The fields of signal and image processing have been deeply influenced by the\nintroduction of deep neural networks. These are successfully deployed in a wide\nrange of real-world applications, obtaining state of the art results and\nsurpassing well-known and well-established classical methods. Despite their\nimpressive success, the architectures used in many of these neural networks\ncome with no clear justification. As such, these are usually treated as "black\nbox" machines that lack any kind of interpretability. A constructive remedy to\nthis drawback is a systematic design of such networks by unfolding\nwell-understood iterative algorithms. A popular representative of this approach\nis the Iterative Shrinkage-Thresholding Algorithm (ISTA) and its learned\nversion -- LISTA, aiming for the sparse representations of the processed\nsignals. In this paper we revisit this sparse coding task and propose an\nunfolded version of a greedy pursuit algorithm for the same goal. More\nspecifically, we concentrate on the well-known Orthogonal-Matching-Pursuit\n(OMP) algorithm, and introduce its unfolded and learned version. Key features\nof our Learned Greedy Method (LGM) are the ability to accommodate a dynamic\nnumber of unfolded layers, and a stopping mechanism based on representation\nerror, both adapted to the input. We develop several variants of the proposed\nLGM architecture and test some of them in various experiments, demonstrating\ntheir flexibility and efficiency.\n