Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage.

This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; in particular, we show that wavelet shrinkage can be considered the exact minimizer of the following problem. Given an image F defined on a square I, minimize over all g in the Besov space B(1)(1)(L (1)(I)) the functional |F-g|(L2)(I)(2)+lambda|g|(B(1)(1 )(L(1(I)))).