Optimizing the multiwavelet shrinkage denoising

Denoising methods based on wavelet domain thresholding or shrinkage have been found to be effective. Recent studies reveal that multivariate shrinkage on multiwavelet transform coefficients further improves the traditional wavelet methods. It is because multiwavelet transform, with appropriate initialization, provides better representation of signals so that their difference from noise can be clearly identified. In this paper, we consider the multiwavelet denoising by using multivariate shrinkage function. We first suggest a simple second-order orthogonal prefilter design method for applying multiwavelet of higher multiplicities. We then study the corresponding thresholds selection using Stein's unbiased risk estimator (SURE) for each resolution level provided that we know the noise structure. Simulation results show that higher multiplicity wavelets usually give better denoising results and the proposed threshold estimator suggests good indication for optimal thresholds.