our results in reconstruction of the fastMRI knee dataset show that the proposed history-cognizant approach reduces residual aliasing artifacts compared to its conventional unrolled counterpart without requiring extra computational power or increasing reconstruction time.

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.

Constrained Magnetic Resonance Spectroscopic Imaging by Learning Nonlinear Low-Dimensional Models

Magnetic resonance spectroscopic imaging (MRSI) is a powerful molecular imaging modality but has very limited speed, resolution, and SNR tradeoffs. Construction of a low-dimensional model to effectively reduce the dimensionality of the imaging problem has recently shown great promise in improving these tradeoffs. This paper presents a new approach to model and reconstruct the spectroscopic signals by learning a nonlinear low-dimensional representation of the general MR spectra. Specifically, we trained a deep neural network to capture the low-dimensional manifold, where the high-dimensional spectroscopic signals reside. A regularization formulation is proposed to effectively integrate the learned model and physics-based data acquisition model for MRSI reconstruction with the capability to incorporate additional spatiospectral constraints. An efficient numerical algorithm was developed to solve the associated optimization problem involving back-propagating the trained network. Simulation and experimental results were obtained to demonstrate the representation power of the learned model and the ability of the proposed formulation in producing SNR-enhancing reconstruction from the practical MRSI data.

A Network-Driven Prior Induced Bregman Model for Parallel MR Imaging

Compressed sensing based parallel imaging (CS-PI) has attracted great attention in fast magnetic resonance imaging (MRI) community. In particular, Bregman iterative model has shown encouraging performance in solving this problem. However, its regularization term still has large room for improvement. In this work, we propose a network-driven prior induced Bregman model, dubbed as Breg-EDAEP, for CS-PI task. In the present model, the implicit property among different channel MR images is preliminarily explored by the network to obtain more structure details in iterative reconstruction procedure. Experiments on various acceleration factors and sampling patterns have shown that the proposed method outperforms the state-of-the-art algorithms. Breg-EDAEP possesses strong capability to restore image details and preserves well structure information.

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.

Conjugate gradient variants for $${\ell}_{p}$$-regularized image reconstruction in low-field MRI

We consider the MRI physics in a low-field MRI scanner, in which permanent magnets are used to generate a magnetic field in the millitesla range. A model describing the relationship between measured signal and image is derived, resulting in an ill-posed inverse problem. In order to solve it, a regularization penalty is added to the least-squares minimization problem. We generalize the conjugate gradient minimal error (CGME) algorithm to the weighted and regularized least-squares problem. Analysis of the convergence of generalized CGME (GCGME) and the classical generalized conjugate gradient least squares (GCGLS) shows that GCGME can be expected to converge faster for ill-conditioned regularization matrices. The $${\ell}_{p}$$ℓp-regularized problem is solved using iterative reweighted least squares for $$p=1$$p=1 and $$p=\frac{1}{2}$$p=12, with both cases leading to an increasingly ill-conditioned regularization matrix. Numerical results show that GCGME needs a significantly lower number of iterations to converge than GCGLS.

SMS MUSSELS: A navigator-free reconstruction for simultaneous multi-slice-accelerated multi-shot diffusion weighted imaging

PURPOSE

To introduce a novel reconstruction method for simultaneous multi-slice (SMS)-accelerated multi-shot diffusion weighted imaging (ms-DWI).

METHODS

SMS acceleration using blipped-CAIPI schemes have been proposed to speed up the acquisition of ms-DWIs. The reconstruction of the data requires (a) phase compensation to combine data from different shots and (b) slice unfolding to separate the data of different slices. The traditional approaches first estimate the phase maps corresponding to each shot and slice which are then employed to iteratively recover the slice unfolded DWIs without phase artifacts. In contrast, the proposed reconstruction directly recovers the slice-unfolded k-space data of the multiple shots for each slice in a single-step recovery scheme. The proposed method is enabled by the low-rank property inherent in the k-space samples of ms-DW acquisition. This enabled to formulate a joint recovery scheme that simultaneously (a) unfolds the k-space data of each slice using a SENSE-based scheme and (b) recover the missing k-space samples in each slice of the multi-shot acquisition employing a structured low-rank matrix completion. Additional smoothness regularization is also utilized for higher acceleration factors. The proposed joint recovery is tested on simulated and in vivo data and compared to similar un-navigated methods.

