A COMBINE WAVELET SEMIPARAMETERIC REGRESSION- SINGULAR IDENTIFICATION DENOISING METHOD

Abstract

Wavelet theory-based algorithms have been successfully developed in the signal processing with the use of compactly supported functions in time domain for multiresolution analysis [1 - 3]. However, like other linear filtering methods, when applying filtering algorithms in order to remove noise from signals, discontinuous part of the signal cannot be recovered [4 - 6]. In present paper, a class of signal containing singular points is considered to propose a combine process for overcomming the mentioned drawback. The proposed process consists of three steps: In the first one, the compact support property of wavelet transform is employed to identify singular points. In the next step, the discontinuous part of signal is characterized by a method with regression converging to singular points from both sides by the use of generalized inverse estimator. In the last one, a combine Wavelet regression (non-parametric) with local regression is performed for recovering the signal with optimally estimated discontinuities. It is expected that the proposed algorithm for recovering singular parts of the signal would take part to improve overall SNR of the process.

Keywords: Wavelet regression, denoising, singular identification