Wavelet Based Interval Varying Algorithm for Optimal Non-Stationary Signal Denoising

Abstract

This paper reviews wavelet-based denoising techniques and presents an effective new algorithm using adaptive threshold method, processing of detailed and approximate coefficient, the optimal choice of level of decomposition for noise reduction in non-stationary signals. The method is based on computing of orthogonal wavelet transform and level-dependent estimation of the threshold. The proposed algorithm is tested with different wavelet bases: Haar, Daubechies; Cubic B-splines; Symplet; Coinflet; biorthogonal wavelets and a comparative analysis is performed. The proposed algorithm was applied to the real signals and has the task of assessing the application of different wavelet bases, threshold techniques, decomposition levels, and times to execute the procedures for accurate and fast-track procedures to reduce interference. The proposed algorithm can be used for single channel real non-stationary signals. For the purpose of comparative analysis of different methods a software program was created by the author, with graphical user interface, that implements the basic denoising techniques, enables the setting of the decomposition level, the wavelet basis, the size of the test signal, and calculates the evaluation characteristics of the denoising process. The software application enables the testing of new denoising algorithms, allows the addition of other types of noise and the investigation of their effects on the signals and is realized in the MATLAB development environment. The proposed results demonstrate that the presented algorithm is suitable for denoising of non-stationary real signals.