Sparse BLIP: BLind Iterative Parallel imaging reconstruction using compressed sensing

IMJENSE: Scan-Specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space measurements to the desired MRI image. Despite the success of many existing reconstruction algorithms, it remains a challenge to reliably reconstruct a high-quality image from highly reduced k-space measurements. Recently, implicit neural representation has emerged as a powerful paradigm to exploit the internal information and the physics of partially acquired data to generate the desired object. In this study, we introduced IMJENSE, a scan-specific implicit neural representation-based method for improving parallel MRI reconstruction. Specifically, the underlying MRI image and coil sensitivities were modeled as continuous functions of spatial coordinates, parameterized by neural networks and polynomials, respectively. The weights in the networks and coefficients in the polynomials were simultaneously learned directly from sparsely acquired k-space measurements, without fully sampled ground truth data for training. Benefiting from the powerful continuous representation and joint estimation of the MRI image and coil sensitivities, IMJENSE outperforms conventional image or k-space domain reconstruction algorithms. With extremely limited calibration data, IMJENSE is more stable than supervised calibrationless and calibration-based deep-learning methods. Results show that IMJENSE robustly reconstructs the images acquired at 5× and 6× accelerations with only 4 or 8 calibration lines in 2D Cartesian acquisitions, corresponding to 22.0% and 19.5% undersampling rates. The high-quality results and scanning specificity make the proposed method hold the potential for further accelerating the data acquisition of parallel MRI.

Equilibrated Zeroth-Order Unrolled Deep Network for Parallel MR Imaging

In recent times, model-driven deep learning has evolved an iterative algorithm into a cascade network by replacing the regularizer's first-order information, such as the (sub)gradient or proximal operator, with a network module. This approach offers greater explainability and predictability compared to typical data-driven networks. However, in theory, there is no assurance that a functional regularizer exists whose first-order information matches the substituted network module. This implies that the unrolled network output may not align with the regularization models. Furthermore, there are few established theories that guarantee global convergence and robustness (regularity) of unrolled networks under practical assumptions. To address this gap, we propose a safeguarded methodology for network unrolling. Specifically, for parallel MR imaging, we unroll a zeroth-order algorithm, where the network module serves as a regularizer itself, allowing the network output to be covered by a regularization model. Additionally, inspired by deep equilibrium models, we conduct the unrolled network before backpropagation to converge to a fixed point and then demonstrate that it can tightly approximate the actual MR image. We also prove that the proposed network is robust against noisy interferences if the measurement data contain noise. Finally, numerical experiments indicate that the proposed network consistently outperforms state-of-the-art MRI reconstruction methods, including traditional regularization and unrolled deep learning techniques.

JSENSE-Pro: Joint sensitivity estimation and image reconstruction in parallel imaging using pre-learned subspaces of coil sensitivity functions

PURPOSE

To improve calibrationless parallel imaging using pre-learned subspaces of coil sensitivity functions.

THEORY AND METHODS

A subspace-based joint sensitivity estimation and image reconstruction method was developed for improved parallel imaging with no calibration data. Specifically, we proposed to use a probabilistic subspace model to capture prior information of the coil sensitivity functions from previous scans acquired using the same receiver system. Both the subspace basis and coefficient distributions were learned from a small set of training data. The learned subspace model was then incorporated into the regularized reconstruction formalism that includes a sparsity prior. The nonlinear optimization problem was solved using alternating minimization algorithm. Public fastMRI brain dataset was retrospectively undersampled by different schemes for performance evaluation of the proposed method.

RESULTS

With no calibration data, the proposed method consistently produced the most accurate coil sensitivity estimation and highest quality image reconstructions at all acceleration factors tested in comparison with state-of-the-art methods including JSENSE, DeepSENSE, P-LORAKS, and Sparse BLIP. Our results are comparable to or even better than those from SparseSENSE, which used calibration data for sensitivity estimation. The work also demonstrated that the probabilistic subspace model learned from T₂ w data can be generalized to aiding the reconstruction of FLAIR data acquired from the same receiver system.

CONCLUSION

A subspace-based method named JSENSE-Pro has been proposed for accelerated parallel imaging without the acquisition of companion calibration data. The method is expected to further enhance the practical utility of parallel imaging, especially in applications where calibration data acquisition is not desirable or limited.

