Learned Over-Parametrized Gradient Descent Method for Non-Negative Least Squares Problem

Akash Sen, C.S. Sastry

Session: General

Keywords: Deep unrolling, Non-negative least squares, Inverse problem, Image denoising

Abstract: The non-negative least squares (NNLS) problem finds a non-negative approximate solution to a linear system. Some well-studied iterative algorithms (such as projection gradient method) find the stated non-negative approximation. Notwithstanding this, a recent technique (known as algorithm unrolling) has emerged as a popular alternative, which maps an iterative algorithm into a deep unrolled network. In literature, the deep unrolled networks have attained importance due to their superiority in performance and interpretability as compared to their classical counterparts. In this work, we propose a framework based on the learned deep networks, (called learned over-parametrized gradient descent or LOGD, for brevity, method) for solving the NNLS problem in a data-driven setup. Numerically we show the promising results of the LOGD network and employ it in image denoising task. Our simulation results demonstrate that the proposed LOGD method performs better than the existing data-driven network and its classical (non-data driven) counterpart.

Submission Number: 93