CN113553997A - Signal processing method, storage medium and system for jointly improving wavelet threshold - Google Patents
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Abstract
The invention discloses a signal processing method, a storage medium and a system for jointly improving a wavelet threshold, relates to the field of signal processing of optical fiber sensing in the photoelectric information technology, and particularly relates to a method for improving the signal-to-noise ratio of a signal. In the method, the signal denoising is carried out by combining the accumulation average method with the wavelet threshold improvement method, so that the signal-to-noise ratio of the output signal can be further improved, and the mean square error is further reduced.
Description
Technical Field
The invention belongs to the field of signal processing of optical fiber sensing in the photoelectric information technology, and particularly relates to a signal processing method, a storage medium and a system for jointly improving a wavelet threshold.
Background
The Brillouin Optical Time Domain Reflectometer (BOTDR) is a technology for realizing optical fiber sensing by utilizing the linear relation between Brillouin frequency shift, stress/strain and temperature, can be applied to many large-scale constructions, such as the safety monitoring of bridge dams, tunnel traffic, transmission power grids and the like, and has wide application prospect. However, since the spontaneous brillouin scattering signal is very weak and has interference of various noises, in the long-distance measurement, the useful signal in the sensing optical fiber is easily submerged in the noises, so that the instrument is difficult to detect accurately, and therefore, it is very important to improve the signal-to-noise ratio of the signal acquired by the BOTDR system.
The traditional denoising method is a linear filtering method based on Fourier transform, which is simple and easy to implement, but has contradiction in improving the signal-to-noise ratio and the resolution. The wavelet transformation energy conversion localizes time-frequency characteristics at the same time, is a multi-resolution analysis method, and is widely applied to signal denoising. In 1995, d.l.donoho et al proposed a wavelet threshold denoising algorithm based on wavelet transform, and attracted extensive attention. Wavelet threshold denoising is to decompose and reconstruct a noise-containing signal on the basis of wavelet transformation, after wavelet decomposition, the coefficient of a useful signal is larger than the coefficient of noise, then the decomposed wavelet coefficient is limited by setting a proper threshold, the wavelet coefficient with the absolute value smaller than the threshold is considered to be mainly caused by the noise and is directly set to be zero, the coefficient with the absolute value larger than the threshold is considered to be caused by the signal, the wavelet coefficient is shrunk (soft threshold method) or reserved (hard threshold method) through certain threshold function processing to obtain an estimated wavelet coefficient, and finally, the estimated wavelet coefficient is reconstructed to obtain a denoised signal.
The denoising effect of wavelet threshold denoising depends on the selection of a threshold and the design of a threshold function, and two common threshold denoising methods are a hard threshold denoising method and a soft threshold denoising method. The hard threshold method can retain more characteristics of spikes and the like of a real signal, but the denoising effect can vibrate due to the discontinuity of the hard threshold at the threshold; the soft threshold method overcomes the defect that the hard threshold method is discontinuous at the threshold, and can generate a smooth result after denoising, but constant deviation always exists between the original wavelet coefficient and the wavelet coefficient subjected to threshold quantization processing, high-frequency information of signals is easily lost, and the denoising effect is influenced to a certain extent.
The accumulation averaging method is a method for increasing the signal-to-noise ratio by accumulating measurement data for a plurality of times, and has been widely used in signal noise reduction processing; however, when the accumulated number of times reaches a certain value, the signal-to-noise ratio is increased significantly, and the required storage space and the measurement time are still increased linearly, which is not favorable for hardware implementation and cannot meet the real-time measurement requirement.
Disclosure of Invention
The invention aims to solve the problem that the defects of discontinuity and constant deviation exist in a common threshold denoising method, and provides a signal processing method for jointly improving a wavelet threshold function.
