A note on wavelet packet summation methods
Stanzin Dorjai, Nikhil Khanna, S. K. Gandhi · Integral Transforms and Special Functions · 2024
The wavelet summation method is a method to obtain a non-linear approximation with ‘nice properties’ for a given signal. This technique has been shown to be effective in non-parametric regression and other fields, including signal denoising. By utilizing a shrinkage rule on the empirical wavelet packet coefficients, wavelet packet summation methods can be obtained. In this paper, we show that the wavelet packet expansion of any finite energy function converges pointwise almost everywhere under the wavelet packet projection, hard sampling, and soft sampling methods.