Signal and Image Denoising via Wavelet Thresholding

{ In this paper we discuss wavelet thresholding in the context of scalar orthogonal, scalar biorthogonal, multiple orthogonal and multiple biorthogonal wavelet transforms. Two types of multiwavelet thresholding are considered: scalar and vector. Both of them take into account the covariance structure of the transform. The form of the universal threshold is carefully formulated. The results of numerical simulations in signal and image denoising are presented. Multiwavelets outperform scalar wavelets for three out of four noisy 1D test signals, and the Chui-Lian scaling functions and wavelets combined with repeated row preprocessing appears to be a good general method. Vector thresholding does not always outperform scalar thresholding. Multiwavelets generally outperform scalar wavelets for image denoising for all four noisy 2D test images, and the results are visually very impressive. Only for`Lenna' and``ngerprints' with signal to noise ratios of 2 do scalar wavelets perform best. As for 1D signal processing, Chui-Lian scaling functions and wavelets combined with repeated row preprocessing appears to be a good general method. For both 1D and 2D cases, the reconstructed signals derived from such a good general method demonstrate much reduced noise levels | typically 50% of the standard deviation of the original noise.