Multi-channel GAN-based calibration-free diffusion-weighted liver imaging with simultaneous coil sensitivity estimation and reconstruction

Introduction

Diffusion-weighted imaging (DWI) with parallel reconstruction may suffer from a mismatch between the coil calibration scan and imaging scan due to motions, especially for abdominal imaging.

Methods

This study aimed to construct an iterative multichannel generative adversarial network (iMCGAN)-based framework for simultaneous sensitivity map estimation and calibration-free image reconstruction. The study included 106 healthy volunteers and 10 patients with tumors.

Results

The performance of iMCGAN was evaluated in healthy participants and patients and compared with the SAKE, ALOHA-net, and DeepcomplexMRI reconstructions. The peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), root mean squared error (RMSE), and histograms of apparent diffusion coefficient (ADC) maps were calculated for assessing image qualities. The proposed iMCGAN outperformed the other methods in terms of the PSNR (iMCGAN: 41.82 ± 2.14; SAKE: 17.38 ± 1.78; ALOHA-net: 20.43 ± 2.11 and DeepcomplexMRI: 39.78 ± 2.78) for b = 800 DWI with an acceleration factor of 4. Besides, the ghosting artifacts in the SENSE due to the mismatch between the DW image and the sensitivity maps were avoided using the iMCGAN model.

Discussion

The current model iteratively refined the sensitivity maps and the reconstructed images without additional acquisitions. Thus, the quality of the reconstructed image was improved, and the aliasing artifact was alleviated when motions occurred during the imaging procedure.

Comparison of compressed sensing and controlled aliasing in parallel imaging acceleration for 3D magnetic resonance imaging for radiotherapy preparation

Magnetic resonance imaging (MRI) for radiotherapy is often based on 3D acquisitions, but suffers from low signal-to-noise ratio due to immobilization device and flexible coil use. The aim of this study was to investigate if Compressed Sensing (CS) improves image quality for 3D Turbo Spin Echo acquisitions compared with Controlled Aliasing k-space-based parallel imaging in equivalent acquisition time for intracranial T1, T2-Fluid-Attenuated Inversion Recovery (FLAIR) and pelvic T2 imaging. Qualitative ratings suffered from large inter-rater variability. CS-T1 brain MRI was superior numerically and qualitatively. CS-T2-FLAIR brain MRI was numerically superior, but rater equivalent. CS-T2 pelvic MRI was equivalent without gain.

DeepSENSE: Learning coil sensitivity functions for SENSE reconstruction using deep learning

PURPOSE

To improve the estimation of coil sensitivity functions from limited auto-calibration signals (ACS) in SENSE-based reconstruction for brain imaging.

METHODS

We propose to use deep learning to estimate coil sensitivity functions by leveraging information from previous scans obtained using the same RF receiver system. Specifically, deep convolutional neural networks were designed to learn an end-to-end mapping from the initial sensitivity to the high-resolution counterpart. Sensitivity alignment was further proposed to reduce the geometric variation caused by different subject positions and imaging FOVs. Cross-validation with a small set of datasets was performed to validate the learned neural network. Iterative SENSE reconstruction was adopted to evaluate the utility of the sensitivity functions from the proposed and conventional methods.

RESULTS

The proposed method produced improved sensitivity estimates and SENSE reconstructions compared to the conventional methods in terms of aliasing and noise suppression with very limited ACS data. Cross-validation with a small set of data demonstrated the feasibility of learning coil sensitivity functions for brain imaging. The network learned on the spoiled GRE data can be applied to predict sensitivity functions for spin-echo and MPRAGE datasets.

CONCLUSION

A deep learning-based method has been proposed for improving the estimation of coil sensitivity functions. Experimental results have demonstrated the feasibility and potential of the proposed method for improving SENSE-based reconstructions especially when the ACS data are limited.

Highly accelerated submillimeter resolution 3D GRASE with controlled T 2 blurring in T 2 -weighted functional MRI at 7 Tesla: A feasibility study

PURPOSE

To achieve highly accelerated submillimeter resolution T 2 -weighted functional MRI at 7T by developing a three-dimensional gradient and spin echo imaging (GRASE) with inner-volume selection and variable flip angles (VFA).

