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

Jia-Mian Wu

Abstract: Compressive sensing magnetic resonance imaging (CS-MRI) accelerates dataacquisition by reconstructing high-quality images from a limited set of k-spacesamples. 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 structurallyinaccurate artifacts. Additionally, the theoretical convergence of PnP methodsremains a signiffcant 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 incorporatestwo implicit regularizers. The ffrst leverages CNN denoisers to exploit imagepriors. The second, introduced here for the ffrst time, isformulated as a CS-MRIreconstruction subproblem and solved using a deep learning-based method topreserve global spatial structure. We solve the proposed model using the alternating direction method of multipliers. We extend existing theoretical results toprove the algorithm’s convergence to a ffxed point under reasonable assumptions. Experiments on two datasets with three sampling masks show that ourmethod outperforms state-of-the-art MRI reconstruction methods. Ablation Compressive sensing magnetic resonance imaging (CS-MRI) accelerates dataacquisition by reconstructing high-quality images from a limited set of k-spacesamples. 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 structurallyinaccurate artifacts. Additionally, the theoretical convergence of PnP methodsremains a signiffcant challenge. In this work, we propose a novel method,Plug-And-pLAy 3D MRI recoNstruction, to bridge the gap between denoisingand MRI reconstruction. Our model employs the tensor tubal nuclear norm(TNN) to capture intrinsic correlations in 3D MRI data. It also incorporatestwo implicit regularizers. The ffrst leverages CNN denoisers to exploit imagepriors. The second, introduced here for the ffrst time, isformulated 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 toprove the algorithm’s convergence to a ffxed point under reasonable assump-tions. Experiments on two datasets with three sampling masks show that ourmethod outperforms state-of-the-art MRI reconstruction methods. Ablation studies conffrm that the TNN and the two implicit regularizers work togetherto improve reconstruction quality.