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

TL;DR

This paper introduces GroupCDL, an interpretable deep learning model for image denoising and MRI reconstruction that leverages learned group-sparsity and circulant attention, achieving performance comparable to black-box models while maintaining interpretability.

Contribution

The authors develop an interpretable convolutional network using learned group-sparsity and circulant attention, extending previous dictionary learning approaches to nonlocal image priors with state-of-the-art results.

Findings

Achieves competitive denoising performance with black-box models.

Extends to state-of-the-art CS-MRI reconstruction.

Demonstrates robustness to noise-level mismatches.

Abstract

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.