METHODS

GRASE imaging has disadvantages in that (a) k-space modulation causes T 2 blurring by limiting the number of slices and (b) a VFA scheme results in partial success with substantial SNR loss. In this work, accelerated GRASE with controlled T 2 blurring is developed to improve a point spread function (PSF) and temporal signal-to-noise ratio (tSNR) with a large number of slices. To this end, the VFA scheme is designed by minimizing a trade-off between SNR and blurring for functional sensitivity, and a new GRASE-optimized random encoding, which takes into account the complex signal decays of T 2 and T 2 ∗ weightings, is proposed by achieving incoherent aliasing for constrained reconstruction. Numerical and experimental studies were performed to validate the effectiveness of the proposed method over regular and VFA GRASE (R- and V-GRASE).

RESULTS

The proposed method, while achieving 0.8 mm isotropic resolution, functional MRI compared to R- and V-GRASE improves the spatial extent of the excited volume up to 36 slices with 52%-68% full width at half maximum (FWHM) reduction in PSF but approximately 2- to 3-fold mean tSNR improvement, thus resulting in higher BOLD activations.

CONCLUSIONS

We successfully demonstrated the feasibility of the proposed method in T 2 -weighted functional MRI. The proposed method is especially promising for cortical layer-specific functional MRI.

Incorporating reference guided priors into calibrationless parallel imaging reconstruction

PURPOSE

To propose and evaluate a new calibrationless parallel imaging method aimed at further improving the reconstruction accuracy of the accelerated multi-channel MR images.

METHOD

We introduce a new calibrationless parallel imaging method. On top of exploiting joint sparsity cross channels of the target image to be reconstructed, it incorporates similar priors on the grey-level intensity and edge orientation, which both come from a high-spatial resolution reference image that can be easily obtained in many clinical MRI scenarios. The mixed l₂-l₁ norm is used to enforce joint sparsity and a multi-scale gradient operator is applied to extract fine edges from the reference image. Additionally, this optimization problem can be solved via a non-linear conjugate gradient algorithm with line search in this work.

RESULTS

The proposed method is compared with the existing state-of-the-art auto-calibration and calibrationless parallel imaging techniques. The experiments on different in-vivo brain MR datasets show that the proposed method has the superior performance in terms of both artifact suppression and detail preservation.

CONCLUSION

The reference guided calibrationless parallel imaging method can significantly improve the performance of joint reconstruction of target channel images. Even when the reduction factor is high, it can keep edge structures well.

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

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

Compressed sensing MRI reconstruction from 3D multichannel data using GPUs

PURPOSE

To accelerate iterative reconstructions of compressed sensing (CS) MRI from 3D multichannel data using graphics processing units (GPUs).

METHODS

The sparsity of MRI signals and parallel array receivers can reduce the data acquisition requirements. However, iterative CS reconstructions from data acquired using an array system may take a significantly long time, especially for a large number of parallel channels. This paper presents an efficient method for CS-MRI reconstruction from 3D multichannel data using GPUs. In this method, CS reconstructions were simultaneously processed in a channel-by-channel fashion on the GPU, in which the computations of multiple-channel 3D-CS reconstructions are highly parallelized. The final image was then produced by a sum-of-squares method on the central processing unit. Implementation details including algorithm, data/memory management, and parallelization schemes are reported in the paper.

RESULTS

Both simulated data and in vivo MRI array data were tested. The results showed that the proposed method can significantly improve the image reconstruction efficiency, typically shortening the runtime by a factor of 30.

CONCLUSIONS

Using low-cost GPUs and an efficient algorithm allowed the 3D multislice compressive-sensing reconstruction to be performed in less than 1 s. The rapid reconstructions are expected to help bring high-dimensional, multichannel parallel CS MRI closer to clinical applications. Magn Reson Med 78:2265-2274, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Optimization of Regularization Parameters in Compressed Sensing of Magnetic Resonance Angiography: Can Statistical Image Metrics Mimic Radiologists' Perception?

In Compressed Sensing (CS) of MRI, optimization of the regularization parameters is not a trivial task. We aimed to establish a method that could determine the optimal weights for regularization parameters in CS of time-of-flight MR angiography (TOF-MRA) by comparing various image metrics with radiologists' visual evaluation. TOF-MRA of a healthy volunteer was scanned using a 3T-MR system. Images were reconstructed by CS from retrospectively under-sampled data by varying the weights for the L1 norm of wavelet coefficients and that of total variation. The reconstructed images were evaluated both quantitatively by statistical image metrics including structural similarity (SSIM), scale invariant feature transform (SIFT) and contrast-to-noise ratio (CNR), and qualitatively by radiologists' scoring. The results of quantitative metrics and qualitative scorings were compared. SSIM and SIFT in conjunction with brain masks and CNR of artery-to-parenchyma correlated very well with radiologists' visual evaluation. By carefully selecting a region to measure, we have shown that statistical image metrics can reflect radiologists' visual evaluation, thus enabling an appropriate optimization of regularization parameters for CS.

