When sparsity meets low-rankness: Transform learning with non-local low-rank constraint for image restoration

Recent works on adaptive sparse signal modeling have demonstrated their usefulness in various image/video processing applications. As the popular synthesis dictionary learning methods involve NP-hard sparse coding and expensive learning steps, transform learning has recently received more interest for its cheap computation. However, exploiting local patch sparsity alone usually limits performance in various image processing tasks. In this work, we propose a joint adaptive patch sparse and group low-rank model, dubbed STROLLR, to better represent natural images. We develop an image restoration framework based on the proposed model, which involves a simple and efficient alternating algorithm. We demonstrate applications, including image denoising and inpainting. Results show promising performance even when compared to state-of-the-art methods.