Overcomplete image representations and locally best model selection

In this paper we formulate a general modeling framework that unifies and extends several state-of-the-art statistical image processing methodologies, including translation-invariant wavelet methods, overcomplete image representations, and best basis selection. At the heart of this framework is a novel hierarchical image model that combines/fuses several basis systems into a single observed image representation through a local model selection (local-MS) criterion, and derives a MAP estimator for each pixel. This framework overcomes several limitations of existing basis selection methods, and is demonstrated to have superior performance in real image analysis applications.