RESULTS

Our experiments show effective slice unfolding and successful recovery of DWIs with minimal phase artifacts using the proposed method. The performance is comparable to existing methods at low acceleration factors and better than existing methods for higher acceleration factors.

CONCLUSIONS

For the slice accelerations considered in this study, the proposed method can successfully recover DWIs from SMS-accelerated ms-DWI acquisitions.

An efficient 3D stack-of-stars turbo spin echo pulse sequence for simultaneous T2-weighted imaging and T2 mapping

PURPOSE

To design a pulse sequence for efficient 3D T2-weighted imaging and T2 mapping.

METHODS

A stack-of-stars turbo spin echo pulse sequence with variable refocusing flip angles and a flexible pseudorandom view ordering is proposed for simultaneous T2-weighted imaging and T2 mapping. An analytical framework is introduced for the selection of refocusing flip angles to maximize relative tissue contrast while minimizing T2 estimation errors and maintaining low specific absorption rate. Images at different echo times are generated using a subspace constrained iterative reconstruction algorithm. T2 maps are obtained by modeling the signal evolution using the extended phase graph model. The technique is evaluated using phantoms and demonstrated in vivo for brain, knee, and carotid imaging.

RESULTS

Numerical simulations demonstrate an improved point spread function with the proposed pseudorandom view ordering compared to golden angle view ordering. Phantom experiments show that T2 values estimated from the stack-of-stars turbo spin echo pulse sequence with variable refocusing flip angles have good concordance with spin echo reference values. In vivo results show the proposed pulse sequence can generate qualitatively comparable T2-weighted images as conventional Cartesian 3D SPACE in addition to simultaneously generating 3D T2 maps.

CONCLUSION

The proposed stack-of-stars turbo spin echo pulse sequence with pseudorandom view ordering and variable refocusing flip angles allows high resolution isotropic T2 mapping in clinically acceptable scan times. The optimization framework for the selection of refocusing flip angles improves T2 estimation accuracy while generating T2-weighted contrast comparable to conventional Cartesian imaging.

Compressed sensing MRI: a review from signal processing perspective

Magnetic resonance imaging (MRI) is an inherently slow imaging modality, since it acquires multi-dimensional k-space data through 1-D free induction decay or echo signals. This often limits the use of MRI, especially for high resolution or dynamic imaging. Accordingly, many investigators has developed various acceleration techniques to allow fast MR imaging. For the last two decades, one of the most important breakthroughs in this direction is the introduction of compressed sensing (CS) that allows accurate reconstruction from sparsely sampled k-space data. The recent FDA approval of compressed sensing products for clinical scans clearly reflect the maturity of this technology. Therefore, this paper reviews the basic idea of CS and how this technology have been evolved for various MR imaging problems.

Model-based reconstruction framework for correction of signal pile-up and geometric distortions in prostate diffusion MRI

PURPOSE

Prostate diffusion-weighted MRI scans can suffer from geometric distortions, signal pileup, and signal dropout attributed to differences in tissue susceptibility values at the interface between the prostate and rectal air. The aim of this work is to present and validate a novel model based reconstruction method that can correct for these distortions.

METHODS

In regions of severe signal pileup, standard techniques for distortion correction have difficulty recovering the underlying true signal. Furthermore, because of drifts and inaccuracies in the determination of center frequency, echo planar imaging (EPI) scans can be shifted in the phase-encoding direction. In this work, using a B0 field map and a set of EPI data acquired with blip-up and blip-down phase encoding gradients, we model the distortion correction problem linking the distortion-free image to the acquired raw corrupted k-space data and solve it in a manner analogous to the sensitivity encoding method. Both a quantitative and qualitative assessment of the proposed method is performed in vivo in 10 patients.

RESULTS

Without distortion correction, mean Dice similarity scores between a reference T2W and the uncorrected EPI images were 0.64 and 0.60 for b-values of 0 and 500 s/mm2 , respectively. Compared to the Topup (distortion correction method commonly used for neuro imaging), the proposed method achieved Dice scores (0.87 and 0.85 versus 0.82 and 0.80) and better qualitative results in patients where signal pileup was present because of high rectal gas residue.

CONCLUSION

Model-based reconstruction can be used for distortion correction in prostate diffusion MRI.

