Low‐rank magnetic resonance fingerprinting

Abstract

Abstract-Magnetic Resonance Fingerprinting (MRF) is a relatively new approach that provides quantitative MRI using randomized acquisition. Extraction of physical quantitative tissue values is preformed off-line, based on acquisition with varying parameters and a dictionary generated according to the Bloch equations. MRF uses hundreds of radio frequency (RF) excitation pulses for acquisition, and therefore high under-sampling ratio in the sampling domain (k-space) is required. This under-sampling causes spatial artifacts that hamper the ability to accurately estimate the quantitative tissue values. In this work, we introduce a new approach for quantitative MRI using MRF, called Low Rank MRF. We exploit the low rank property of the temporal domain, on top of the well-known sparsity of the MRF signal in the generated dictionary domain. We present an iterative scheme that consists of a gradient step followed by a low rank projection using the singular value decomposition. Experiments on real MRI data demonstrate superior results compared to conventional implementation of compressed sensing for MRF at 15% sampling ratio.

Low rank alternating direction method of multipliers reconstruction for MR fingerprinting

“…The update of the Lagrangian multiplier (Eq. [21]) has the standard form used for ADMM algorithms (23) and increasingly addresses those errors inx j ÀD jD H jx j that remain unchanged over multiple iterations. In the light of a regularized inverse problem, the Lagrangian multiplier in Eq.…”

“…Therefore, global convergence of MRF reconstruction algorithmsincluding the proposed one-is usually not guaranteed and a good initial guess is essential. The present article addresses this issue by a low rank (LR) approximation (15)(16)(17)(18)(19)(20)(21)(22) of the voxels' signal evolution, to which the alternating direction method of multipliers (ADMM) (13,14,23) is applied. The proposed algorithm splits the MRF reconstruction problem into two sub-problems that are solved alternately: A linear inverse problem with data consistency at its core and a dictionary matching step.…”

Low rank magnetic resonance fingerprinting

“…Although works that exploit the low rank structure of MRF sequences have been published in the past by others [27][28][29][30]32,[35][36][37] and also by us 31 , our solution is unique mainly in the combination of convex modelling and the ability to enable a solution with quantitative values that do not exist in the dictionary. Our solution is based on soft-thresholding the singular values 44 , which is mathematically justified in Appendix A.…”

“…This saves reconstruction time, but does not necessarily improve the quality of the reconstructed maps or the acquisition time. The first introduction of a low-rank constraint for improved reconstruction in MRF was proposed by Zhao et al 29,30 followed by a sub-space constrained low-rank approach introduced by us 31 . Extensions of these ideas include adding a sparse term to the low-rank-based reconstruction 32 (a.k.a robust PCA 33 ) and representing the data as low-rank in the k-space domain 34,35 .…”

“…In this paper we extend our initial idea presented in our conference paper 31 and enforce a low-rank constraint in the image domain together with constraining the solution to the dictionary subspace. In particular, we exploit the low-rank property of the temporal MRF domain, via an iterative scheme that consists of a gradient step followed by a projection onto the subspace spanned by the dictionary elements in order to constrain the structure of the tissue behaviour simulated in the dictionary.…”