Minimum description length denoising with histogram models

In this paper, we relax the usual assumptions in denoising that the data consist of a "true" signal to which normally distributed noise is added. Instead of regarding noise as the high-frequency part in the data to be removed either by a "hard" or "soft" threshold, we define it as that part in the data which is harder to compress than the rest with the class of models considered. Here, we model the data by two histograms: one for the denoised signal and the other for the noise, both represented by wavelet coefficients. A code length can be calculated for each part, and by the principle of minimum description length the optimal decomposition results by minimization of the sum of the two code lengths.