The Power of Complementary Regularizers: Image Recovery via Transform Learning and Low-Rank Modeling

TL;DR

This paper introduces STROLLR, a novel image recovery framework combining transform learning with joint low-rank regularization to exploit local and non-local image properties, improving performance in denoising, inpainting, and MRI reconstruction.

Contribution

It proposes a new simultaneous sparsity and low-rank model using transform learning, offering computational efficiency and enhanced image recovery performance.

Findings

Outperforms state-of-the-art methods in denoising and inpainting

Effective in compressed sensing MRI reconstruction

Demonstrates the benefits of combined regularization over individual approaches

Abstract

Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.