Simultaneous use of individual and joint regularization terms in compressive sensing: Joint reconstruction of multi‐channel multi‐contrast MRI acquisitions

Multi‐contrast images are commonly acquired together to maximize complementary diagnostic information, albeit at the expense of longer scan times. A time‐efficient strategy to acquire high‐quality multi‐contrast images is to accelerate individual sequences and then reconstruct undersampled data with joint regularization terms that leverage common information across contrasts. However, these terms can cause features that are unique to a subset of contrasts to leak into the other contrasts. Such leakage‐of‐features may appear as artificial tissues, thereby misleading diagnosis. The goal of this study is to develop a compressive sensing method for multi‐channel multi‐contrast magnetic resonance imaging (MRI) that optimally utilizes shared information while preventing feature leakage. Joint regularization terms group sparsity and colour total variation are used to exploit common features across images while individual sparsity and total variation are also used to prevent leakage of distinct features across contrasts. The multi‐channel multi‐contrast reconstruction problem is solved via a fast algorithm based on Alternating Direction Method of Multipliers. The proposed method is compared against using only individual and only joint regularization terms in reconstruction. Comparisons were performed on single‐channel simulated and multi‐channel in‐vivo datasets in terms of reconstruction quality and neuroradiologist reader scores. The proposed method demonstrates rapid convergence and improved image quality for both simulated and in‐vivo datasets. Furthermore, while reconstructions that solely use joint regularization terms are prone to leakage‐of‐features, the proposed method reliably avoids leakage via simultaneous use of joint and individual terms, thereby holding great promise for clinical use. We describe a compressive sensing reconstruction method (SIMIT) for multi‐contrast MRI that simultaneously uses joint and individual regularization terms. The method is compared to using only individual (Indiv‐only) or only joint (Joint‐only) terms, using simulated and in‐vivo datasets (N = 11 participants). Simultaneously using individual and joint regularization terms yields improved image quality by optimally sharing common information while reliably avoiding leakage of unique features across contrasts.