Efficient Dynamic Parallel MRI Reconstruction for the Low-Rank Plus Sparse Model

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of under-sampled dynamic parallel magnetic resonance imaging (MRI) data. Solving for the low-rank and the sparse components involves non-smooth composite convex optimization, and algorithms for this problem can be categorized into proximal gradient methods and variable splitting methods. This paper investigates new efficient algorithms for both schemes. While current proximal gradient techniques for the L+S model involve the classical iterative soft thresholding algorithm (ISTA), this paper considers two accelerated alternatives, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other with the recent proximal optimized gradient method (POGM). In the augmented Lagrangian (AL) framework, we propose an efficient variable splitting scheme based on the form of the data acquisition operator, leading to simpler computation than the conjugate gradient (CG) approach required by existing AL methods. Numerical results suggest faster convergence of the efficient implementations for both frameworks, with POGM providing the fastest convergence overall and the practical benefit of being free of algorithm tuning parameters.

Multi-modal synergistic PET and MR reconstruction using mutually weighted quadratic priors

PURPOSE

To propose a framework for synergistic reconstruction of PET-MR and multi-contrast MR data to improve the image quality obtained from noisy PET data and from undersampled MR data.

THEORY AND METHODS

Weighted quadratic priors were devised to preserve common boundaries between PET-MR images while reducing noise, PET Gibbs ringing, and MR undersampling artifacts. These priors are iteratively reweighted using normalized multi-modal Gaussian similarity kernels. Synergistic PET-MR reconstructions were built on the PET maximum a posteriori expectation maximization algorithm and the MR regularized sensitivity encoding method. The proposed approach was compared to conventional methods, total variation, and prior-image weighted quadratic regularization methods. Comparisons were performed on a simulated [18 F]fluorodeoxyglucose-PET and T1 /T2 -weighted MR brain phantom, 2 in vivo T1 /T2 -weighted MR brain datasets, and an in vivo [18 F]fluorodeoxyglucose-PET and fluid-attenuated inversion recovery/T1 -weighted MR brain dataset.

RESULTS

Simulations showed that synergistic reconstructions achieve the lowest quantification errors for all image modalities compared to conventional, total variation, and weighted quadratic methods. Whereas total variation regularization preserved modality-unique features, this method failed to recover PET details and was not able to reduce MR artifacts compared to our proposed method. For in vivo MR data, our method maintained similar image quality for 3× and 14× accelerated data. Reconstruction of the PET-MR dataset also demonstrated improved performance of our method compared to the conventional independent methods in terms of reduced Gibbs and undersampling artifacts.

CONCLUSION

The proposed methodology offers a robust multi-modal synergistic image reconstruction framework that can be readily built on existing established algorithms.

Accelerated free-breathing 3D T1ρ cardiovascular magnetic resonance using multicoil compressed sensing

BACKGROUND

Endogenous contrast T1ρ cardiovascular magnetic resonance (CMR) can detect scar or infiltrative fibrosis in patients with ischemic or non-ischemic cardiomyopathy. Existing 2D T1ρ techniques have limited spatial coverage or require multiple breath-holds. The purpose of this project was to develop an accelerated, free-breathing 3D T1ρ mapping sequence with whole left ventricle coverage using a multicoil, compressed sensing (CS) reconstruction technique for rapid reconstruction of undersampled k-space data.

METHODS

We developed a cardiac- and respiratory-gated, free-breathing 3D T1ρ sequence and acquired data using a variable-density k-space sampling pattern (A = 3). The effect of the transient magnetization trajectory, incomplete recovery of magnetization between T1ρ-preparations (heart rate dependence), and k-space sampling pattern on T1ρ relaxation time error and edge blurring was analyzed using Bloch simulations for normal and chronically infarcted myocardium. Sequence accuracy and repeatability was evaluated using MnCl2 phantoms with different T1ρ relaxation times and compared to 2D measurements. We further assessed accuracy and repeatability in healthy subjects and compared these results to 2D breath-held measurements.

