Scale-Invariant V-Transform Signal De-Noising

Abstract

Approximation,reconstruction and denoising of signals with traditional wavelet transform sometimes exhibit visual artifacts,for example,Gibbs phenomena in the vicinity of discontinuities,which are caused by the continuous property of the wavelet basis.We present a novel method for signal de-noising using Scale-Invariant V-Transform(SIVT).The V-system is the generalization of the well-known Haar wavelet basis function and it is multi-wavelets in invariant set.An aporia of signal denoising is that the local signal reconstruction at the singular points.Based on the analysis for the signal singular points,combining local signal resampling and orthogonal transform,a novel technical framework—SIVT has been proposed for signal de-noising.The test results reveal the SIVT reconstructions exhibit higher visual quality and numerical measurement of SNR than wavelet-based reconstructions.Existing theory of SIVT suggests that these new approaches can perform significantly better than wavelet methods in certain signal reconstruction problems.