Fast reconstruction for multichannel compressed sensing using a hierarchically semiseparable solver

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.

Knowledge Based Versus Data Based: A Historical Perspective on a Continuum of Methodologies for Medical Image Analysis

The advent of big data and deep learning algorithms has promoted a major shift toward data-driven methods in medical image analysis recently. However, the medical image analysis field has a long and rich history inclusive of both knowledge-driven and data-driven methodologies. In the present article, we provide a historical review of an illustrative sample of medical image analysis methods and locate them along a knowledge-driven versus data-driven continuum. In doing so, we highlight the historical importance as well as current-day relevance of more traditional, knowledge-based artificial intelligence approaches and their complementarity with fully data-driven techniques such as deep learning.

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 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.

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.

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple MR tissue parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization.

A Novel Compressed Sensing Method for Magnetic Resonance Imaging: Exponential Wavelet Iterative Shrinkage-Thresholding Algorithm with Random Shift

Aim. It can help improve the hospital throughput to accelerate magnetic resonance imaging (MRI) scanning. Patients will benefit from less waiting time. Task. In the last decade, various rapid MRI techniques on the basis of compressed sensing (CS) were proposed. However, both computation time and reconstruction quality of traditional CS-MRI did not meet the requirement of clinical use. Method. In this study, a novel method was proposed with the name of exponential wavelet iterative shrinkage-thresholding algorithm with random shift (abbreviated as EWISTARS). It is composed of three successful components: (i) exponential wavelet transform, (ii) iterative shrinkage-thresholding algorithm, and (iii) random shift. Results. Experimental results validated that, compared to state-of-the-art approaches, EWISTARS obtained the least mean absolute error, the least mean-squared error, and the highest peak signal-to-noise ratio. Conclusion. EWISTARS is superior to state-of-the-art approaches.

A review of 3D first-pass, whole-heart, myocardial perfusion cardiovascular magnetic resonance

A comprehensive review is undertaken of the methods available for 3D whole-heart first-pass perfusion (FPP) and their application to date, with particular focus on possible acceleration techniques. Following a summary of the parameters typically desired of 3D FPP methods, the review explains the mechanisms of key acceleration techniques and their potential use in FPP for attaining 3D acquisitions. The mechanisms include rapid sequences, non-Cartesian k-space trajectories, reduced k-space acquisitions, parallel imaging reconstructions and compressed sensing. An attempt is made to explain, rather than simply state, the varying methods with the hope that it will give an appreciation of the different components making up a 3D FPP protocol. Basic estimates demonstrating the required total acceleration factors in typical 3D FPP cases are included, providing context for the extent that each acceleration method can contribute to the required imaging speed, as well as potential limitations in present 3D FPP literature. Although many 3D FPP methods are too early in development for the type of clinical trials required to show any clear benefit over current 2D FPP methods, the review includes the small but growing quantity of clinical research work already using 3D FPP, alongside the more technical work. Broader challenges concerning FPP such as quantitative analysis are not covered, but challenges with particular impact on 3D FPP methods, particularly with regards to motion effects, are discussed along with anticipated future work in the field.

Real diffusion-weighted MRI enabling true signal averaging and increased diffusion contrast

This project aims to characterize the impact of underlying noise distributions on diffusion-weighted imaging. The noise floor is a well-known problem for traditional magnitude-based diffusion-weighted MRI (dMRI) data, leading to biased diffusion model fits and inaccurate signal averaging. Here, we introduce a total-variation-based algorithm to eliminate shot-to-shot phase variations of complex-valued diffusion data with the intention to extract real-valued dMRI datasets. The obtained real-valued diffusion data are no longer superimposed by a noise floor but instead by a zero-mean Gaussian noise distribution, yielding dMRI data without signal bias. We acquired high-resolution dMRI data with strong diffusion weighting and, thus, low signal-to-noise ratio. Both the extracted real-valued and traditional magnitude data were compared regarding signal averaging, diffusion model fitting and accuracy in resolving crossing fibers. Our results clearly indicate that real-valued diffusion data enables idealized conditions for signal averaging. Furthermore, the proposed method enables unbiased use of widely employed linear least squares estimators for model fitting and demonstrates an increased sensitivity to detect secondary fiber directions with reduced angular error. The use of phase-corrected, real-valued data for dMRI will therefore help to clear the way for more detailed and accurate studies of white matter microstructure and structural connectivity on a fine scale.

