Optimum wavelet design for noise reduction and feature extraction

In this paper an optimum wavelet for denoising and detection applications is designed. The approach is based on searching for a wavelet basis that provides the best non linear approximation of a given signal. It is shown that such a basis will have the best wavelet denoising performance in the sense of signal estimation error. In addition, such a wavelet can represent the signal more compactly with a few large coefficients which can be considered as the features of the signal. Simulation and experimental results are presented to compare the designed wavelet performance with that of standard wavelets. The optimum wavelet proves effective by providing up to 1.2 dB improvement in the simulations and up to 1dB improvement in the experiments over the same length Daubechies wavelet in denoising signals. The optimum wavelet is also successfully used for extracting specific features which can not be detected by Daubechies wavelet from the experimental signals.