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.

翻译：结合基于模型的迭代算法与数据驱动的深度学习方法的优势，深度展开网络已成为求解逆成像问题的流行工具。尽管深度展开网络已成功应用于许多线性逆问题，但非线性问题往往会削弱该方法的性能。受优化算法中常用的动量加速技术启发，我们提出一种循环动量加速框架，该框架利用长短期记忆循环神经网络模拟动量加速过程。循环动量加速模块借助长短期记忆循环神经网络学习并保留先前梯度信息的能力。我们将循环动量加速应用于两种主流的深度展开网络——学习型近端梯度下降法和学习型原始-对偶法，分别得到LPGD-RMA和LPD-RMA。我们针对两个非线性逆问题提供了实验结果：非线性反卷积问题以及边界测量受限的电阻抗断层成像问题。在第一个实验中，我们观察到循环动量加速带来的改进幅度随问题的非线性程度显著增加。第二个示例的结果进一步表明，循环动量加速方案能显著提升深度展开网络在强病态问题中的性能。