The technical scheme adopted by the invention for solving the problems is as follows: a method of signal processing with joint improvement of wavelet threshold, comprising the steps of:
s1 simulates Brillouin scattering signals acquired by a BOTDR system data acquisition module, and the model is as follows:
where x (t) is a noisy signal, s (t) is an original signal, and n (t) is a noisy signal. The snr can be expressed as:
s2, M noise signals are superposed, for S (t), M times of superposition become Ms (t), and for noise signal n (t), effective value after superposition becomes Ms (t)
Therefore, the snr of the signal after M times of superposition becomes:
from the above equation, the signal-to-noise ratio is improved after M times of accumulation averaging
Doubling;
s3, carrying out H-layer wavelet decomposition on the noise-stained signal obtained by the accumulation average method to obtain a high-frequency wavelet coefficient
Wherein
Representing the kth coefficient in the detail coefficient group of the j layer of the wavelet decomposition;
calculating threshold value by using improved threshold value calculation method, and using a group of wavelet coefficients obtained by comparing the threshold value with improved wavelet threshold value function
Performing threshold quantization to obtain estimated low-frequency wavelet coefficient
；
High-frequency wavelet coefficient from layer 1 to layer H after threshold quantization
And low frequency wavelet coefficients of the H-th layer
Performing wavelet inverse transformation, and performing signal reconstruction to obtain a reconstructed signal;
further, the brillouin scattering signal acquired by the analog BOTDR system data acquisition module includes:
constructing a sine function, and adding white noise to the sine function by adopting a randn function to obtain a one-dimensional noise-dyeing signal;
further, toPerforming H-layer wavelet decomposition on the one-dimensional noise-contaminated signal obtained by the accumulative average method to obtain a high-frequency wavelet coefficient
The method comprises the following steps:
performing 5-layer wavelet decomposition on the one-dimensional noise-contaminated signal obtained after the accumulation and the averaging by adopting a db4 wavelet basis function to obtain a high-frequency wavelet coefficient
；
Further, a db4 wavelet basis function is adopted to carry out 5-layer wavelet decomposition on the one-dimensional noise-staining signal obtained after the accumulation and the averaging to obtain a high-frequency wavelet coefficient
The method comprises the following steps:
selecting sym6, sym7, sym8, db1, db3 and db4 wavelet bases to perform wavelet decomposition on wavelets, setting the decomposition layer number to be 3-5 layers, performing matlab simulation comparative analysis, and performing 5-layer wavelet decomposition on the one-dimensional noise-dyed signal by using db4 as the wavelet bases to obtain a high-frequency wavelet coefficient
；
Further, calculating a threshold value by adopting an improved threshold value calculation method, and comparing the threshold value with an improved wavelet threshold value function to obtain a group of wavelet coefficients
Performing threshold quantization to obtain estimated low-frequency wavelet coefficient
The method comprises the following steps:
calculating the threshold value by adopting an improved threshold value calculation method, wherein the expression of the improved threshold value calculation method is as follows:
wherein
The threshold value of the j layer, j is a decomposition layer, N is the length of a signal, and sigma is the standard deviation of noise, and in practical application, sigma is always unknown, so the estimated value of sigma is used, and median (x) represents the median operation;
combining the wavelet coefficients
Substituted into the improved wavelet threshold function expression
Performing threshold quantization to obtain estimated wavelet coefficient
Wherein the improved wavelet threshold function expression is:
wherein μ is an adjustment factor that improves the threshold function, and μ > 0;
further, the method also comprises the step of introducing an output signal-to-noise ratio (SNR) and a mean square error (RMSE) to verify the denoising effect of the function, wherein the calculation formulas are respectively as follows:
after the signal is denoised, the higher the signal-to-noise ratio of the signal is and the smaller the mean square error is, the closer the denoised signal is to the original signal is, and the better the denoising effect is.
A storage medium having recorded thereon a signal processing method of jointly improving wavelet thresholds as described above.
A computer-implemented system for computing a signal processing method having a jointly improved wavelet threshold as described above.
The technical method has the following beneficial effects that:
the newly proposed wavelet threshold function not only overcomes the defect of discontinuity of the traditional wavelet threshold function, but also effectively solves the problem of constant deviation of the traditional wavelet threshold function, and simultaneously adopts the accumulative average method combined with the improved wavelet threshold method to process the noise-contaminated signal, thereby effectively improving the signal-to-noise ratio, reducing the mean square error and enabling the processed signal to be as close to the original signal as possible.
Drawings
FIG. 1 is a signal processing flow diagram according to the present invention;
FIG. 2 shows the original signal of noise-contaminated signal SNR of-5.88 db and the noise-contaminated signal;
FIG. 3 shows the original signal of noise-contaminated signal SNR of-11.98 db and the noise-contaminated signal;
FIG. 4 is a schematic diagram of an improved threshold function;
FIG. 5 is a diagram of the denoising effect of the signal-to-noise ratio of a noise-contaminated signal of-5.88 db;
FIG. 6 is a diagram of the cumulative joint denoising effect of the noise signal SNR of-5.88 db;
FIG. 7 is a diagram of the noise-removing effect of-11.98 db in the signal-to-noise ratio of a noise-contaminated signal;
FIG. 8 is a diagram of the signal-to-noise ratio of the noise-contaminated signal-11.98 db cumulative joint denoising effect.
