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：融合基于模型的迭代算法与数据驱动深度学习的优势，深度展开网络已成为解决逆成像问题的热门工具。尽管深度展开网络已成功应用于诸多线性逆问题，但非线性问题往往会削弱该方法的性能。受优化算法中常用动量加速技术的启发，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。循环动量加速模块通过发挥长短期记忆网络学习并保留先前梯度信息的能力，将循环动量加速模块分别应用于两种主流深度展开网络——学习型近端梯度下降与学习型原始对偶方法，从而得到LPGD-RMA和LPD-RMA两种改进算法。我们针对两类非线性逆问题进行实验验证：非线性反卷积问题以及具有有限边界测量的电阻抗层析成像问题。第一组实验表明，循环动量加速带来的性能提升随问题非线性程度的增强而显著增大。第二组实验的结果进一步证明，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表现。