Learned Primal Dual Splitting for Self-Supervised Noise-Adaptive MRI Reconstruction

Magnetic resonance imaging (MRI) reconstruction has largely been dominated by deep neural networks (DNN); however, many state-of-the-art architectures use black-box structures, which hinder interpretability and improvement. Here, we propose an interpretable DNN architecture for self-supervised MRI reconstruction and denoising by directly parameterizing and learning the classical primal-dual splitting, dubbed LPDSNet. This splitting algorithm allows us to decouple the observation model from the signal prior. Experimentally, we show other interpretable architectures without this decoupling property exhibit failure in the self-supervised learning regime. We report state-of-the-art self-supervised joint MRI reconstruction and denoising performance and novel noise-level generalization capabilities, where in contrast black-box networks fail to generalize.

GroupCDL: Interpretable Denoising and Compressed Sensing MRI via Learned Group-Sparsity and Circulant Attention

Nonlocal self-similarity within images has become an increasingly popular prior in deep-learning models. Despite their successful image restoration performance, such models remain largely uninterpretable due to their black-box construction. Our previous studies have shown that interpretable construction of a fully convolutional denoiser (CDLNet), with performance on par with state-of-the-art black-box counterparts, is achievable by unrolling a convolutional dictionary learning algorithm. In this manuscript, we seek an interpretable construction of a convolutional network with a nonlocal self-similarity prior that performs on par with black-box nonlocal models. We show that such an architecture can be effectively achieved by upgrading the L1 sparsity prior (soft-thresholding) of CDLNet to an image-adaptive group-sparsity prior (group-thresholding). The proposed learned group-thresholding makes use of nonlocal attention to perform spatially varying soft-thresholding on the latent representation. To enable effective training and inference on large images with global artifacts, we propose a novel circulant-sparse attention. We achieve competitive natural-image denoising performance compared to black-box nonlocal DNNs and transformers. The interpretable construction of our network allows for a straightforward extension to Compressed Sensing MRI (CS-MRI), yielding state-of-the-art performance. Lastly, we show robustness to noise-level mismatches between training and inference for denoising and CS-MRI reconstruction.