Signal and Image Denoising via Wavelet Thresholding: Orthogonal and Biorthogonal, Scalar and Multiple Wavelet Transforms

The method of signal denoising via wavelet thresholding was popularised by Donoho and Johnstone (1994, 1995) and is now widely applied in science and engineering. It is based on thresholding of wavelet coefficients arising from the standard scalar orthogonal discrete wavelet transform (DWT). Recently this approach has been extended to incorporate thresholding coefficients arising from the discrete multiple wavelet transform (DMWT). Complications are introduced by the fact that non-orthogonal prefilters are required before the DMWT. Strela et al. (1999) applied scalar thresholding to the output from the Geronimo et al. (1994) DMWT with prefiltering, while Downie and Silverman (1998) gave a multivariate thresholding approach which takes account of the correlation in the DMWT coefficients induced by the prefiltering.

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