Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and a regularizer. Classically, handcrafted regularizers are used, which are commonly outperformed by state-of-the-art deep learning approaches. In this work, we combine the variational formulation of inverse problems with deep learning by introducing the data-driven general-purpose total deep variation regularizer. In its core, a convolutional neural network extracts local features on multiple scales and in successive blocks. This combination allows for a rigorous mathematical analysis including an optimal control formulation of the training problem in a mean-field setting and a stability analysis with respect to the initial values and the parameters of the regularizer. In addition, we experimentally verify the robustness against adversarial attacks and numerically derive upper bounds for the generalization error. Finally, we achieve state-of-the-art results for numerous imaging tasks.

介绍了一种新的数据驱动的总变分正则化器，将反问题的变分公式与深度学习相结合，使用卷积神经网络提取多尺度和连续块中的局部特征， 实现了全局优化控制和相对于正则化器的参数和初值的稳定性分析，并在众多成像任务上实现了最先进的结果。

全局深度变分：反问题的稳定正则化器