Efficient Compressed Sensing SENSE pMRI Reconstruction With Joint Sparsity Promotion

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

P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data

PURPOSE

To propose and evaluate P-LORAKS a new calibrationless parallel imaging reconstruction framework.

THEORY AND METHODS

LORAKS is a flexible and powerful framework that was recently proposed for constrained MRI reconstruction. LORAKS was based on the observation that certain matrices constructed from fully sampled k-space data should have low rank whenever the image has limited support or smooth phase, and made it possible to accurately reconstruct images from undersampled or noisy data using low-rank regularization. This paper introduces P-LORAKS, which extends LORAKS to the context of parallel imaging. This is achieved by combining the LORAKS matrices from different channels to yield a larger but more parsimonious low-rank matrix model of parallel imaging data. This new model can be used to regularize the reconstruction of undersampled parallel imaging data, and implicitly imposes phase, support, and parallel imaging constraints without needing to calibrate phase, support, or sensitivity profiles.

RESULTS

The capabilities of P-LORAKS are evaluated with retrospectively undersampled data and compared against existing parallel MRI reconstruction methods. Results show that P-LORAKS can improve parallel imaging reconstruction quality, and can enable the use of new k-space trajectories that are not compatible with existing reconstruction methods.

CONCLUSION

The P-LORAKS framewok provides a new and effective way to regularize parallel imaging reconstruction.

Efficient compressed sensing SENSE parallel MRI reconstruction with joint sparsity promotion and mutual incoherence enhancement

Magnetic resonance imaging (MRI) is considered a key modality for the future as it offers several advantages, including the use of non-ionizing radiation and having no known side effects on the human body, and has recently begun to serve as a key component of multi-modal neuroimaging. However, two major intrinsic problems exist: slow acquisition and intrusive acoustic noise. Parallel MRI (pMRI) techniques accelerate acquisition by reducing the duration and coverage of conventional gradient encoding. The under-sampled k-space data is detected with several receiver coils surrounding the object, using distinct spatial encoding information for each coil element to reconstruct the image. However, this scanning remains slow compared to typical clinical imaging (e.g. X-ray CT). Compressed Sensing (CS), a sampling theory based on random sub-sampling, has potential to further reduce the sampling used in pMRI, accelerating acquisition further. In this work, we propose a new CS SENSE pMRI reconstruction model promoting joint sparsity across channels and enhancing mutual incoherence to improve reconstruction accuracy from limited k-space data. For fast image reconstruction and fair comparisons, all reconstructions are computed with split-Bregman and variable splitting techniques. Numerical results show that, with the introduced methods, reconstruction performance can be crucially improved with limited amount of k-space data.

Incorporating reference in parallel imaging and compressed sensing

PURPOSE

To develop a new compressed sensing parallel imaging technique called READ-PICS that can effectively incorporate prior information from a reference scan for MR image reconstruction from highly undersampled multichannel measurements.

METHODS

READ-PICS incorporates information from a high-spatial-resolution reference prior using the generalized series model, to achieve increased image sparsity and mitigated noise amplification simultaneously. To further improve the ill-conditioning of the parallel imaging system, an annular area in the central residual k-space is used for calibration. Additionally, the mixed L1-L2 norm of the coefficients from the prior component and residual component is used to enforce joint sparsity.

RESULTS

The evaluations on parametric imaging and multiscan experiment demonstrate superior performance of READ-PICS in terms of detail preservation and noise suppression compared to state-of-the-art technique, L1-Iterative self-consistent parallel imaging reconstruction, and prescan required method, correlation imaging.

CONCLUSIONS

The proposed method can significantly increase signal sparsity and improve the ill-conditioning of the parallel imaging system using reference adaptive regularization. This technique can be easily adapted to other imaging applications where multiple images need to be acquired sequentially and a reference prior is also available.