Detailed Description
The technical solutions in the embodiments of the present disclosure will be clearly and completely described below with reference to the drawings in the embodiments of the present disclosure, and it is obvious that the described embodiments are only a part of the embodiments of the present disclosure, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments disclosed herein without making any creative effort, shall fall within the protection scope of the present disclosure.
As shown in fig. 1 to 8, a signal processing method for jointly improving wavelet threshold includes the following steps:
step S1: simulating an original signal;
in the present embodiment, the analog original signal expression described in step S1 is:
step S2: adding white noise into the original signal to obtain a one-dimensional noise-dyeing signal;
step S3: denoising the obtained one-dimensional noise-dyeing signal by an accumulation average method;
the accumulation frequency is generally set to be an exponential multiple of 2, but when the accumulation frequency reaches a certain value, the signal-to-noise ratio improvement speed is obviously slowed down, and the required storage space and the measurement time are still linearly increased, in the embodiment, the one-dimensional noise-dyeing signal is subjected to accumulation processing for 512 times;
step S4: performing 5-layer wavelet decomposition on the noise-stained signal obtained in the step S3, selecting db4 as a wavelet base to perform wavelet decomposition on the input signal, and obtaining a high-frequency wavelet coefficient
And a lowest level of approximation coefficients, wherein
Representing the kth coefficient in the detail coefficient group of the j layer of the wavelet decomposition;
in the embodiment, the wavelet bases sym6, sym7, sym8, db1, db3 and db4 are selected for wavelet decomposition, db4 is selected as the wavelet base through matlab simulation comparative analysis, after db4 is selected as the wavelet base, the decomposition layer number of 3-5 layers is also subjected to comparative analysis, and finally 5 layers are selectedDecomposing the layer number, namely selecting db4 wavelet base to carry out 5-layer wavelet decomposition on the one-dimensional noise-stained signal to obtain a high-frequency wavelet coefficient
；
Step S5: designing an improved wavelet threshold function, calculating a threshold value by adopting an improved threshold value rule, and utilizing the threshold value and the improved wavelet threshold function to perform comparison on the high-frequency wavelet coefficient obtained in the step S4
Performing threshold quantization to obtain estimated low-frequency wavelet coefficient
；
In this embodiment, step S5 specifically includes the following steps:
step S51: calculating the threshold value by adopting an improved threshold value rule, wherein an improved threshold value expression is as follows:
wherein
The threshold value of the j layer, j is a decomposition layer, N is the length of a signal, and sigma is the standard deviation of noise, and in practical application, sigma is always unknown, so the estimated value of sigma is used, and median (x) represents the median operation;
step S52: using the threshold and the improved wavelet threshold function to perform the wavelet transform on the high frequency wavelet coefficients obtained in step S4
Performing threshold quantization to obtain estimated low-frequency wavelet coefficient
(ii) a Wherein the expression of the modified threshold wavelet threshold function is:
wherein μ is an adjustment factor that improves the threshold function, and μ > 0; the actual value of the adjustment factor can be adjusted in a self-adaptive manner according to the use condition, so that the adjustment factor has stronger self-adaptability;
the continuity of the threshold function is proved and the existing fixed deviation problem is improved by using a mathematical method;
continuity: when in use
Time → th:
it is known that
Therefore, it can be seen that the new function is continuous at + th;
the same principle is that: when in use
On time → th:
it is known that
Therefore, it can be seen that the new function is also continuous at-th;
to sum up: the improved threshold function constructed by the scheme is continuous at +/-th, and the continuity of the improved threshold function shows that the improved threshold function can avoid Gibbs oscillation;
the progressiveness: when in use
→ + ∞time:
the same principle is that: when in use
→ infinity time;
to sum up: the asymptote of the improved threshold function constructed by the scheme is
This indicates that with
The fixed deviation is reduced when the value is increased;
deviation property:
to sum up:
this further verifies that the bias will have less and less impact on the improved threshold function of the scheme;
step S6: high frequency wavelet coefficients of layer 1 to layer 5 after threshold quantization processing
And low frequency wavelet coefficients of layer 5
Performing wavelet inverse transformation, and performing signal reconstruction to obtain a reconstructed signal;
furthermore, the method of the present invention further includes introducing an output signal-to-noise ratio (SNR) and a mean square error (RMSE) to verify the denoising effect, and the calculation formulas are respectively:
