Unrolled Proximal Gradient Descent Method for Non-Negative Least Squares Problem

The non-negative least squares (NNLS) aims at finding a non-negative approximation of a matrix system. Such an approximation has been realized in the literature via some iterative methods. Recently, unrolling algorithms have gained significant attention due to their superior approximation results compared to data-driven methods. With a view to obtaining a better approximation, in this work, we deal with the NNLS in a deep learning framework by unrolling the Proximal Gradient Descent Method (PGDM). In the proposed method (referred to as unrolled or learned PGDM), we project the points to the non-negative orthant, which naturally gives rise to the ReLU function in the network as a proximal operator. The network is trained end-to-end in a deep-learning framework. We demonstrate empirically that the Unrolled PGDM (UPGDM) performs better in signal recovery than its classical counterpart involving iterative PGDM.