CN114444548A - Wavelet sound denoising method and system based on robustness principal component analysis - Google Patents

Wavelet sound denoising method and system based on robustness principal component analysis Download PDF

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CN114444548A
CN114444548A CN202210119888.5A CN202210119888A CN114444548A CN 114444548 A CN114444548 A CN 114444548A CN 202210119888 A CN202210119888 A CN 202210119888A CN 114444548 A CN114444548 A CN 114444548A
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吴华明
陈合谱
张业超
戴磊
肖文波
伏燕军
肖永生
黄丽贞
段军红
何兴道
苏荃
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Nanchang Hangkong University
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Abstract

The invention relates to a wavelet sound denoising method and system based on robust principal component analysis, wherein the method comprises the following steps: acquiring a noise-containing sound signal; separating the noise-containing sound signals by adopting a robust principal component analysis method to obtain separated noise-containing sound signals; filtering the separated noise-containing sound signals by using a wavelet threshold denoising algorithm to obtain filtered noise-containing sound signals; and carrying out low-pass filtering on the filtered sound signal containing the noise to obtain a noise-reduced sound signal. The invention can improve the quality of the sound signal.

Description

Wavelet sound denoising method and system based on robustness principal component analysis
Technical Field
The invention relates to the field of sound denoising, in particular to a wavelet sound denoising method and system based on robust principal component analysis.
Background
The DAS has the outstanding advantages of high sensitivity, good corrosion resistance, strong anti-electromagnetic interference capability and the like, and has important application value in the fields of voice communication, perimeter security and the like. In practical application, sound signals collected by the DAS system are inevitably interfered by external noise and internal noise, which may seriously reduce the quality of the sound signals, and further affect the popularization and application of the DAS system, so that noise filtering is necessary. In order to improve the quality of noisy sound signals, numerous expert and scholars have proposed various solutions. The existing scholars design a set of comprehensive filtering scheme based on an improved wavelet threshold algorithm, the scheme can effectively filter the same-frequency noise in signals, and a multi-window spectrum estimation spectral subtraction method based on end point detection is adopted to play a role in noise suppression. However, the application range of the above method is too limited, and the filtering effect is not ideal under the condition of complex noise or low signal-to-noise ratio, so that effective information contained in the signal cannot be accurately acquired.
Disclosure of Invention
The invention aims to provide a wavelet sound denoising method and system based on robust principal component analysis, so as to improve the quality of sound signals.
In order to achieve the purpose, the invention provides the following scheme:
a wavelet sound denoising method based on robust principal component analysis comprises the following steps:
acquiring a noise-containing sound signal;
separating the noise-containing sound signals by adopting a robust principal component analysis method to obtain separated noise-containing sound signals;
filtering the separated noise-containing sound signals by using a wavelet threshold denoising algorithm to obtain filtered noise-containing sound signals;
and carrying out low-pass filtering on the filtered noise-containing sound signal to obtain a noise-reduced sound signal.
Optionally, the filtering the separated noisy sound signal by using a wavelet threshold denoising algorithm to obtain a filtered noisy sound signal specifically includes:
performing wavelet decomposition on the separated noise-containing sound signals to obtain high-frequency wavelet coefficients of different layers and a last low-frequency wavelet coefficient;
setting a threshold and a threshold function according to the high-frequency wavelet coefficients, and performing threshold filtering on the high-frequency wavelet coefficients with different layers to obtain the filtered high-frequency wavelet coefficients with different layers;
and reconstructing the filtered high-frequency wavelet coefficients with different layers and the last low-frequency wavelet coefficient to obtain the filtered noise-containing sound signal.
Optionally, the setting a threshold and a threshold function according to the high-frequency wavelet coefficients to perform threshold filtering on the high-frequency wavelet coefficients with different layers to obtain the filtered high-frequency wavelet coefficients with different layers specifically includes:
judging whether the absolute value of the high-frequency wavelet coefficient of each layer is larger than a set threshold value of the high-frequency wavelet coefficient; if yes, carrying out zero setting processing on the high-frequency wavelet coefficient; if not, processing the high-frequency wavelet coefficients of each layer by using the threshold function to obtain the filtered high-frequency wavelet coefficients of different layers.
Optionally, the expression of the threshold function is:
y(x,λ)＝(1-μ1)·x+μ1·sign(x)·(|x|-λ·μ2)
wherein y (x, lambda) is the value of the high-frequency wavelet coefficient after threshold filtering, x is the high-frequency wavelet coefficient, lambda is the threshold, mu1＝exp[-(|x|-λ)2]，μ1Sign (x) is a sign function for the weighting factors,
Figure BDA0003498031220000023
Figure BDA0003498031220000021
μ2is a regulatory factor.
