Calibration-Less Multi-Coil Compressed Sensing Magnetic Resonance Image Reconstruction Based on OSCAR Regularization

Abstract

Over the last decade, the combination of compressed sensing (CS) with acquisition over multiple receiver coils in magnetic resonance imaging (MRI) has allowed the emergence of faster scans while maintaining a good signal-to-noise ratio (SNR). Self-calibrating techniques, such as ESPiRIT, have become the standard approach to estimating the coil sensitivity maps prior to the reconstruction stage. In this work, we proceed differently and introduce a new calibration-less multi-coil CS reconstruction method. Calibration-less techniques no longer require the prior extraction of sensitivity maps to perform multi-coil image reconstruction but usually alternate estimation sensitivity map estimation and image reconstruction. Here, to get rid of the nonconvexity of the latter approach we reconstruct as many MR images as the number of coils. To compensate for the ill-posedness of this inverse problem, we leverage structured sparsity of the multi-coil images in a wavelet transform domain while adapting to variations in SNR across coils owing to the OSCAR (octagonal shrinkage and clustering algorithm for regression) regularization. Coil-specific complex-valued MR images are thus obtained by minimizing a convex but nonsmooth objective function using the proximal primal-dual Condat-Vù algorithm. Comparison and validation on retrospective Cartesian and non-Cartesian studies based on the Brain fastMRI data set demonstrate that the proposed reconstruction method outperforms the state-of-the-art (ℓ1-ESPIRiT, calibration-less AC-LORAKS and CaLM methods) significantly on magnitude images for the T1 and FLAIR contrasts. Additionally, further validation operated on 8 to 20-fold prospectively accelerated high-resolution ex vivo human brain MRI data collected at 7 Tesla confirms the retrospective results. Overall, OSCAR-based regularization preserves phase information more accurately (both visually and quantitatively) compared to other approaches, an asset that can only be assessed on real prospective experiments.

Convergence of proximal gradient algorithm in the presence of adjoint mismatch *

“…An estimate of x is obtained by adopting a sparse inducing formulation, reminiscent from the literature on compressive sensing [13,30,31,35,42]. We solve the penalized least squares problem (10) with g = ρ W • 1 , W ∈ R N×N being the orthogonal symlet 2 wavelet transform on 2 resolution levels, and ρ > 0 the associated regularization parameter.…”

Safe rules for the identification of zeros in the solutions of the SLOPE problem

“…First, it was shown in several works that, for some proper choices of parameters γ k 's, SLOPE promotes sparse solutions with some form of "clustering" 2 of the nonzero coefficients, see e.g., [7,20,28,36]. This feature has been exploited in many application domains: portfolio optimization [29,43], genetics [25], magnetic-resonance imaging [15], subspace clustering [35], deep neural networks [45], etc. Moreover, it has been pointed out in a series of works that SLOPE has very good statistical properties: it leads to an improvement of the false detection rate (as compared to LASSO) for moderately-correlated dictionaries [6,24] and is minimax optimal in some asymptotic regimes, see [31,37].…”