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The fields of signal and image processing have been deeply influenced by theintroduction of deep neural networks. These are successfully deployed in a widerange of real-world applications, obtaining state of the art results andsurpassing well-known and well-established classical methods. Despite theirimpressive success, the architectures used in many of these neural networkscome with no clear justification. As such, these are usually treated as "blackbox" machines that lack any kind of interpretability. A constructive remedy tothis drawback is a systematic design of such networks by unfoldingwell-understood iterative algorithms. A popular representative of this approachis the Iterative Shrinkage-Thresholding Algorithm (ISTA) and its learnedversion -- LISTA, aiming for the sparse representations of the processedsignals. In this paper we revisit this sparse coding task and propose anunfolded version of a greedy pursuit algorithm for the same goal. Morespecifically, we concentrate on the well-known Orthogonal-Matching-Pursuit(OMP) algorithm, and introduce its unfolded and learned version. Key featuresof our Learned Greedy Method (LGM) are the ability to accommodate a dynamicnumber of unfolded layers, and a stopping mechanism based on representationerror, both adapted to the input. We develop several variants of the proposedLGM architecture and test some of them in various experiments, demonstratingtheir flexibility and efficiency.

Learned Greedy Method (LGM): A Novel Neural Architecture for Sparse Coding and Beyond