  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.
