Fast Approximation Of Non-Negative Sparse Recovery Via Deep Learning

Non-negative sparse recovery refers to recovering non-negative sparse source signals from linear observations. This model arises naturally in many image processing applications such as super-resolution and image inpainting. In this paper, we propose two efficient neural networks for fast approximation of non-negative sparse recovery. We also derive upper bounds on network sizes measured by the numbers of layers and neurons to achieve a specified approximation error. Numerical experiments demonstrate the effectiveness and robustness of the proposed networks and show their potential in solving more complicated signal recovery problems with non-stationary transformation process and noisy observation.