End-to-end deep neural networks (DNNs) have become the state-of-the-art (SOTA) for solving inverse problems. Despite their outstanding performance, during deployment, such networks are sensitive to minor variations in the testing pipeline and often fail to reconstruct small but important details, a feature critical in medical imaging, astronomy, or defence. Such instabilities in DNNs can be explained by the fact that they ignore the forward measurement model during deployment, and thus fail to enforce consistency between their output and the input measurements. To overcome this, we propose a framework that transforms any DNN for inverse problems into a measurement-consistent one. This is done by appending to it an implicit layer (or deep equilibrium network) designed to solve a model-based optimization problem. The implicit layer consists of a shallow learnable network that can be integrated into the end-to-end training while keeping the SOTA DNN fixed. Experiments on single-image super-resolution show that the proposed framework leads to significant improvements in reconstruction quality and robustness over the SOTA DNNs.

翻译：端到端深度神经网络（DNNs）已成为求解逆问题的最先进技术（SOTA）。尽管其性能出色，但在部署过程中，此类网络对测试流程中的微小变化非常敏感，且常常无法重建微小但重要的细节——这一特征在医学成像、天文学或国防领域至关重要。DNNs的这种不稳定性可归因于其在部署时忽略了前向测量模型，因此未能强制其输出与输入测量之间的一致性。为解决这一问题，我们提出了一种框架，可将任何用于逆问题的DNN转换为测量一致性网络。具体做法是，在该网络后附加一个隐式层（或深度平衡网络），该层旨在求解一个基于模型的优化问题。该隐式层由一个浅层可学习网络构成，可在保持SOTA DNN固定的同时，将其集成到端到端训练中。在单图像超分辨率上的实验表明，所提框架在重建质量和鲁棒性方面相较于SOTA DNNs均有显著提升。