The Power of Complementary Regularizers: Image Recovery via Transform Learning and Low-Rank Modeling
This work addresses image reconstruction challenges in processing applications, offering incremental improvements by integrating existing techniques for enhanced performance.
The authors tackled the problem of image recovery by proposing a model that combines adaptive sparse representation and low-rank regularization to better exploit both local and non-local image structures, achieving promising performance in denoising, inpainting, and compressed sensing MRI compared to state-of-the-art methods.
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.