Fundamental equivalences between set-theoretic and maximum-entropy methods in multiple-domain image restoration

Several powerful, but heuristic techniques in the image denoising literature have used overcomplete image representations. A general framework for incorporating information from multiple representations based on fundamental statistical estimation principles was presented in Ishwar and Moulin (1999) where, information about image attributes from multiple wavelet transforms was incorporated as moment constraints on the underlying image prior. In this paper we explore the fundamental equivalence between the stochastic setting of multiple-domain restoration in Ishwar and Moulin and its deterministic set-theoretic counterpart. The main technical tool is the Lagrange multiplier theory of constrained optimization. The insights gained by this analysis allow us to derive a state-of-the-art denoising algorithm