Statistically based multiwavelet denoising

Abstract

In this work, we consider a statistically based multiwavelet thresholding method which acts on the empirical wavelet coefficients in groups, rather than individually, in order to obtain an edge-preserving image denoising technique. Our strategy allows us to exploit the dependencies between neighboring coefficients to make a simultaneous thresholding decision, so that estimation accuracy is increased. By interpreting the multiwavelet analysis in a statistical context, we propose a new weighted multiwavelet matrix thresholding rule, based on the statistical modeling of empirical coefficients. This allows the thresholding decision to be adapted to the local structure of the underlying image, hence producing edge-preserving denoising. Extensive numerical results are presented showing the performance of our denoising procedure.