Denoising with flexible histogram models on Minimum Description length principle

TL;DR

This paper introduces a novel denoising technique that uses flexible histogram models and the Minimum Description Length principle to separate noise from signal in wavelet coefficients, relaxing traditional Gaussian assumptions.

Contribution

It proposes a new denoising approach employing variable bin width histograms and MDL, differing from traditional thresholding methods.

Findings

Effective noise removal demonstrated on simulated data

Comparable or improved performance over existing methods

Flexible histogram models adapt to data distribution

Abstract

Denoising has always been theoretically considered as removal of high frequency disturbances having Gaussian distribution. Here we relax this assumption and the method used here is completely different from traditional thresholding schemes. The data are converted to wavelet coefficients, a part of which represents the denoised signal and the remaining part the noise. The coefficients are distributed to bins in two types of histograms using the principles of Minimum Description Lengthi(MDL). One histogram represents noise which can not be compressed easily and the other represents data which can be coded in small code length. The histograms made can have variable width for bins. The proposed denoising method based on variable bin width histograms and MDL principle is tested on simulated and real data and compared with other well known denoising methods.