Scale-Invariant V-Transform and Its Application to Signal De-noising

An aporia of signal de-noising is that the local signal reconstruction at the singular points. Based on the analysis for the signal singular points, combining signal scaling and orthogonal transform, This paper present a novel method called Scale-Invariant V-Transform (SIVT) for signal de-noising based on V-System, which is polynomial multi-wavelets in invariant set. SIVT employs multiple redundant basis of various scale to suppress the artifacts appearing in the singular points of denoised signal. 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.