Monotonically Convergent Regularization by Denoising
This addresses a critical stability issue in imaging applications for researchers and practitioners using deep learning priors, though it is incremental as it builds directly on the RED framework.
The paper tackled the unstable convergence of Regularization by Denoising (RED) algorithms in inverse problems by developing a new monotone RED (MRED) algorithm, which demonstrated stability in simulations for image deblurring and compressive sensing recovery even when traditional RED diverged.
Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not require nonexpansiveness of the deep denoising prior. Simulations on image deblurring and compressive sensing recovery from random matrices show the stability of MRED even when the traditional RED algorithm diverges.