ACCURATE SIGNAL ESTIMATION NEAR DISCONTINUITIES
T. R. DOWNIE · International Journal of Wavelets Multiresolution and Information Processing · 2004
Wavelet thresholding is an effective method for noise reduction of a wide class of naturally occurring signals. However, bias near to a discontinuity and Gibbs phenomenon are a drawback in wavelet thresholding. The extent to which this is a problem is investigated. The Haar wavelet basis is good at approximating discontinuities, but is bad at approximating other signal artefacts. A method of detecting jumps in a signal is developed that uses non-decimated Haar wavelet coefficients. This is designed to be used in conjunction with most existing thresholding methods. A detailed simulation study is carried out and results show that when discontinuities are present a substantial reduction in bias can be obtained, leading to a corresponding reduction in mean square error.