Stability Bounds for the Unfolded Forward-Backward Algorithm
arXiv:2412.17888 · doi:10.1007/s10851-025-01258-6
Abstract
We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an objective function that combines a data-fidelity term, a Tikhonov-type regularization term, and a potentially nonsmooth convex penalty. The robustness of this inversion method to input perturbations is analyzed theoretically. Ensuring robustness complies with the principles of inverse problem theory, as it ensures both the continuity of the inversion method and the resilience to small noise - a critical property given the known vulnerability of deep neural networks to adversarial perturbations. A key novelty of our work lies in examining the robustness of the proposed network to perturbations in its bias, which represents the observed data in the inverse problem. Additionally, we provide numerical illustrations of the analytical Lipschitz bounds derived in our analysis.
arXiv admin note: substantial text overlap with arXiv:2105.15044
References in corpus (8)
- Deep Convolutional Neural Network for Inverse Problems in Imaging
- MoDL: Model Based Deep Learning Architecture for Inverse Problems
- Solving ill-posed inverse problems using iterative deep neural networks
- Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems
- Solving Inverse Problems With Deep Neural Networks -- Robustness Included?
- SIMBA: Scalable Inversion in Optical Tomography using Deep Denoising Priors
- Parseval Proximal Neural Networks
- PALMA, an improved algorithm for DOSY signal processing