Statistics Seminars: Denoising real data using complex wavelets
18 October 2002 00:00 in CM221
"Wavelet shrinkage is an effective nonparametric regression technique when the underlying curve has irregular features such as spikes or discontinuities. The basic idea is simple: take the discrete wavelet transform (DWT) of data consisting of a signal corrupted by noise; shrink the wavelet coefficients to remove the noise; and then invert the DWT to form an estimate of the true underlying curve. Various authors have proposed methods of doing this using real-valued wavelets. Complex-valued versions of some wavelets exist, but are rarely used. We propose two shrinkage techniques which use complex wavelets. Simulation results show that both methods give smaller errors than using state of the art shrinkage rules with real-valued wavelets. "
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