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1、Wavelet De-noising First, the wavelet threshold de-noising the signal estimate Signal processing signal de-noising is one of the classic. De-noising methods include traditional linear filtering method and nonlinear filtering methods, such as median filter and wiener filtering. De-noising method is n
2、ot traditional is the entropy of the signal increased after transformation, can not describe the characteristics of non-stationary signals and can not get the signal correlation. To overcome these shortcomings, people began to signal de-noising using the wavelet transform to solve the problem. Wavel
3、et transform has the following favorable characteristics: (1) Low Entropy of: the sparse distribution of wavelet coefficients, so that reduces the entropy of the transformed signal; (2) Multi-resolution features: Yu to characterize the signal can be very non-stationary features such as edges, spikes
4、, breakpoints, etc.;(3) To relevance: the relevance of the signal can be removed, and the noise in wavelet transform has whitening trend, the more beneficial than the time-domain de-noising;(4) Selected based flexibility: the flexibility to choose the wavelet basis function can therefore be required
5、 according to the signal characteristics and select the appropriate wavelet de-noisingIn the field of wavelet de-noising has been more widely used. Thresholding method is a simple, better methods of wavelet de-noising. Thresholding method is the idea of layers of wavelet decomposition coefficients o
6、f the model is larger than and smaller than a certain threshold value of the coefficient of treatment, and then re-processed the wavelet coefficients of an anti-transformation, through the reconstructed de-noised Signal. The following functions from the threshold and threshold estimation of both thr
7、esholding methods are introduced. 1.Threshold function Commonly used threshold function is mainly hard and soft threshold function threshold function.(1) Hard threshold function. Expression is(w)=wI(wT).(2) Soft threshold function. Expression is(w)=(w-sgn(w)T)I(wT)In general, the hard thresholding m
8、ethod can preserve the signal edge of the other local features, soft threshold is relatively smooth, but will cause the edge of the blurring distortion. To overcome these shortcomings, recently proposed a semi-soft threshold function. It can take into account the soft threshold and hard threshold me
9、thod has the advantage, and its expression is (w)=sgn(w) The basis of the soft threshold, you can improve them with their more advanced. It can be seen in the noise (wavelet coefficients) and the useful signal (wavelet coefficients) there is a smooth transition between the areas, more in line with t
10、he natural signal / image of continuous features. Its expression is (w)=2. Threshold estimation Donoho proposed in 1994 VisuShrink method (or uniform thresholding method). It is for the multi-dimensional joint distribution of independent normal variables, when the dimension tends to infinity the con
11、clusions of the maximum estimate of the minimum constraints derived optimal threshold. The choice of thresholds meets: T=Donoho prove that given estimates of the signal is Besov set, obtained in a number of risks similar to the ideal function of the risk of noise reduction. A unified method of Donoh
12、o threshold effect in the practical application unsatisfactory, resulting in the phenomenon of over kill, put forward in 1997 Janse unbiased estimate based on the threshold calculation. Risk function is defined as:Orthogonality of wavelet transform, the risk function can be written in the same form
13、in the wavelet domain Set So Finally, the expression of risk function can be obtained: Where is the indicator function, taking the number of two small. Thus, the best threshold selection can be obtained by minimizing the risk function, i.e. MATLAB to achieve the threshold of signal de-noising, inclu
14、ding the threshold and the thresholding for the two parties . The following description of them. Second, the wavelet de-noising function in MATLAB 1) Thresholds Implemented in MATLAB function of signal threshold for a ddencmp, thselect, wbmpen and wdcbm, following the use of their simple instruction
15、s. Ddencmp call the format of the following three (1)THR，SORH，KEEPAPP，CRIT=ddencmp(IN1，IN2, X) (2)THR，SORH，KEEPAPP，CRIT=ddencmp(IN1，wp，X) (3)THR，SORH，KEEPAPP=ddencmp(IN1，wv，X)Function ddencmp used to obtain in the process of de-noising or compression the default threshold. Input parameter X is one or two dimensional signals; IN1 value for the den or crop, den, said the de-noising, crop that is compressed; IN2 value for the wv or wp, wv, said selection of wavelet , wp said the choice of wavelet packets. Return value is the return threshold THR; SORH is soft or hard threshold th
