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Mathematical Problems in Engineering
Volume 2016, Article ID 3195492, 8 pages
http://dx.doi.org/10.1155/2016/3195492
Research Article

A New Wavelet Threshold Function and Denoising Application

1School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China
2Faculty of Electricity and Information Engineering, Northeast Petroleum University, Daqing 163318, China

Received 10 December 2015; Revised 19 March 2016; Accepted 13 April 2016

Academic Editor: Huiyu Zhou

Copyright © 2016 Lu Jing-yi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In order to improve the effects of denoising, this paper introduces the basic principles of wavelet threshold denoising and traditional structures threshold functions. Meanwhile, it proposes wavelet threshold function and fixed threshold formula which are both improved here. First, this paper studies the problems existing in the traditional wavelet threshold functions and introduces the adjustment factors to construct the new threshold function basis on soft threshold function. Then, it studies the fixed threshold and introduces the logarithmic function of layer number of wavelet decomposition to design the new fixed threshold formula. Finally, this paper uses hard threshold, soft threshold, Garrote threshold, and improved threshold function to denoise different signals. And the paper also calculates signal-to-noise (SNR) and mean square errors (MSE) of the hard threshold functions, soft thresholding functions, Garrote threshold functions, and the improved threshold function after denoising. Theoretical analysis and experimental results showed that the proposed approach could improve soft threshold functions with constant deviation and hard threshold with discontinuous function problems. The proposed approach could improve the different decomposition scales that adopt the same threshold value to deal with the noise problems, also effectively filter the noise in the signals, and improve the SNR and reduce the MSE of output signals.