RESULTS

The error in T1ρ due to incomplete recovery of magnetization between T1ρ-preparations was T1ρhealthy = 6.1% and T1ρinfarct = 10.8% at 60 bpm and T1ρhealthy = 13.2% and T1ρinfarct = 19.6% at 90 bpm. At a heart rate of 60 bpm, error from the combined effects of readout-dependent magnetization transients, k-space undersampling and reordering was T1ρhealthy = 12.6% and T1ρinfarct = 5.8%. CS reconstructions had improved edge sharpness (blur metric = 0.15) compared to inverse Fourier transform reconstructions (blur metric = 0.48). There was strong agreement between the mean T1ρ estimated from the 2D and accelerated 3D data (R2 = 0.99; P < 0.05) acquired on the MnCl2 phantoms. The mean R1ρ estimated from the accelerated 3D sequence was highly correlated with MnCl2 concentration (R2 = 0.99; P < 0.05). 3D T1ρ acquisitions were successful in all human subjects. There was no significant bias between undersampled 3D T1ρ and breath-held 2D T1ρ (mean bias = 0.87) and the measurements had good repeatability (COV2D = 6.4% and COV3D = 7.1%).

CONCLUSIONS

This is the first report of an accelerated, free-breathing 3D T1ρ mapping of the left ventricle. This technique may improve non-contrast myocardial tissue characterization in patients with heart disease in a scan time appropriate for patients.

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.

Simultaneous multi slice (SMS) balanced steady state free precession first-pass myocardial perfusion cardiovascular magnetic resonance with iterative reconstruction at 1.5 T

BACKGROUND

Simultaneous-Multi-Slice (SMS) perfusion imaging has the potential to acquire multiple slices, increasing myocardial coverage without sacrificing in-plane spatial resolution. To maximise signal-to-noise ratio (SNR), SMS can be combined with a balanced steady state free precession (bSSFP) readout. Furthermore, application of gradient-controlled local Larmor adjustment (GC-LOLA) can ensure robustness against off-resonance artifacts and SNR loss can be mitigated by applying iterative reconstruction with spatial and temporal regularisation. The objective of this study was to compare cardiovascular magnetic resonance (CMR) myocardial perfusion imaging using SMS bSSFP imaging with GC-LOLA and iterative reconstruction to 3 slice bSSFP.

METHODS

Two contrast-enhanced rest perfusion sequences were acquired in random order in 8 patients: 6-slice SMS bSSFP and 3 slice bSSFP. All images were reconstructed with TGRAPPA. SMS images were also reconstructed using a non-linear iterative reconstruction with L1 regularisation in wavelet space (SMS-iter) with 7 different combinations for spatial (λσ) and temporal (λτ) regularisation parameters. Qualitative ratings of overall image quality (0 = poor image quality, 1 = major artifact, 2 = minor artifact, 3 = excellent), perceived SNR (0 = poor SNR, 1 = major noise, 2 = minor noise, 3 = high SNR), frequency of sequence related artifacts and patient related artifacts were undertaken. Quantitative analysis of contrast ratio (CR) and percentage of dark rim artifact (DRA) was performed.

RESULTS

Among all SMS-iter reconstructions, SMS-iter 6 (λσ 0.001 λτ 0.005) was identified as the optimal reconstruction with the highest overall image quality, least sequence related artifact and higher perceived SNR. SMS-iter 6 had superior overall image quality (2.50 ± 0.53 vs 1.50 ± 0.53, p = 0.005) and perceived SNR (2.25 ± 0.46 vs 0.75 ± 0.46, p = 0.010) compared to 3 slice bSSFP. There were no significant differences in sequence related artifact, CR (3.62 ± 0.39 vs 3.66 ± 0.65, p = 0.88) or percentage of DRA (5.25 ± 6.56 vs 4.25 ± 4.30, p = 0.64) with SMS-iter 6 compared to 3 slice bSSFP.

CONCLUSIONS

SMS bSSFP with GC-LOLA and iterative reconstruction improved image quality compared to a 3 slice bSSFP with doubled spatial coverage and preserved in-plane spatial resolution. Future evaluation in patients with coronary artery disease is warranted.

Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting

High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times. Here we present a novel compressed sensing (CS) reconstruction approach using shearlets as a sparsifying transform allowing for fast 3D CMR (3DShearCS) using 3D radial phase encoding (RPE). An iterative reweighting scheme was applied during image reconstruction to ensure fast convergence and high image quality. Shearlets are mathematically optimal for a simplified model of natural images and have been proven to be more efficient than classical systems such as wavelets. 3DShearCS was compared to three other commonly used reconstruction approaches. Image quality was assessed quantitatively using general image quality metrics and using clinical diagnostic scores from expert reviewers. The proposed technique had lower relative errors, higher structural similarity and higher diagnostic scores compared to the other reconstruction techniques especially for high undersampling factors, i.e. short scan times. 3DShearCS provided ensured accurate depiction of cardiac anatomy for fast imaging and could help to promote 3D high-resolution CMR in clinical practice.

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.

Simultaneous multislice magnetic resonance fingerprinting with low-rank and subspace modeling

Magnetic resonance fingerprinting (MRF) is a new quantitative imaging paradigm that enables simultaneous acquisition of multiple magnetic resonance tissue parameters (e.g., T₁, T₂, and spin density). Recently, MRF has been integrated with simultaneous multislice (SMS) acquisitions to enable volumetric imaging with faster scan time. In this paper, we present a new image reconstruction method based on low-rank and subspace modeling for improved SMS-MRF. Here the low-rank model exploits strong spatiotemporal correlation among contrast-weighted images, while the subspace model captures the temporal evolution of magnetization dynamics. With the proposed model, the image reconstruction problem is formulated as a convex optimization problem, for which we develop an algorithm based on variable splitting and the alternating direction method of multipliers. The performance of the proposed method has been evaluated by numerical experiments, and the results demonstrate that the proposed method leads to improved accuracy over the conventional approach. Practically, the proposed method has a potential to allow for a 3× speedup with minimal reconstruction error, resulting in less than 5 sec imaging time per slice.

Fast iteratively reweighted least squares algorithms for analysis-based sparse reconstruction

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation (TV) regularization. The proposed algorithm is based on the iterative reweighted least squares (IRLS) framework, and is accelerated by the preconditioned conjugate gradient method. The proposed method is motivated by that, the Hessian matrix for many applications is diagonally dominant. The convergence rate of the proposed algorithm is empirically shown to be almost the same as that of the traditional IRLS algorithms, that is, linear convergence. Moreover, with the specifically devised preconditioner, the computational cost for the subproblem is significantly less than that of traditional IRLS algorithms, which enables our approach to handle large scale problems. In addition to the fast convergence, it is straightforward to apply our method to standard sparsity, group sparsity, overlapping group sparsity and TV based problems. Experiments are conducted on practical applications of compressive sensing magnetic resonance imaging. Extensive results demonstrate that the proposed algorithm achieves superior performance over 14 state-of-the-art algorithms in terms of both accuracy and computational cost.

A multi-band double-inversion radial fast spin-echo technique for T2 cardiovascular magnetic resonance mapping of the heart

BACKGROUND

Double inversion recovery (DIR) fast spin-echo (FSE) cardiovascular magnetic resonance (CMR) sequences are used clinically for black-blood T2-weighted imaging. However, these sequences suffer from slice inefficiency due to the non-selective inversion pulses. We propose a multi-band (MB) encoded DIR radial FSE (MB-DIR-RADFSE) technique to simultaneously excite two slices. This sequence has improved signal-to-noise ratio per unit time compared to a single slice excitation. It is also motion robust and enables the reconstruction of high-resolution black-blood T2-weighted images and T2 maps for the excited slices.

METHODS

Hadamard encoded MB pulses were used in MB-DIR-RADFSE to simultaneously excite two slices. A principal component based iterative reconstruction was used to jointly reconstruct black-blood T2-weighted images and T2 maps. Phantom and in vivo experiments were performed to evaluate T2 mapping performance and results were compared to a T2-prepared balanced steady state free precession (bSSFP) method. The inter-segment variability of the T2 maps were assessed using data acquired on healthy subjects. A reproducibility study was performed to evaluate reproducibility of the proposed technique.

