The Discrete Multiple Wavelet Transform andThresholding
نویسندگان
چکیده
Orthogonal wavelet bases have recently been developed using multiple mother wavelet functions. Applying the discrete multiple wavelet transform requires the input data to be preprocessed to obtain a more economical decomposition. We discuss the properties of several prepro-cessing methods and their eeect on the thresholding results. We propose a multivariate thresholding method for multiwavelets where each wavelet coeecient vector is thresholded as opposed to each element. A multiwavelet universal threshold is obtained using the asymptotic behaviour of the 2 distribution. A simulation study demonstrates that when using the Geronimo multiwavelet with an appropriate prepro-cessing method and bivariate thresholding, better results are obtained compared with using either univariate thresholding methods or thresh-olding Daubechies wavelets.
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