Wavelet shrinkage estimators of Hilbert transform

Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given signal and is widely used in data compression, signal processing, statistics, etc. Based on wavelet shrinkage estimators of the original function f, we construct the estimators of its Hilbert transform Hf with the help of a representation due to Beylkin, Coifman and Rokhlin. The almost everywhere convergence and norm convergence of the proposed estimators are established.