2 Denoising via Thresholding and Model Selection

In the context of wavelet denoising and compression, we study minimum description length (MDL) criteria for model selection criteria as exible forms of thresholding. Mixture MDL methods based on a single Laplacian, a two-piece Laplacian, and a generalized Gaussian prior are shown to be adaptive thresholding rules. While achieving mean squared error performance comparable with other popular thresholding schemes, the MDL procedures tend to keep far fewer coeecients. From this property, we demonstrate that our methods represent excellent tools for simultaneous denoising and compression. We make this claim precise by analyzing MDL thresholding in two optimality frameworks; one in which we measure rate and distortion based on quantized coeecients and one in which we do not quantize, but instead record rate simply as the number of non-zero coeecients.