  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.
