Boosting of Mutual-Structure Denoising: A Plug-and-Play Solution for Compressive Sampling MRI Reconstruction With Theoretical Guarantees

The field of accelerated magnetic resonance imaging (AMRI) has garnered significant attention, focusing on reconstructing target image from compressively sampled k-space data to address an ill-posed linear inverse problem. In this study, we exploit the multiparameterization of MRI to propose a new plug-and-play prior (P$^{3}$) for enhancing reconstruction quality. We begin by introducing a mutual-structure guided P$^{3}$ (MS-GP$^{3}$) framework, based on jointly penalized least-squares regression (JPLSR), to selectively transfer common priors from a reference image to the target one, thereby minimizing errors caused by indiscriminate structural replication. Furthermore, we establish a self-sharpening weighting (SSW) scheme that effectively differentiates between the sharp and smooth image components, contributing to a boosted variant of MS-GP$^{3}$ (BMS-GP$^{3}$) for further improvement in artifact suppression and detail restoration. Finally, embedding BMS-GP$^{3}$ in half-quadratic splitting (HQS) iterations yields an advanced AMRI algorithm, dubbed BMS-GP$^{3}$-HQS, which not only outperforms state-of-the-art (SOTA) methods but also provides robust theoretical guarantees, including ensured convergence and resilience to noise.