Optionally, the high-frequency wavelet coefficient set threshold comprises a first-layer high-frequency wavelet coefficient set threshold and other-layer high-frequency wavelet coefficient set thresholds;
the expression of the threshold setting of the first-layer high-frequency wavelet coefficient is as follows:
Figure BDA0003498031220000022
wherein λ is1Setting a threshold value for the high-frequency wavelet coefficient of the first layer, wherein me is the median value of the high-frequency wavelet coefficient of the jth layer, and N1The length of the first layer high-frequency wavelet coefficient;
the expression of the set threshold of the high-frequency wavelet coefficients of other layers is as follows:
Figure BDA0003498031220000031
wherein λ isjIs the threshold value of the high-frequency wavelet coefficient of the j-th layer, and j is the layer number of the high-frequency wavelet coefficient.
A wavelet sound denoising system based on robust principal component analysis, comprising:
the acquisition module is used for acquiring a noise-containing sound signal;
the separation module is used for separating the noise-containing sound signals by adopting a robustness principal component analysis method to obtain the separated noise-containing sound signals;
a wavelet threshold denoising module, configured to filter the separated noisy sound signal by using a wavelet threshold denoising algorithm to obtain a filtered noisy sound signal;
and the low-pass filtering module is used for carrying out low-pass filtering on the filtered noise-containing sound signal to obtain a noise-reduced sound signal.
Optionally, the wavelet threshold denoising module specifically includes:
the wavelet decomposition unit is used for performing wavelet decomposition on the separated noise-containing sound signals to obtain high-frequency wavelet coefficients with different layers and a last layer of low-frequency wavelet coefficient;
the threshold filtering unit is used for performing threshold filtering on the high-frequency wavelet coefficients with different layers according to a threshold value and a threshold function set by the high-frequency wavelet coefficients to obtain the filtered high-frequency wavelet coefficients with different layers;
and the reconstruction unit is used for reconstructing the filtered high-frequency wavelet coefficients with different layers and the last low-frequency wavelet coefficient to obtain the filtered noise-containing sound signal.
Optionally, the threshold filtering unit specifically includes:
the judgment subunit is used for judging whether the absolute value of the high-frequency wavelet coefficient of each layer is greater than the set threshold of the high-frequency wavelet coefficient; if yes, carrying out zero setting processing on the high-frequency wavelet coefficient; if not, processing the high-frequency wavelet coefficients of each layer by using the threshold function to obtain the filtered high-frequency wavelet coefficients of different layers.
Optionally, the expression of the threshold function is:
y(x,λ)＝(1-μ1)·x+μ1·sign(x)·(|x|-λ·μ2)
wherein y (x, lambda) is the value of the high-frequency wavelet coefficient after threshold filtering, x is the high-frequency wavelet coefficient, lambda is the threshold, mu1＝exp[-(|x|-λ)2]，μ1Sign (x) is a sign function for the weighting factors,
Figure BDA0003498031220000041
Figure BDA0003498031220000042
μ2is a regulatory factor.
Optionally, the high-frequency wavelet coefficient set threshold comprises a first-layer high-frequency wavelet coefficient set threshold and other-layer high-frequency wavelet coefficient set thresholds;
the expression of the threshold setting of the first-layer high-frequency wavelet coefficient is as follows:
Figure BDA0003498031220000043
wherein λ is1Setting a threshold value for the high-frequency wavelet coefficient of the first layer, wherein me is the median value of the high-frequency wavelet coefficient of the jth layer, N1The length of the first layer high-frequency wavelet coefficient;
the expression of the set threshold of the high-frequency wavelet coefficients of other layers is as follows:
Figure BDA0003498031220000044
wherein λ isjIs the threshold value of the high-frequency wavelet coefficient of the j-th layer, and j is the layer number of the high-frequency wavelet coefficient.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention obtains a noise-containing sound signal; separating the noise-containing sound signals by adopting a robust principal component analysis method to obtain separated noise-containing sound signals; filtering the separated noise-containing sound signals by using a wavelet threshold denoising algorithm to obtain filtered noise-containing sound signals; and carrying out low-pass filtering on the filtered noise-containing sound signal to obtain a noise-reduced sound signal. The invention realizes sound noise reduction by fusing a robust principal component analysis method, a wavelet threshold denoising algorithm and a low-pass filtering method, thereby improving the sound quality.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a wavelet sound denoising method based on robust principal component analysis according to the present invention;
FIG. 2 is a flow chart of a wavelet sound denoising method based on robust principal component analysis according to the present invention in practical application;
FIG. 3 is a schematic structural diagram of a DAS system based on the linear Sagnac principle according to the present invention;
FIG. 4 is a flowchart of a method for robust principal component analysis provided by the present invention;
FIG. 5 is a comparison of soft threshold function, hard threshold function, what threshold function was proposed and the improved threshold function of the present invention;
FIG. 6 is a parameter optimization diagram of signal-to-noise ratio (SNR) and speech quality assessment test value (PESQ) after signal noise reduction corresponding to different weighting factors according to the present invention;
fig. 7 is a waveform diagram of the actually measured signal provided by the present invention after being processed by different denoising algorithms.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the wavelet sound denoising method based on robust principal component analysis provided by the present invention includes:
step 201: a noisy sound signal is obtained. In practical applications, acquiring a noisy sound signal is acquired by a DAS system based on the linear Sagnac principle, as shown in fig. 3.
