  Sparse coding is typically solved by iterative optimization techniques, such
as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and
learning weights of ISTA using neural networks is a practical way to accelerate
estimation. In this paper, we study the selection of adapted step sizes for
ISTA. We show that a simple step size strategy can improve the convergence rate
of ISTA by leveraging the sparsity of the iterates. However, it is impractical
in most large-scale applications. Therefore, we propose a network architecture
where only the step sizes of ISTA are learned. We demonstrate that for a large
class of unfolded algorithms, if the algorithm converges to the solution of the
Lasso, its last layers correspond to ISTA with learned step sizes. Experiments
show that our method is competitive with state-of-the-art networks when the
solutions are sparse enough.
