Study On Signal Denoising Based On Wavelet Transform

Signals are easy to be contaminated by noises due to signal generators, sensors and other equipments during the acquisition and transmission process. Therefore, most obtained signals in practical applications are noisy. Processing directly on the noisy signals will affect the feature recognition, classification and other follow-up steps. The aims of signal denoising are not only removing noises in signals, but also preserving the greatest extent of original signal information. In recent years, with the development and improvement of wavelet theories, the signal denoising method based on the wavelet transform has become a hot research topic. The method can be divided into two categories: one based on statistical models and the other threshold method, among which the threshold method is simple and effective, and therefore, it has been widely used.In this paper, the signal denoising method based on wavelet threshold is studied, and the focuses are the wavelet domain selection and the threshold function design. For one-dimensional signal, aiming at the shortcomings that wavelet transform does not have the shift invariance feature and dual-tree complex wavelet can not further decompose high frequency components, according to the characteristics of the improved dual-tree complex wavelet packet transform theory, combined with the advantages of Neighcoeff method, one method is presented used for one-dimension signal similar to Bumps and Quadchirp, and improved denoising performance; For two-dimensional signal(image),aiming at the spectrum aliasing phenomenon of contourlet transform and the NeighLevel model's limitation that it can not describe the weight relationship of neighboring wavelet coefficients within a scale, the author has improved the NeighLevel threshold contraction criteria to help to characterize the relationship between wavelet coefficients and better denoising effect of images. The main work in this paper is as follows:①. The improved dual-tree complex wavelet transform is studied. Each sub-band of it has good analytical performance and it overcomes the frequency leakage phenomenon of some sub-bands during its decomposition process, thus producing satisfactory reconstruction results, combined with the NeighCoeff threshold contraction algorithm which takes into account the relationship between neighboring wavelet coefficients, it is used for one dimensional signal denoising. Compared with the traditional wavelet threshold method, dual-tree complex wavelet two-variable model, dual-tree complex wavelet and non-analytic dual complex wavelet packet based NeighCoeff method, this method can produce better denoisng effect.②. Non-aliasing contourlet transform theory and the NeighLevel Model which is used to describe the relationship of coefficients within and between neighboring scales are studied, and improvements are made about this model according to the mutual information theory between neighboring wavelet coefficients. Combined with the Non-aliasing contourlet theory in multi-scale geometric analysis theory, an improved image denoising method using NeighLevel model is proposed to better describe the weight relationship between the current wavelet coefficient and coefficients at different positions within the same scale. Compared with the CWT-NeighLevel model, the peak signal to noise ratio is improved by 0.6% -7% with this new method. Besides, the spectrum aliasing phenomenon by contourlet transform and the directional information deficiency of complex wavelet transform are overcome, and good visual effect at edge features can be maintained.