  The fields of signal and image processing have been deeply influenced by the
introduction of deep neural networks. These are successfully deployed in a wide
range of real-world applications, obtaining state of the art results and
surpassing well-known and well-established classical methods. Despite their
impressive success, the architectures used in many of these neural networks
come with no clear justification. As such, these are usually treated as "black
box" machines that lack any kind of interpretability. A constructive remedy to
this drawback is a systematic design of such networks by unfolding
well-understood iterative algorithms. A popular representative of this approach
is the Iterative Shrinkage-Thresholding Algorithm (ISTA) and its learned
version -- LISTA, aiming for the sparse representations of the processed
signals. In this paper we revisit this sparse coding task and propose an
unfolded version of a greedy pursuit algorithm for the same goal. More
specifically, we concentrate on the well-known Orthogonal-Matching-Pursuit
(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, both adapted to the input. We develop several variants of the proposed
LGM architecture and test some of them in various experiments, demonstrating
their flexibility and efficiency.
