Scale-band-dependent thresholding for signal denoising usingundecimated discrete wavelet packet

The purpose of this paper is to study signal denoising by thresholding coeecients of undecimated discrete wavelet packet transforms (UDWPT). The undecimated lterbank implementation of UDWPT is rst considered, and the best basis selection algorithm that prunes the complete undecimated discrete wavelet packet binary tree is studied for the purpose of signal denoising. Distinct from the usual approach which selects the best subtree based on the original (unthresholded) transform coeecients, our selection is based on the thresholded coeecients, since we believe discarding the small coeecients permits to choose the best basis from the set of coeecients that will really contribute to the reconstructed signal. Another feature of the algorithm is the thresholding scheme. To threshold coeecients which are correlated diierently from scale to scale and from band to band, a uniform threshold is not appropriate. Alternatively, two scale-band-dependent thresholding schemes are designed: a correlation-dependent model and a Monte Carlo simulation-based model. The cost function for the pruning algorithm is speciically designed for the purpose of signal denoising. We consider it prootable to split a band if more noise can be discarded by thresholding while signal components are preserved. So, higher SNR is desirable in the process of selection. Experiments conducted for 1-D and 2-D signals shows that the algorithm achieves good SNR performance while preserving high frequency details of signals.