Step 202: and separating the noise-containing sound signals by adopting a robust principal component analysis method to obtain the separated noise-containing sound signals. In practical applications, the sound separation result obtained after the separation includes the separated noise-containing sound signal and the separated noise signal.
Step 203: and filtering the separated noise-containing sound signals by using a wavelet threshold denoising algorithm to obtain the filtered noise-containing sound signals.
Step 203, specifically comprising:
and carrying out wavelet decomposition on the separated noise-containing sound signals to obtain high-frequency wavelet coefficients with different layers and a last low-frequency wavelet coefficient. And decomposing according to the wavelet basis function selected by wavelet decomposition and the decomposition layer number to obtain high-frequency wavelet coefficients of different layer numbers and a last layer of low-frequency wavelet coefficients.
And setting a threshold and a threshold function according to the high-frequency wavelet coefficients, and performing threshold filtering on the high-frequency wavelet coefficients with different layers to obtain the filtered high-frequency wavelet coefficients with different layers. The threshold filtering is performed on the high-frequency wavelet coefficients with different layer numbers according to the set threshold and the threshold function of the high-frequency wavelet coefficients to obtain the filtered high-frequency wavelet coefficients with different layer numbers, and the method specifically comprises the following steps: judging whether the absolute value of the high-frequency wavelet coefficient of each layer is larger than the set threshold of the high-frequency wavelet coefficient; if yes, carrying out zero setting processing on the high-frequency wavelet coefficient; if not, processing the high-frequency wavelet coefficients of each layer by using the threshold function to obtain the filtered high-frequency wavelet coefficients of different layers.
The expression of the threshold function is:
y(x,λ)＝(1-μ1)·x+μ1·sign(x)·(|x|-λ·μ2)
wherein y (x, lambda) is the value of the high-frequency wavelet coefficient after threshold filtering, x is the high-frequency wavelet coefficient, lambda is the threshold, mu1＝exp[-(|x|-λ)2]，μ1Sign (x) is a sign function for the weighting factors,
Figure BDA0003498031220000061
Figure BDA0003498031220000062
μ2is a regulatory factor.
And reconstructing the filtered high-frequency wavelet coefficients with different layers and the last layer of low-frequency wavelet coefficients to obtain the filtered noise-containing sound signal.
Step 204: and carrying out low-pass filtering on the filtered noise-containing sound signal to obtain a noise-reduced sound signal. In practical applications, low-pass filtering is performed using a low-pass filter.
In practical application, the high-frequency wavelet coefficient set threshold comprises a first-layer high-frequency wavelet coefficient set threshold and other-layer high-frequency wavelet coefficient set thresholds.
The expression of the threshold setting of the first-layer high-frequency wavelet coefficient is as follows:
Figure BDA0003498031220000063
wherein λ is1Setting a threshold value for the high-frequency wavelet coefficient of the first layer, wherein me is the median value of the high-frequency wavelet coefficient of the jth layer, and N1Is the first layer high frequency wavelet coefficient length.
The expression of the set threshold of the high-frequency wavelet coefficients of other layers is as follows:
Figure BDA0003498031220000064
wherein λ isjIs the threshold value of the high-frequency wavelet coefficient of the j-th layer, and j is the layer number of the high-frequency wavelet coefficient.
