Stabilizing RED using the Koopman Operator
arXiv:2509.05736 · doi:10.1109/LSP.2025.3604690
Abstract
The widely used RED (Regularization-by-Denoising) framework uses pretrained denoisers as implicit regularizers for model-based reconstruction. Although RED generally yields high-fidelity reconstructions, the use of black-box denoisers can sometimes lead to instability. In this letter, we propose a data-driven mechanism to stabilize RED using the Koopman operator, a classical tool for analyzing dynamical systems. Specifically, we use the operator to capture the local dynamics of RED in a low-dimensional feature space, and its spectral radius is used to detect instability and formulate an adaptive step-size rule that is model-agnostic, has modest overhead, and requires no retraining. We test this with several pretrained denoisers to demonstrate the effectiveness of the proposed Koopman stabilization.
arXiv commentAccepted to IEEE Signal Processing Letters, 2025
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