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26 October 1999 Scale-band-dependent thresholding for signal denoising using undecimated discrete wavelet packet transforms
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The purpose of this paper is to study signal denoising by thresholding coefficients of undecimated discrete wavelet packet transforms (UDWPT). The undecimated filterbank implementation of UDWPT is first 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 coefficients, our selection is based on the thresholded coefficients, since we believe discarding the small coefficients permits to choose the best basis from the set of coefficients that will really contribute to the reconstructed signal. Another feature of the algorithm is the thresholding scheme. To threshold coefficients which are correlated differently 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 specifically designed for the purpose of signal denoising. We consider it profitable 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 1D and 2D signals shows that the algorithm achieves good SNR performance while preserving high frequency details of signals.
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Huipin Zhang, Aria Nosratinia, C. Sidney Burrus, Jun Tian, and Raymond O. Wells Jr. "Scale-band-dependent thresholding for signal denoising using undecimated discrete wavelet packet transforms", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999);

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