Adopting zero setting processing by the threshold function on the high-frequency wavelet coefficient with the absolute value smaller than the threshold, and processing the high-frequency wavelet coefficient with the absolute value larger than or equal to the threshold by using the expression of the threshold function; and reconstructing the high-frequency wavelet coefficients of different layers after threshold filtering processing and the low-frequency wavelet coefficients of the last layer to obtain the noise-containing sound signals after filtering.
The threshold is designed according to the characteristic that the noise contained in the high-frequency wavelet coefficient is reduced along with the increase of the wavelet decomposition layer number; the threshold function has no constant deviation, the convergence rate is high, the threshold is continuous, and the phenomenon of false Gibbson can be prevented. Optimizing parameters in the method by using a coordinate axis descent method, wherein the parameters comprise: the method comprises the steps of weighting factors in a robustness principal component analysis method, wavelet basis functions and decomposition layer numbers in an improved wavelet threshold denoising algorithm, and normalization cut-off frequency in a low-pass filter. A robust principal component analysis method, an improved wavelet threshold denoising algorithm and a low-pass filtering method are fused to achieve sound denoising and improve sound quality.
The invention provides an improved wavelet sound denoising method based on robust principal component analysis, which comprises the following steps: acquiring a noise-containing sound signal through a DAS (data acquisition system); separating the noise-containing sound signals by adopting a robust principal component analysis method; filtering the separated noise-containing sound signals by using an improved wavelet threshold denoising algorithm; and (4) passing the filtered noise-containing sound signal through a low-pass filter to obtain a noise-reduced sound signal. The invention realizes sound noise reduction by fusing a plurality of filtering algorithms, can accurately restore sound signals in a strong noise environment and improves the quality of the sound signals.
As shown in fig. 2, the present invention further provides a specific step of a wavelet sound denoising method based on robust principal component analysis in practical application:
step 101: acquiring a noise-containing sound signal: the DAS is built according to the linear Sagnac principle to monitor the surrounding complex environment and collect the noise-containing sound signals. The DAS system structure is shown in FIG. 3, wherein Laser is light source, PD is photoelectric detector, DAQ is data acquisition card, and PC is computer; 1, 2, 3 each represent 3 inputs of a 3 × 3 coupler a; 4, 5, 6 denote 3 outputs of the 3 × 3 coupler a; b represents a delay fiber; 7 and 8 respectively represent two input ends of the 2 × 1 coupler c, 9 represents an output end of the 2 × 1 coupler, and 10 represents a disturbance intrusion point position; d represents a 1 × 2 coupler; 11 denotes the concatenated fibre at the output of the 1 x 2 coupler d. cw denotes the clockwise light path, the path of which is 1-a-6-b-8-c-9-10-d-11-d-10-9-c-7-4-a-3, cww denotes the counterclockwise light path, the path of which is 1-a-4-7-c-9-10-d-11-d-10-9-c-8-b-6-a-3.
Step 102: separating the noise-containing sound signals by adopting a robust principal component analysis method: the method uses a mathematical representation of the sound signal separation problem:
Figure BDA0003498031220000081
wherein rank (·) represents the rank of the matrix, | · | | | non-calculation0L representing a matrix0Norm, λ is a weighting factor, a represents a low rank sound signal, E represents a sparse noise signal, and D represents a noisy sound signal.
The solution of the above equation is mainly carried out in two steps (as shown in fig. 4):
the first step is to introduce the matrix kernel norm and L1Norm, converting the non-convex function in the above formula into a convex function;
the second step is to solve the convex function using the augmented lagrange multiplier method. Firstly constructing a Lagrange function with a penalty term by using an ALM to solve a convex function, then carrying out parameter iteration optimization by using a coordinate axis descent method, solving by using a soft threshold function in an iteration process, and finally, when a target matrix A is obtained*And E*Satisfies | | D-A*-E*||FAnd D does not countFHas a ratio of 10-7Or when the iteration number reaches 1000 times, outputting the final A*And E*Output of A*E output for the separated noisy sound signal*To separate the noise signal, | · | non-calculationFIs the F-norm of the matrix.
Step 103: filtering the separated noise-containing sound signal by using an improved wavelet threshold denoising algorithm: firstly, performing wavelet decomposition on the separated noise-containing sound signal, decomposing according to a selected wavelet basis function and a decomposition layer number to obtain high-frequency wavelet coefficients of different layers and a last layer of low-frequency wavelet coefficient, secondly, performing threshold filtering processing on the high-frequency wavelet coefficients of different layers by using an improved threshold and a threshold function, adopting zeroing processing on the high-frequency wavelet coefficients of which the absolute values are smaller than the threshold by using the improved threshold function, and processing the high-frequency wavelet coefficients of which the absolute values are larger than or equal to the threshold by using an improved threshold function expression; and finally, reconstructing the high-frequency wavelet coefficients of different layers after threshold filtering processing and the low-frequency wavelet coefficients of the last layer to obtain the noise-containing sound signals after filtering.