under the condition of different signal-to-noise ratios of simulated noise signals, the denoising method and the traditional threshold denoising method are adopted to denoise the signals, and the output signal-to-noise ratio and the mean square error of the denoising method and the traditional threshold are obtained;
table 1: noise reduction effect comparison results of different methods under noise signal to noise ratio of-5.88 db
| Denoising method | Signal-to-noise ratio (SNR) | Mean Square Error (RMSE) |
| One-dimensional noise signal | -5.8754 | 5.0120 |
| Soft threshold method | 5.4018 | 1.3682 |
| Hard threshold method | 4.6773 | 1.4872 |
| Improved threshold method | 5.7091 | 1.3206 |
| Cumulative averaging method | 18.0596 | 0.3186 |
| Accumulation joint soft threshold method | 19.3931 | 0.2733 |
| Accumulation joint hard threshold method | 23.3763 | 0.1728 |
| Accumulation joint improvement threshold method | 24.7935 | 0.1467 |
Table 2: noise reduction effect comparison results of different methods under noise signal to noise ratio of-11.98 db
| Denoising method | Signal-to-noise ratio (SNR) | Mean Square Error (RMSE) |
| One-dimensional noise signal | -11.9763 | 10.1170 |
| Soft threshold method | 1.9412 | 2.0379 |
| Hard threshold method | 1.9412 | 2.0379 |
| Improved threshold method | 2.0334 | 2.0164 |
| Cumulative averaging method | 12.4703 | 0.6064 |
| Accumulation joint soft threshold method | 15.7114 | 0.4175 |
| Accumulation joint hard threshold method | 19.0580 | 0.2840 |
| Accumulation joint improvement threshold method | 20.5497 | 0.2392 |
In this embodiment, as shown in fig. 5 to 8, denoising effect graphs of different threshold functions are shown, and it can be seen by combining the results of comparing and analyzing denoising effects of different methods in tables 1 and 2 that although the conventional wavelet threshold method can also improve the signal-to-noise ratio of signals and reduce the mean square error, the method for jointly improving the wavelet threshold provided in this embodiment can further improve the signal-to-noise ratio, reduce the mean square error, and maximally and effectively restore signals.
Principle of operation
The signal processing is carried out on the noise-contaminated signal by adopting the accumulation average method and combining the method for improving the wavelet threshold value, so that the signal-to-noise ratio can be effectively improved, the mean square error is reduced, and the processed signal is as close to the original signal as possible.
The above embodiments are only for illustrating the technical idea of the invention, and the protection scope of the invention is not limited thereby, and any modification made on the basis of the technical solution according to the technical idea of the invention falls within the protection scope of the invention. The technology not related to the invention can be realized by the prior art.
Claims (10)
1. A method of signal processing with combined wavelet threshold improvement, the method comprising the steps of: performing multi-layer wavelet decomposition on the noise-stained signals subjected to the accumulation processing to obtain a high-frequency wavelet coefficient; performing threshold quantization processing on the high-frequency wavelet coefficient to obtain a low-frequency wavelet coefficient; and performing wavelet inverse transformation on the high-frequency wavelet coefficient and the low-frequency wavelet coefficient of each layer after threshold quantization processing, and performing signal reconstruction to obtain a reconstructed signal.
2. A method for signal processing with combined wavelet threshold improvement as claimed in claim 1, wherein said noisy signal is obtained by constructing a sine function and adding white noise thereto.
3. A method of wavelet processing combined with wavelet thresholding as claimed in claim 1, wherein said noise-corrupted signal is wavelet decomposed using one of the wavelet bases sym6, sym7, sym8, db1, db3, db 4.
4. A method for signal processing with combined wavelet threshold improvement according to claim 1, wherein the number of decomposition layers of said wavelet decomposition is set to 3-5 layers.
5. A method for processing a signal in combination with an improved wavelet threshold according to claim 1, wherein the method for obtaining the low frequency wavelet system comprises the following steps:
the first step is as follows: calculating a threshold value by adopting an improved threshold value rule;
the second step is that: and performing threshold quantization processing on the high-frequency wavelet coefficient by using the threshold and the improved wavelet threshold function to obtain the low-frequency wavelet coefficient.
6. A method as claimed in claim 1, wherein the number of accumulated processing times of the noise-contaminated signal is an exponential multiple of 2.
7. The method of claim 1, wherein the method comprises introducing an output signal-to-noise ratio and a mean-square error to verify denoising effect.
8. A method for combined wavelet threshold signal processing as claimed in claim 1, wherein said high frequency wavelet coefficients are obtained by 5-layer wavelet decomposition of said noisy signal over a db4 wavelet basis.
9. A storage medium characterized in that it records a signal processing method of jointly improving wavelet thresholds according to claim 1.
10. A computer-implemented system for performing the method of signal processing in conjunction with wavelet thresholding of claim 1.
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