Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problems

TL;DR

This paper introduces a recurrent momentum acceleration framework using LSTM-RNNs to enhance deep unrolling networks for nonlinear inverse problems, significantly improving their performance in challenging scenarios.

Contribution

The paper proposes a novel RMA framework with LSTM-RNNs to boost deep unrolling networks' effectiveness on nonlinear inverse problems, addressing limitations of existing methods.

Findings

RMA improves performance more as nonlinearity increases

RMA significantly enhances DuNets in ill-posed problems

Experimental results validate the effectiveness of RMA in nonlinear inverse problems

Abstract

Combining the strengths of model-based iterative algorithms and data-driven deep learning solutions, deep unrolling networks (DuNets) have become a popular tool to solve inverse imaging problems. While DuNets have been successfully applied to many linear inverse problems, nonlinear problems tend to impair the performance of the method. Inspired by momentum acceleration techniques that are often used in optimization algorithms, we propose a recurrent momentum acceleration (RMA) framework that uses a long short-term memory recurrent neural network (LSTM-RNN) to simulate the momentum acceleration process. The RMA module leverages the ability of the LSTM-RNN to learn and retain knowledge from the previous gradients. We apply RMA to two popular DuNets -- the learned proximal gradient descent (LPGD) and the learned primal-dual (LPD) methods, resulting in LPGD-RMA and LPD-RMA respectively. We provide experimental results on two nonlinear inverse problems: a nonlinear deconvolution problem, and an electrical impedance tomography problem with limited boundary measurements. In the first experiment we have observed that the improvement due to RMA largely increases with respect to the nonlinearity of the problem. The results of the second example further demonstrate that the RMA schemes can significantly improve the performance of DuNets in strongly ill-posed problems.