RARE/turbo spin echo imaging with Simultaneous Multislice Wave-CAIPI

PURPOSE

To enable highly accelerated RARE/Turbo Spin Echo (TSE) imaging using Simultaneous MultiSlice (SMS) Wave-CAIPI acquisition with reduced g-factor penalty.

METHODS

SMS Wave-CAIPI incurs slice shifts across simultaneously excited slices while playing sinusoidal gradient waveforms during the readout of each encoding line. This results in an efficient k-space coverage that spreads aliasing in all three dimensions to fully harness the encoding power of coil sensitivities. The novel MultiPINS radiofrequency (RF) pulses dramatically reduce the power deposition of multiband (MB) refocusing pulse, thus allowing high MB factors within the Specific Absorption Rate (SAR) limit.

RESULTS

Wave-CAIPI acquisition with MultiPINS permits whole brain coverage with 1 mm isotropic resolution in 70 s at effective MB factor 13, with maximum and average g-factor penalties of gmax  = 1.34 and gavg  = 1.12, and without √R penalty. With blipped-CAIPI, the g-factor performance was degraded to gmax  = 3.24 and gavg  = 1.42; a 2.4-fold increase in gmax relative to Wave-CAIPI. At this MB factor, the SAR of the MultiBand and PINS pulses are 4.2 and 1.9 times that of the MultiPINS pulse, while the peak RF power are 19.4 and 3.9 times higher.

CONCLUSION

Combination of the two technologies, Wave-CAIPI and MultiPINS pulse, enables highly accelerated RARE/TSE imaging with low SNR penalty at reduced SAR.

Fast iterative algorithm for the reconstruction of multishot non-cartesian diffusion data

PURPOSE

To accelerate the motion-compensated iterative reconstruction of multishot non-Cartesian diffusion data.

METHOD

The motion-compensated recovery of multishot non-Cartesian diffusion data is often performed using a modified iterative sensitivity-encoded algorithm. Specifically, the encoding matrix is replaced with a combination of nonuniform Fourier transforms and composite sensitivity functions, which account for the motion-induced phase errors. The main challenge with this scheme is the significantly increased computational complexity, which is directly related to the total number of composite sensitivity functions (number of shots × number of coils). The dimensionality of the composite sensitivity functions and hence the number of Fourier transforms within each iteration is reduced using a principal component analysis-based scheme. Using a Toeplitz-based conjugate gradient approach in combination with an augmented Lagrangian optimization scheme, a fast algorithm is proposed for the sparse recovery of diffusion data.

RESULTS

The proposed simplifications considerably reduce the computation time, especially in the recovery of diffusion data from under-sampled reconstructions using sparse optimization. By choosing appropriate number of basis functions to approximate the composite sensitivities, faster reconstruction (close to 9 times) with effective motion compensation is achieved.

CONCLUSION

The proposed enhancements can offer fast motion-compensated reconstruction of multishot diffusion data for arbitrary k-space trajectories.

Accelerated 1 H MRSI using randomly undersampled spiral-based k-space trajectories

PURPOSE

To develop and evaluate the performance of an acquisition and reconstruction method for accelerated MR spectroscopic imaging (MRSI) through undersampling of spiral trajectories.

THEORY AND METHODS

A randomly undersampled spiral acquisition and sensitivity encoding (SENSE) with total variation (TV) regularization, random SENSE+TV, is developed and evaluated on single-slice numerical phantom, in vivo single-slice MRSI, and in vivo three-dimensional (3D)-MRSI at 3 Tesla. Random SENSE+TV was compared with five alternative methods for accelerated MRSI.

RESULTS

For the in vivo single-slice MRSI, random SENSE+TV yields up to 2.7 and 2 times reduction in root-mean-square error (RMSE) of reconstructed N-acetyl aspartate (NAA), creatine, and choline maps, compared with the denoised fully sampled and uniformly undersampled SENSE+TV methods with the same acquisition time, respectively. For the in vivo 3D-MRSI, random SENSE+TV yields up to 1.6 times reduction in RMSE, compared with uniform SENSE+TV. Furthermore, by using random SENSE+TV, we have demonstrated on the in vivo single-slice and 3D-MRSI that acceleration factors of 4.5 and 4 are achievable with the same quality as the fully sampled data, as measured by RMSE of reconstructed NAA map, respectively.

CONCLUSION

With the same scan time, random SENSE+TV yields lower RMSEs of metabolite maps than other methods evaluated. Random SENSE+TV achieves up to 4.5-fold acceleration with comparable data quality as the fully sampled acquisition. Magn Reson Med 74:13-24, 2015. © 2014 Wiley Periodicals, Inc.