We develop a new approach to image denoising based on complexity regularization. This technique presents a flexible alternative to the more conventional l2 , l1 , and Besov regularization methods. Different complexity measures are considered, in particular those induced by state? of?the?art image coders. We focus on a Gaussian denoising problem and derive a connection between complexity?regularized denoising and operational rate?distortion optimization. This connection suggests the use of efficient algorithms for computing complexity-regularized estimates. Bounds on denoising performance are derived in terms of an index of resolvability that characterizes the compressibility of the true image. Comparisons with state-of-the-art denoising algorithms are given. Work supported by the National Science Foundation under award MIP-9732995 (CAREER). This work was presented in part at ICIP'97. 1