The improved threshold is of the form:
Figure BDA0003498031220000091
wherein λ isjIs the threshold value of the j-th layer high frequency wavelet coefficient, me is the median value of the j-th layer high frequency wavelet coefficient, N1Is the first layer high frequency wavelet coefficient length.
The improved threshold function is expressed as follows:
Figure BDA0003498031220000092
wherein y (x, lambda) is the value of the high-frequency wavelet coefficient after threshold filtering, x is the high-frequency wavelet coefficient, lambda is the threshold, mu1＝exp[-(|x|-λ)2]，μ1Sign (x) is a sign function for the weighting factors,
Figure BDA0003498031220000093
Figure BDA0003498031220000094
μ2is a regulatory factor.
Step 104: and passing the filtered noise-containing sound signal through a low-pass filter to obtain a final noise-reduced sound signal.
Comparing the soft threshold function, the hard threshold function, the existing threshold function with the improved threshold function of the present invention, it can be seen that the improved threshold function of the present invention has no constant deviation, fast convergence speed, continuity at the threshold, and can prevent the occurrence of the pseudo-gibson phenomenon, and the four threshold function pairs are as shown in fig. 5.
The parameters in the noise reduction method of the invention are optimized by using a coordinate axis descent method, and the parameters to be optimized comprise: the weight factors in the robust principal component analysis method, the wavelet basis functions and the decomposition layer number in the improved wavelet threshold denoising algorithm, and the normalized cut-off frequency in the low-pass filter, and the optimization results are shown in fig. 6, tables 1, 2, and 3:
TABLE 1 SNR and PESQ after denoising of different wavelet basis functions
Figure BDA0003498031220000095
Figure BDA0003498031220000101
TABLE 2 SNR and PESQ after noise reduction for different decomposition levels of sym5
Figure BDA0003498031220000102
TABLE 3 SNR and PESQ after denoising for different normalized cut-off frequencies
Figure BDA0003498031220000103
Wherein, SNR is the signal-to-noise ratio of the noise-reduced sound signal, and PESQ is the objective speech quality evaluation of the noise-reduced sound signal.
Partial verification results, as shown in fig. 7 and table 4:
TABLE 4 evaluation index of the actually measured signal 1 after different de-noising algorithm processing
Figure BDA0003498031220000104
Figure BDA0003498031220000111
Wherein RMSE is a root mean square error of the noise-reduced sound signal. The denoising method proposed by He le et al, which is why, Fengxin, Wu Huaming et al, is adopted in the research of the linear optical fiber Sagnac interferometer acoustic sensor and the denoising method thereof.
Compared with the prior art, the invention has the advantages that: according to the characteristics of sound signals collected by the DAS, a robustness principal component analysis method is adopted to process the sound signals, and an improved wavelet threshold denoising algorithm and a low-pass filtering method are fused to form an improved wavelet sound denoising method based on robustness principal component analysis, the method can effectively improve the sound signal quality under the environment with low signal-to-noise ratio, and as shown in Table 4, the SNR is improved by 22.756, the RMSE is reduced by 0.3658, and the PESQ is improved by 0.652.
The invention also provides a wavelet sound denoising system based on robust principal component analysis, comprising:
and the acquisition module is used for acquiring the noise-containing sound signal.
And the separation module is used for separating the noise-containing sound signals by adopting a robustness principal component analysis method to obtain the separated noise-containing sound signals.
And the wavelet threshold denoising module is used for filtering the separated noise-containing sound signals by using a wavelet threshold denoising algorithm to obtain the filtered noise-containing sound signals.
And the low-pass filtering module is used for carrying out low-pass filtering on the filtered noise-containing sound signal to obtain a noise-reduced sound signal.
In practical application, the wavelet threshold denoising module specifically includes:
and the wavelet decomposition unit is used for performing wavelet decomposition on the separated noise-containing sound signals to obtain high-frequency wavelet coefficients with different layers and a last layer of low-frequency wavelet coefficient.
