PALADIN: a novel plug-and-play 3D CS-MRI reconstruction method

Abstract Compressive sensing magnetic resonance imaging (CS-MRI) accelerates data acquisition by reconstructing high-quality images from a limited set of k -space samples. To solve this ill-posed inverse problem, the plug-and-play (PnP) framework integrates image priors using convolutional neural network (CNN) denoisers. However, CNN denoisers often prioritize local details and may neglect broader degradation effects, leading to visually plausible but structurally inaccurate artifacts. Additionally, the theoretical convergence of PnP methods remains a significant challenge. In this work, we propose a novel method, Plug-And-pLAy 3D MRI recoNstruction, to bridge the gap between denoising and MRI reconstruction. Our model employs the tensor tubal nuclear norm (TNN) to capture intrinsic correlations in 3D MRI data. It also incorporates two implicit regularizers. The first leverages CNN denoisers to exploit image priors. The second, introduced here for the first time, is formulated as a CS-MRI reconstruction subproblem and solved using a deep learning-based method to preserve global spatial structure. We solve the proposed model using the alternating direction method of multipliers. We extend existing theoretical results to prove the algorithm’s convergence to a fixed point under reasonable assumptions. Experiments on two datasets with three sampling masks show that our method outperforms state-of-the-art MRI reconstruction methods. Ablation studies confirm that the TNN and the two implicit regularizers work together to improve reconstruction quality.