A soft thresholding approach for MDL denoising

The existing MDL method for wavelet denoising is extended with a soft thresholding approach. We assume that the wavelet coefficients are comprised of an informative part and a noise part. We propose a soft thresholding method based on the earlier MDL hard thresholding approach equivalent to fitting two Gaussian density functions to the wavelet coefficients, one for the informative part in the data and the other for noise. Our approach is data-dependent and since it is completely characterized by the properties of the MDL hard thresholding solution, it does not require any additional parameters to be estimated. We show that our method improves the results of the existing MDL denoising method for both artificial and natural test signals.