Stability Bounds for the Unfolded Forward-Backward Algorithm
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 24 of its 48 references that are in the map. First posted on arXiv 23 Dec 2024.
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24 of 48 references.
References · 24
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12 more
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