Learning step sizes for unfolded sparse coding
This work addresses the computational bottleneck in sparse coding for applications like signal processing, but it is incremental as it builds on existing unfolded ISTA methods.
The paper tackles the problem of accelerating sparse coding by learning step sizes for the Iterative Shrinkage-Thresholding Algorithm (ISTA), showing that a simple step size strategy improves convergence but is impractical for large-scale use. They propose a network architecture that learns only the step sizes, demonstrating it is competitive with state-of-the-art networks when solutions are sufficiently sparse.
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.