CN110032968B - Denoising method based on dual-tree complex wavelet and self-adaptive semi-soft threshold method - Google Patents
Denoising method based on dual-tree complex wavelet and self-adaptive semi-soft threshold method Download PDFInfo
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- CN110032968B CN110032968B CN201910286915.6A CN201910286915A CN110032968B CN 110032968 B CN110032968 B CN 110032968B CN 201910286915 A CN201910286915 A CN 201910286915A CN 110032968 B CN110032968 B CN 110032968B
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Abstract
The invention relates to a denoising method based on dual-tree complex wavelet and self-adaptive semi-soft threshold method, comprising the following steps: collecting the reflected optical signal at a set sampling frequency; performing dual-tree complex wavelet decomposition on the optical signal, and calculating wavelet sub-band coefficients of the optical signal containing noise at each layer and variances of each layer after the dual-tree wavelet decomposition; and obtaining a lower threshold and an upper threshold by adopting a Bayes self-adaptive semi-soft threshold method, and performing dual-tree complex wavelet inverse transformation by using wavelet sub-band coefficients in the range of the lower threshold and the upper threshold to obtain the denoised optical signal. The invention combines the excellent characteristic of the dual-tree complex wavelet transform with the advantage that the self-adaptive semi-soft threshold filtering can effectively remove the signal noise, and can better filter the noise in the signal.
Description
Technical Field
The invention belongs to the technical field of infrared reflection signal denoising, and particularly relates to a denoising method based on dual-tree complex wavelet and a self-adaptive semi-soft threshold method.
Background
The infrared reflected signal is affected by factors such as sensor oscillation and electronic device interference in the production process, so that the quality of the digital signal obtained after conversion is reduced, and a large number of peaks are generated in the waveform. In order to ensure the correctness of the subsequent processing, the signal needs to be denoised. The application of the signal denoising technology is expanded from the aerospace field to various fields and industries such as biomedicine, information science, resource environment science, astronomy, physics, industry, agriculture, national defense, education, art and the like, and has great influence on economy, military, culture and daily life of people. Therefore, the research of the signal denoising technology has extremely important application value.
There are many signal denoising methods, which are mainly divided into a space domain and a frequency domain. The traditional signal denoising is mainly realized in a space domain, and the main methods include mean filtering, median filtering and wiener filtering. However, the denoising effect of these methods is not ideal, and although noise can be removed, the denoised signal may be distorted. The frequency domain denoising method is to transform a signal from a space domain to a frequency domain, denoise a transform coefficient in the frequency domain, and inversely transform the denoised coefficient back to the space domain to achieve the purpose of denoising. Commonly used methods are fourier transform, wavelet transform, dual-tree wavelet transform, and the like. "seismic signal denoising [ J ]" (Duyue peak, wang jin Ju. Symposium university of Hefei university (Nature science edition), 2018,41 (7)) of dual-tree complex wavelet domain statistical model ", use dual-tree complex wavelet transform method to obtain wavelet coefficient value and variance of each sampling point after each layer of dual-tree wavelet decomposition, and then reconstruct and estimate wavelet coefficient value of signal through dual-tree complex wavelet inverse transform, obtain denoised signal. The method has the defect that the uniform threshold value is easy to excessively filter the wavelet coefficient, so that signal distortion is caused.
Disclosure of Invention
The invention provides a denoising method based on dual-tree complex wavelet and self-adaptive semi-soft threshold method, which combines the excellent characteristics of dual-tree complex wavelet transform with the advantage that self-adaptive semi-soft threshold filtering can effectively remove signal noise, and can better filter noise in signals.
In order to solve the technical problem, the denoising method based on the dual-tree complex wavelet and the adaptive semi-soft threshold method comprises the following steps:
step one, using a set sampling frequency f c Collecting the reflected optical signal with 250000 ≤ f c Less than or equal to 1500000Hz, and the sampling interval is 0 to 200;
step two, performing dual-tree complex wavelet decomposition on the optical signal acquired in the step one, and setting the highest level N of decomposition, wherein N is less than or equal to 10; calculating the wavelet sub-band coefficient of each layer of the optical signal containing noise and the variance of each layer after the dual-tree wavelet decomposition;
step three, obtaining a lower threshold lambda by adopting a Bayes self-adaptive semi-soft threshold method 1 And an upper threshold lambda 2 ；
1) Estimating the noise variance according to the D.L.Donoho formula
Wherein Y is i,j Wavelet sub-band coefficient, median (| Y) of sampling point i after j-th layer dual-tree wavelet decomposition of optical signal j,i |) is the median of the absolute value of the wavelet sub-band coefficient of the j-th layer;
2) Calculating the variance of the optical signal according to equation (2)
Wherein
The variance of the j layer after the optical signal dual-tree wavelet decomposition is obtained;
3) Determining a lower threshold λ 1 And an upper threshold λ 2 ；
λ 1 ＝min(T B ,T G )；λ 2 ＝max(T B ,T G )
Wherein
Step four, the value is smaller than the lower threshold lambda 1 And is greater than the upper threshold lambda 2 Using a lower threshold lambda 1 And an upper threshold lambda 2 And performing dual-tree complex wavelet inverse transformation on the wavelet sub-band coefficients in the range to obtain the denoised optical signal.
Said sampling frequency is preferably f c =1200000Hz, the sampling interval is preferably 50.
