提出带惯性的深度逆向先验训练方法，提升图像重建的收敛速度与恢复精度。
Implicit Regularization of the Deep Inverse Prior Trained with Inertia
- 采用具有黏性与几何海森项阻尼的惯性机制训练网络
- 连续情形下实现指数加速收敛，优于传统梯度流
- 离散算法具备良好恢复保证，适合图像重建等逆问题
使用神经网络求解逆问题时，缺乏理论上的恢复保证。本文为自监督神经网络应用于逆问题（如深度图像/逆向先验）提供了收敛与恢复保证，训练过程引入惯性机制，包含黏性与几何海森驱动阻尼。研究了连续时间情形（动力系统轨迹）与离散情形（自适应步长的惯性算法）。在连续情况下，网络可实现比梯度流更快的最优加速指数收敛率；在离散情形中，所提惯性算法虽收敛率较弱但仍具备相似的恢复保证。
原文摘要 · Abstract (English)
Solving inverse problems with neural networks benefits from very few theoretical guarantees when it comes to the recovery guarantees. We provide in this work convergence and recovery guarantees for self-supervised neural networks applied to inverse problems, such as Deep Image/Inverse Prior, and trained with inertia featuring both viscous and geometric Hessian-driven dampings. We study both the continuous-time case, i.e., the trajectory of a dynamical system, and the discrete case leading to an inertial algorithm with an adaptive step-size. We show in the continuous-time case that the network can be trained with an optimal accelerated exponential convergence rate compared to the rate obtained with gradient flow. We also show that training a network with our inertial algorithm enjoys similar recovery guarantees though with a less sharp linear convergence rate.
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