RESULTS

Phantom experiments show that the T2 values estimated from MB-DIR-RADFSE are comparable to the spin-echo based reference, while T2-prepared bSSFP over-estimated T2 values. The relative contrast of the black-blood images from the multi-band scheme was comparable to those from a single slice acquisition. The myocardial segment analysis on 8 healthy subjects indicated a significant difference (p-value < 0.01) in the T2 estimates from the apical slice when compared to the mid-ventricular slice. The mean T2 estimate from 12 subjects obtained using T2-prepared bSSFP was significantly higher (p-value = 0.012) compared to MB-DIR-RADFSE, consistent with the phantom results. The Bland-Altman analysis showed excellent reproducibility between the MB-DIR-RADFSE measurements, with a mean T2 difference of 0.12 ms and coefficient of reproducibility of 2.07 in 15 clinical subjects. The utility of this technique is demonstrated in two subjects where the T2 maps show elevated values in regions of pathology.

CONCLUSIONS

The use of multi-band pulses for excitation improves the slice efficiency of the double inversion fast spin-echo pulse sequence. The use of a radial trajectory and a joint reconstruction framework allows reconstruction of TE images and T2 maps for the excited slices.

CNN-Based Projected Gradient Descent for Consistent CT Image Reconstruction

We present a new image reconstruction method that replaces the projector in a projected gradient descent (PGD) with a convolutional neural network (CNN). Recently, CNNs trained as image-to-image regressors have been successfully used to solve inverse problems in imaging. However, unlike existing iterative image reconstruction algorithms, these CNN-based approaches usually lack a feedback mechanism to enforce that the reconstructed image is consistent with the measurements. We propose a relaxed version of PGD wherein gradient descent enforces measurement consistency, while a CNN recursively projects the solution closer to the space of desired reconstruction images. We show that this algorithm is guaranteed to converge and, under certain conditions, converges to a local minimum of a non-convex inverse problem. Finally, we propose a simple scheme to train the CNN to act like a projector. Our experiments on sparse-view computed-tomography reconstruction show an improvement over total variation-based regularization, dictionary learning, and a state-of-the-art deep learning-based direct reconstruction technique.

Sparse and Low-Rank Decomposition of a Hankel Structured Matrix for Impulse Noise Removal

Recently, the annihilating filter-based low-rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting method. Based on the observation that smoothness or textures within an image patch correspond to sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the associated rank-deficient Hankel matrices in an image domain to estimate any missing pixels. By extending this idea, we propose a novel impulse-noise removal algorithm that uses the sparse and low-rank decomposition of a Hankel structured matrix. This method, referred to as the robust ALOHA, is based on the observation that an image corrupted with the impulse noise has intact pixels; consequently, the impulse noise can be modeled as sparse components, whereas the underlying image can still be modeled using a low-rank Hankel structured matrix. To solve the sparse and low-rank matrix decomposition problem, we propose an alternating direction method of multiplier approach, with initial factorized matrices coming from a low-rank matrix-fitting algorithm. To adapt local image statistics that have distinct spectral distributions, the robust ALOHA is applied in a patch-by-patch manner. Experimental results from impulse noise for both single-channel and multichannel color images demonstrate that the robust ALOHA is superior to existing approaches, especially during the reconstruction of complex texture patterns.

Fast nonlinear susceptibility inversion with variational regularization

PURPOSE

Quantitative susceptibility mapping can be performed through the minimization of a function consisting of data fidelity and regularization terms. For data consistency, a Gaussian-phase noise distribution is often assumed, which breaks down when the signal-to-noise ratio is low. A previously proposed alternative is to use a nonlinear data fidelity term, which reduces streaking artifacts, mitigates noise amplification, and results in more accurate susceptibility estimates. We hereby present a novel algorithm that solves the nonlinear functional while achieving computation speeds comparable to those for a linear formulation.

METHODS

We developed a nonlinear quantitative susceptibility mapping algorithm (fast nonlinear susceptibility inversion) based on the variable splitting and alternating direction method of multipliers, in which the problem is split into simpler subproblems with closed-form solutions and a decoupled nonlinear inversion hereby solved with a Newton-Raphson iterative procedure. Fast nonlinear susceptibility inversion performance was assessed using numerical phantom and in vivo experiments, and was compared against the nonlinear morphology-enabled dipole inversion method.

RESULTS

Fast nonlinear susceptibility inversion achieves similar accuracy to nonlinear morphology-enabled dipole inversion but with significantly improved computational efficiency.

CONCLUSION

The proposed method enables accurate reconstructions in a fraction of the time required by state-of-the-art quantitative susceptibility mapping methods. Magn Reson Med 80:814-821, 2018. © 2018 International Society for Magnetic Resonance in Medicine.