Complexity--Regularized Image Denoising

by Juan Liu and Pierre Moulin

The problem addressed in this paper is denoising of images corrupted
by additive white Gaussian noise. We investigate the use of complexity
regularization techniques, which present a flexible alternative to
the more conventional $l^2$, $l^1$, and Besov regularization methods.
Different forms of complexity regularization are studied. We derive a
connection between complexity--regularized denoising and operational
rate--distortion optimization, and
demonstrate the useful role of state--of--the--art image coders in
this problem.  We establish bounds on denoising performance in terms of
an index of resolvability that characterizes the compressibility
of the true image. The performance loss due to compression is
quantified, and numerical comparisons with state-of-the-art denoising
algorithms are given.