Performance Analysis Of Threshold Denoising Via Different Kinds Of Mother Wavelets And Wavelet-Thresholding Denoising Method Based On Energy Cell

The noise exists inevitably in date processing. Wavelet has good localizing quality at time domain and frequency domain simultaneously and the characteristic of multi-resolution ratio analysis, so it can fulfill all kinds of wave-filtering needs such as low-pass, high-pass, sink wave, random noise denoising. Compare with readitional wave-filtering methods, wavelet has incomparable advantage. Wavelet has become an effective means of signal analysis and is intituled as math microscope of signal analysis.Wavelet can analyze signal at time domain and frequency simultaneously, so it can denoise effectively. This is an important application area of wavelet. Because the mother wavelets is a gather, that which mother wavelet can get best denoising effect at practical application is an await-resolving research subject which has practiceal value.Another important problem is threshold selection. The threshold selection has immediacy relation to the result of denosing. Partial wavelet coefficients can't be set zero when the threshold is undersize so parts of noises are retained and some useful signals will be taked off when the threshold is iusto major so parts of useful signals are lost. These cases result in dissatisfactory denoising. So how to select threshold effectively to avoid lose useful signal is problem worth to research.Some research is processed here on the problems above as follow:(1). In exordium the research purpose and means is introduced. The denoising methods in common use are presented and compared with each other, then wavelet denoising method and threshold selection is introduced emphatically.(2). An ideal spectrum signal prototype is constructed based on the infrared ray spectrum of octane level measure to evaluate the performances of wavelet based threshold denoising approaches via different combinations of mother wavelet functions and thresholds. The feasibility of this metnod is discussed first. A performance index (η) is defined to assess the signal to noise ratios (SNR) of denoising results, in consideration of the trade-off between the SNR and the distortion of the original signal after wavelet denoising, the better. Four families of mother wavelets, four threshold selection rules and three threshold rescaling methods are tested in a series of experiments to estimate the functioning of those wavelets and thresholding parameters.(3). A novel energy cell based wavelet-thresholding denoising method is presented basedon the 'rigrsure' threshold selection scheme. The energy cell is used not only on threshold selection but also on coefficients disposing after threshold selecting. The wavelet coefficients of real signals are strengthened in the process of wavelet denoising to distinguish them from those of noise more efficiently, and, as result, the significant loss of information in the signal content is reduced. The retained wavelet coefficients are restored after thresholding to avoid anamorphosis. This method is propitious to signals with high SNR and part relative high frequentcy informations. The element and the step of this method are presented. The simulation analysis using the ideal spectrum signal prototype which is constructed based on the infrared ray spectrum of octane level measure indicates that this method gives better signal to noise ratios and performance index (g) than conventional wavelet thresholding method via different kinds of mother wavelets.At the end, a summary is carried out on the research, and the problems existing at wavelet denoising method researching and practical application are discussed.