Fast Recovery of Compressed Multi-Contrast Magnetic Resonance Images

In many settings, multiple Magnetic Resonance Imaging (MRI) scans are performed with different contrast characteristics at a single patient visit. Unfortunately, MRI data-acquisition is inherently slow creating a persistent need to accelerate scans. Multi-contrast reconstruction deals with the joint reconstruction of different contrasts simultaneously. Previous approaches suggest solving a regularized optimization problem using group sparsity and/or color total variation, using composite-splitting denoising and FISTA. Yet, there is significant room for improvement in existing methods regarding computation time, ease of parameter selection, and robustness in reconstructed image quality. Selection of sparsifying transformations is critical in applications of compressed sensing. Here we propose using non-convex p-norm group sparsity (with p < 1), and apply color total variation (CTV). Our method is readily applicable to magnitude images rather than each of the real and imaginary parts separately. We use the constrained form of the problem, which allows an easier choice of data-fidelity error-bound (based on noise power determined from a noise-only scan without any RF excitation). We solve the problem using an adaptation of Alternating Direction Method of Multipliers (ADMM), which provides faster convergence in terms of CPU-time. We demonstrated the effectiveness of the method on two MR image sets (numerical brain phantom images and SRI24 atlas data) in terms of CPU-time and image quality. We show that a non-convex group sparsity function that uses the p-norm instead of the convex counterpart accelerates convergence and improves the peak-Signal-to-Noise-Ratio (pSNR), especially for highly undersampled data.