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Purpose: Recent studies have witnessed that self-attention modules can better solve the vision understanding problems by capturing long-range dependencies. However, there are very few works designing a lightweight self-attention module to improve the quality of MRI reconstruction. Furthermore, it can be observed that several important self-attention modules (e.g., the non-local block) cause high computational complexity and need a huge number of GPU memory when the size of the input feature is large. The purpose of this study is to design a lightweight yet effective spatial orthogonal attention module (SOAM) to capture long-range dependencies, and develop a novel spatial orthogonal attention generative adversarial network, termed as SOGAN, to achieve more accurate MRI reconstruction., Methods: We first develop a lightweight SOAM, which can generate two small attention maps to effectively aggregate the long-range contextual information in vertical and horizontal directions, respectively. Then, we embed the proposed SOAMs into the concatenated convolutional autoencoders to form the generator of the proposed SOGAN., Results: The experimental results demonstrate that the proposed SOAMs improve the quality of the reconstructed MR images effectively by capturing long-range dependencies. Besides, compared with state-of-the-art deep learning-based CS-MRI methods, the proposed SOGAN reconstructs MR images more accurately, but with fewer model parameters., Conclusions: The proposed SOAM is a lightweight yet effective self-attention module to capture long-range dependencies, thus, can improve the quality of MRI reconstruction to a large extent. Besides, with the help of SOAMs, the proposed SOGAN outperforms the state-of-the-art deep learning-based CS-MRI methods., (© 2020 American Association of Physicists in Medicine.)

Low-rank structure is a powerful priori characteristic that is exploited in constrained magnetic resonance imaging (MRI). In this paper, we build two low rank matrices T V and T H from weighted k-space data according to the duality between the sparsity in the difference image and the low-rankness of a reciprocal spectral domain. Then, we propose a two-step constrained MR image reconstruction method. First, the vertical and horizontal difference images are recovered via enforcing low-rankness of matrices T V and T H . Then, the image is reconstructed via the least squares method. In the first step, the nuclear norm of a matrix is replaced by the minimum Frobenius norm of two factorization matrices and the alternating direction method of multipliers (ADMM) algorithm is applied to recover the difference images. This singular value decomposition (SVD) free method leads to fast reconstruction. The experimental results demonstrate that the proposed method outperforms other low rank based methods., (Copyright © 2019 Elsevier Inc. All rights reserved.)

The analysis model has been previously exploited as an alternative to the classical sparse synthesis model for designing image reconstruction methods. Applying a suitable analysis operator on the image of interest yields a cosparse outcome which enables us to reconstruct the image from undersampled data. In this work, we introduce additional prior in the analysis context and theoretically study the uniqueness issues in terms of analysis operators in general position and the specific 2D finite difference operator. We establish bounds on the minimum measurement numbers which are lower than those in cases without using analysis model prior. Based on the idea of iterative cosupport detection (ICD), we develop a novel image reconstruction model and an effective algorithm, achieving significantly better reconstruction performance. Simulation results on synthetic and practical magnetic resonance (MR) images are also shown to illustrate our theoretical claims.

This work aims to develop a novel magnetic resonance (MR) image reconstruction approach motivated by the recently proposed sampling framework with union-of-subspaces model (SUoS). Based on SUoS, we propose a mathematical formalism that effectively integrates a block sparsity constraint and support information which is estimated in an iterative fashion. The resulting optimization problem consists of a data fidelity term and a support detection based block sparsity (SDBS) promoting term penalizing entries within the complement of the estimated support. We provide optional strategies for block assignment, and we also derive unique and robust recovery conditions in terms of the structured restricted isometric property (RIP), namely the block-RIP. The block-RIP constant we derive is lower than that of the previous structured sparse method, which leads to a reduction of the measurements. Simulation results for reconstructing individual and multiple T1/T2-weighted images demonstrate the consistency with our theoretical claims, and show considerable improvement in comparison with methods using only block sparsity or support information., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Compressed sensing (CS) based methods make it possible to reconstruct magnetic resonance (MR) images from undersampled measurements, which is known as CS-MRI. The reference-driven CS-MRI reconstruction schemes can further decrease the sampling ratio by exploiting the sparsity of the difference image between the target and the reference MR images in pixel domain. Unfortunately existing methods do not work well given that contrast changes are incorrectly estimated or motion compensation is inaccurate. In this paper, we propose to reconstruct MR images by utilizing the sparsity of the difference image between the target and the motion-compensated reference images in wavelet transform and gradient domains. The idea is attractive because it requires neither the estimation of the contrast changes nor multiple times motion compensations. In addition, we apply total generalized variation (TGV) regularization to eliminate the staircasing artifacts caused by conventional total variation (TV). Fast composite splitting algorithm (FCSA) is used to solve the proposed reconstruction problem in order to improve computational efficiency. Experimental results demonstrate that the proposed method can not only reduce the computational cost but also decrease sampling ratio or improve the reconstruction quality alternatively.