Over-complete representations of images such as undecimated wavelets have enjoyed immense popularity in recent years. Though they are efficient for modeling singularities and edges, natural images also consist of textures that are difficult to capture with any canonical transformation. In this work, we develop a new modeling strategy with a rigorous treatment of textured regions. Using principal components analysis as an approximate classifier for edges and textures, we partition an image into compressible and incompressible regions-with corresponding models matching their behaviors. A posterior median-based denoising method using these models is described with preliminary results that demonstrate the effectiveness of this approach.