Complexity-Regularized Image Denoising

We develop a new approach to image denoising based on complexity regularization. This technique presents a flexible alternative to the more conventional l, l, 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.