MDL Denoising Revisited

We refine and extend an earlier minimum description length (MDL) denoising criterion for wavelet-based denoising. We start by showing that the denoising problem can be reformulated as a clustering problem, where the goal is to obtain separate clusters for informative and noninformative wavelet coefficients, respectively. This suggests two refinements, adding a code-length for the model index, and extending the model in order to account for subband-dependent coefficient distributions. A third refinement is the derivation of soft thresholding inspired by predictive universal coding with weighted mixtures. We propose a practical method incorporating all three refinements, which is shown to achieve good performance and robustness in denoising both artificial and natural signals.