MDL Denoising Revisited

TL;DR

This paper improves MDL-based wavelet denoising by reformulating it as a clustering problem and introducing three refinements, resulting in a more effective and robust denoising method for artificial and natural signals.

Contribution

It introduces a new MDL denoising approach with three key refinements, enhancing performance and robustness over previous methods.

Findings

Achieves improved denoising performance on artificial signals.

Demonstrates robustness on natural signals.

Incorporates soft thresholding inspired by predictive universal coding.

Abstract

We refine and extend an earlier 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 non-informative 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 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.