The invention has the beneficial effects that: the dual-tree complex wavelet transform has time-frequency local analysis characteristics, and simultaneously has approximate translation invariance and multi-direction selectivity. The invention provides a method based on dual-tree complex wavelet transform and self-adaptive semi-soft threshold filtering, which can quickly select a proper threshold according to the number of decomposition layers and effectively filter noise.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flowchart of a denoising method based on dual-tree complex wavelet and adaptive semi-soft threshold method according to the present invention.
Fig. 2a is a noiseless plot of the original optical signal.
Fig. 2b is a contaminated plot of a noisy optical signal.
Fig. 2c is a graph of the filtering of an optical signal after noise cancellation using the present invention.
Fig. 3 is a graph of the filtering of an optical signal after denoising using a prior art dual density dual-tree complex wavelet method.
Detailed Description
As shown in fig. 1, the denoising method based on dual-tree complex wavelet and adaptive semi-soft threshold method of the present invention includes the following steps:
step one, using PCI collecting card to set sampling frequency f c Collecting the reflected optical signal, where f is selected c =1200000Hz, the sampling interval is chosen to be 50;
step two, performing dual-tree complex wavelet decomposition on the optical signal acquired in the step one, and setting the highest level N of decomposition, wherein N is less than or equal to 10; calculating wavelet sub-band coefficients of each layer of a noisy optical signal and variances of each layer after dual-tree wavelet decomposition (see seismic signal denoising [ J ] ", duyue peak, wangjin chrysanthemum. Symposium Federatum university (Nature science edition), 2018,41 (7)) of a dual-density dual-tree complex wavelet domain statistical model;
step three, obtaining a lower threshold lambda by adopting a Bayes self-adaptive semi-soft threshold method 1 And an upper threshold lambda 2 ；
1) Estimating the noise variance according to the D.L.Donoho formula by using a robust median
Wherein Y is i,j Representing optical messagesWavelet sub-band coefficient of ith sample point after j-th layer dual-tree wavelet decomposition, median (| Y) j,i |) is the median of the absolute values of the wavelet sub-band coefficients of the j-th layer;
2) Calculating the variance of the optical signal according to equation (2)
Wherein
The variance of the j-th layer after the optical signal dual-tree wavelet decomposition is obtained;
3) Determining a lower threshold λ 1 And an upper threshold lambda 2 ；
λ 1 ＝min(T B ,T G )；λ 2 ＝max(T B ,T G )
Wherein
N is the number of decomposition layers;
step four, the value is smaller than a lower threshold lambda 1 And is greater than the upper threshold lambda 2 Wavelet sub-band coefficient filtering using a lower threshold lambda 1 And an upper threshold lambda 2 Wavelet sub-band coefficients within range are inverse dual-tree complex wavelet transformed (see seismic signal denoising of "dual density dual-tree complex wavelet domain statistical model [ J]", duyue Peak, wangjin Ju, school of Fertilizer industry university (Nature science edition), 2018,41 (7)), to obtain an optical signal after noise reduction.
As shown in fig. 2a, fig. 2b, fig. 2c, and fig. 3, compared with the dual density dual-tree complex wavelet method in the prior art, the denoised signal obtained by denoising the original signal according to the present invention uses Root Mean Square Error (RMSE), signal-to-noise ratio (SNR), and smoothness (R) as evaluation indexes, and the smaller the root mean square error, the better the signal-to-noise ratio, the better the smoothness change. Table 1 shows the results for different evaluation criteria.
TABLE 1 evaluation indexes of denoising effect in different evaluation modes
Claims (2)
1. A denoising method based on dual-tree complex wavelet and self-adaptive semi-soft threshold method is characterized by comprising the following steps:
step one, setting a sampling frequency f c Collecting the reflected optical signal with 250000 ≤ f c Less than or equal to 1500000Hz, and the sampling interval is 0 to 200;
step two, performing dual-tree complex wavelet decomposition on the optical signal acquired in the step one, and setting the highest level N of decomposition, wherein N is less than or equal to 10; calculating the wavelet sub-band coefficient of the optical signal containing noise at each layer and the variance of each layer after the dual-tree wavelet decomposition;
step three, obtaining a lower threshold lambda by adopting a Bayes self-adaptive semi-soft threshold method 1 And an upper threshold λ 2 ；
1) Estimating the noise variance according to the D.L.Donoho formula
Wherein Y is i,j Wavelet sub-band coefficient, median (| Y) of sampling point i after j-th layer dual-tree wavelet decomposition of optical signal j,i |) is the median of the absolute values of the wavelet sub-band coefficients of the j-th layer;
2) Calculating the variance of the optical signal according to equation (2)
Wherein
The variance of the j-th layer after the optical signal dual-tree wavelet decomposition is obtained;
3) Determining a lower threshold λ 1 And an upper threshold λ 2 ；
λ 1 ＝min(T B ,T G )；λ 2 ＝max(T B ,T G )
Wherein
Step four, the value is smaller than a lower threshold lambda 1 And is greater than the upper threshold lambda 2 Wavelet sub-band coefficient filtering using a lower threshold lambda 1 And an upper threshold lambda 2 And performing dual-tree complex wavelet inverse transformation on the wavelet sub-band coefficients in the range to obtain the denoised optical signal.
2. The denoising method based on dual-tree complex wavelet and adaptive semi-soft threshold method according to claim 1, wherein f is c =1200000Hz, the sampling interval is chosen to be 50.
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