Learned Greedy Method (LGM): A novel neural architecture for sparse coding and beyond

The fields of signal and image processing have been deeply influenced by the introduction of deep neural networks. Despite their impressive success, the architectures used in these solutions come with no clear justification, being “black box” machines that lack interpretability. A constructive remedy to this drawback is a systematic design of networks by unfolding well-understood iterative algorithms. A popular representative of this approach is LISTA, evaluating sparse representations of processed signals. In this paper, we revisit this task and propose an unfolded version of a greedy pursuit algorithm for the same goal. More specifically, we concentrate on the well-known OMP algorithm, and introduce its unfolded and learned version. Key features of our Learned Greedy Method (LGM) are the ability to accommodate a dynamic number of unfolded layers, and a stopping mechanism based on representation error. We develop several variants of the proposed LGM architecture and demonstrate their flexibility and efficiency.