MDL Denoising Revisited

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.Comment: Submitted to IEEE Transactions on Information Theory, June 200

An MDL framework for sparse coding and dictionary learning

The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these models, such as under-fitting or over-fitting given sets of data, are still not well characterized in the literature. As a result, the success of sparse modeling depends on hand-tuning critical parameters for each data and application. This work aims at addressing this by providing a practical and objective characterization of sparse models by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to model selection in statistical inference. The resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which, by virtue of the MDL principle, are completely parameter free. Furthermore, such framework allows to incorporate additional prior information to existing models, such as Markovian dependencies, or to define completely new problem formulations, including in the matrix analysis area, in a natural way. These virtues will be demonstrated with parameter-free algorithms for the classic image denoising and classification problems, and for low-rank matrix recovery in video applications

Robust denoising of electrophoresis and mass spectrometry signals with minimum description length principle

AbstractThe need for high-throughput assays in molecular biology places increasing requirements on the applied signal processing and modelling methods. In order to be able to extract useful information from the measurements, the removal of undesirable signal characteristics such as random noise is required. This can be done in a quite elegant and efficient way by the minimum description length (MDL) principle, which treats and separates `noise' from the useful information as that part in the data that cannot be compressed. In its current form the MDL denoising method assumes the Gaussian noise model but does not require any ad hoc parameter settings. It provides a basis for high-speed automated processing systems without requiring continual user interventions to validate the results as in the conventional signal processing methods. Our analysis of the denoising problem in mass spectrometry, capillary electrophoresis genotyping, and sequencing signals suggests that the MDL denoising method produces robust and intuitively appealing results sometimes even in situations where competing approaches perform poorly

MDL and Wavelet Denoising with Soft Thresholding

We propose a soft thresholding approach to the minimum description length wavelet denoising. Our method is based on combining two-part coding with normalized maximum likelihood universal models to give a soft thresholding denoising criterion. Experiments with the proposed MDL soft thresholding method indicate that our denoising criterion leads to fairly similar performance as with the well-known VisuShrink method.JRC.G.4-Maritime affair