Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components

Abstract

Purpose To apply the low-rank plus sparse (L+S) matrix decomposition model to reconstruct undersampled dynamic MRI as a superposition of background and dynamic components in various problems of clinical interest. Theory and Methods The L+S model is natural to represent dynamic MRI data. Incoherence between k−t space (acquisition) and the singular vectors of L and the sparse domain of S is required to reconstruct undersampled data. Incoherence between L and S is required for robust separation of background and dynamic components. Multicoil L+S reconstruction is formulated using a convex optimization approach, where the nuclear-norm is used to enforce low-rank in L and the l1-norm to enforce sparsity in S. Feasibility of the L+S reconstruction was tested in several dynamic MRI experiments with true acceleration including cardiac perfusion, cardiac cine, time-resolved angiography, abdominal and breast perfusion using Cartesian and radial sampling. Results The L+S model increased compressibility of dynamic MRI data and thus enabled high acceleration factors. The inherent background separation improved background suppression performance compared to conventional data subtraction, which is sensitive to motion. Conclusion The high acceleration and background separation enabled by L+S promises to enhance spatial and temporal resolution and to enable background suppression without the need of subtraction or modeling.

Dynamic Magnetic Resonance Imaging Reconstruction Based on Nonconvex Low-Rank Model

“…According to the theory of RPCA, Otazo et al [13] used the nuclear norm of and the 1 norm of instead of the rank of and the 0 norm of in (1), respectively, and proposed a convex optimization problem ( + model):…”

“…In [12], 3D cardiac MRI was reconstructed by combining + decomposition with prior knowledge. In [13], a new + model was proposed, which decomposed a series of dynamic MR images with temporal and spatial correlation into LR matrices and sparse matrices. As a result, the dynamic MRI could be divided into the foreground and background to help diagnosis.…”

svt: Singular Value Thresholding in MATLAB

“…The most direct approach for SVT is applying full SVD through svd and then soft-threshold the singular values. This approach is in practice used in many matrix learning problems according to the distributed code, e.g., Kalofolias, Bresson, Bronstein, and Vandergheynst (2014); Chi et al (2013); Parikh and Boyd (2013) ;Yang, Wang, Zhang, and Zhao (2013);Zhou, Liu, Wan, and Yu (2014); Zhou and Li (2014); Zhang et al (2017); Otazo, Candès, and Sodickson (2015); Goldstein, Studer, and Baraniuk (2015), to name a few. However, the built-in function svd is for full SVD of a dense matrix, and hence is very time-consuming and computationally expensive for large-scale problems.…”

Low storage space for compressive sensing: semi-tensor product approach

“…Low-rank matrices and rank-one matrices are attractive because they need less storage space than general measurement matrices [17][18][19][20]. Indeed, if the measurement matrix is sparse, it takes less storage space and incurs less computational cost.…”