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

Loubna El Gueddari,Emilie Chouzenoux,Philippe Ciuciu,Chaithya Giliyar Radhakrishna

doi:10.3390/jimaging7030058

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 (-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.

Highlights

Compressed sensing (CS) [1,2,3,4] has made a breakthrough in the MR community and in clinics with recent Food and Drug Administration (FDA) approval [5] as it provides ways to drastically shorten scan times especially when adopting non-Cartesian sampling schemes [6,7,8,9,10,11] in the k-space
We have proposed a novel calibration-less MR image reconstruction method that relies on octagonal shrinkage and clustering algorithm for regression (OSCAR)-norm regularization
We have implemented four variants and shown that the global, scalewise and subbandwise provide very close results in terms of image quality with a best compromise in numerical complexity for the subbandwise version. All these variants fit within the same primal-dual optimization algorithm that converges to the global optimizer given the convexity of the cost function and the technical conditions met on the primal and dual step sizes

Summary

Introduction

Compressed sensing (CS) [1,2,3,4] has made a breakthrough in the MR community and in clinics with recent Food and Drug Administration (FDA) approval [5] as it provides ways to drastically shorten scan times especially when adopting non-Cartesian sampling schemes (radial, Propeller, spiral, Sparkling) [6,7,8,9,10,11] in the k-space. Non-Cartesian sampling patterns offer many advantages such as robustness to motion or better sampling efficiency [6,7,8,10,11]. For these reasons, non-Cartesian 2D acquisitions make the use of higher acceleration factors feasible as compared to Cartesian sampling. Two ingredients may contribute to achieving this goal—on the one hand, moving to 3D non-Cartesian imaging provides an increased SNR [11,12].

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Conclusion