And the threshold filtering unit is used for performing threshold filtering on the high-frequency wavelet coefficients with different layers according to the set threshold and the threshold function of the high-frequency wavelet coefficients to obtain the filtered high-frequency wavelet coefficients with different layers.
And the reconstruction unit is used for reconstructing the filtered high-frequency wavelet coefficients with different layers and the last low-frequency wavelet coefficient to obtain the filtered noise-containing sound signal.
In practical application, the threshold filtering unit specifically includes:
the judgment subunit is used for judging whether the absolute value of the high-frequency wavelet coefficient of each layer is greater than the set threshold of the high-frequency wavelet coefficient; if yes, carrying out zero setting processing on the high-frequency wavelet coefficient; if not, processing the high-frequency wavelet coefficients of each layer by using the threshold function to obtain the high-frequency wavelet coefficients of different layers after filtering.
In practical applications, the expression of the threshold function is:
y(x,λ)＝(1-μ1)·x+μ1·sign(x)·(|x|-λ·μ2)
wherein y (x, lambda) is the value of the high-frequency wavelet coefficient after threshold filtering, x is the high-frequency wavelet coefficient, lambda is the threshold, mu1＝exp[-(|x|-λ)2]，μ1Sign (x) is a sign function for the weighting factors,
Figure BDA0003498031220000121
Figure BDA0003498031220000122
μ2is a regulatory factor.
In practical application, the high-frequency wavelet coefficient set threshold comprises a first-layer high-frequency wavelet coefficient set threshold and other-layer high-frequency wavelet coefficient set thresholds.
The expression of the threshold setting of the first-layer high-frequency wavelet coefficient is as follows:
Figure BDA0003498031220000123
wherein λ is1Setting a threshold value for the high-frequency wavelet coefficient of the first layer, wherein me is the median value of the high-frequency wavelet coefficient of the jth layer, N1Is the first layer high frequency wavelet coefficient length.
The expression of the set threshold of the high-frequency wavelet coefficients of other layers is as follows:
Figure BDA0003498031220000124
wherein λ isjIs the threshold value of the high-frequency wavelet coefficient of the j-th layer, and j is the layer number of the high-frequency wavelet coefficient.
The invention obtains a noise-containing sound signal through a distributed optical fiber sound sensing system (DAS); separating the noise-containing sound signals by adopting a robust principal component analysis method; filtering the separated noise-containing sound signals by using an improved wavelet threshold and threshold function denoising algorithm; and passing the filtered noise-containing sound signal through a low-pass filter to obtain a noise-reduced sound signal. The invention realizes sound noise reduction by fusing a plurality of filtering algorithms, can accurately restore sound signals in a strong noise environment and improves the quality of the sound signals.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A wavelet sound denoising method based on robust principal component analysis is characterized by comprising the following steps:
acquiring a noise-containing sound signal;
separating the noise-containing sound signals by adopting a robust principal component analysis method to obtain separated noise-containing sound signals;
filtering the separated noise-containing sound signals by using a wavelet threshold denoising algorithm to obtain filtered noise-containing sound signals;
and carrying out low-pass filtering on the filtered noise-containing sound signal to obtain a noise-reduced sound signal.
2. The wavelet sound denoising method based on robust principal component analysis according to claim 1, wherein the filtering the separated noisy sound signal by using a wavelet threshold denoising algorithm to obtain a filtered noisy sound signal specifically comprises:
performing wavelet decomposition on the separated noise-containing sound signals to obtain high-frequency wavelet coefficients of different layers and a last low-frequency wavelet coefficient;
setting a threshold and a threshold function according to the high-frequency wavelet coefficients, and performing threshold filtering on the high-frequency wavelet coefficients with different layers to obtain the filtered high-frequency wavelet coefficients with different layers;
and reconstructing the filtered high-frequency wavelet coefficients with different layers and the last low-frequency wavelet coefficient to obtain the filtered noise-containing sound signal.
3. The wavelet sound denoising method based on robust principal component analysis according to claim 2, wherein the threshold filtering is performed on the high frequency wavelet coefficients of different layer numbers according to the high frequency wavelet coefficients setting threshold and threshold function to obtain the filtered high frequency wavelet coefficients of different layer numbers, specifically comprising:
judging whether the absolute value of the high-frequency wavelet coefficient of each layer is larger than a set threshold value of the high-frequency wavelet coefficient; if yes, carrying out zero setting processing on the high-frequency wavelet coefficient; if not, processing the high-frequency wavelet coefficients of each layer by using the threshold function to obtain the filtered high-frequency wavelet coefficients of different layers.
4. The wavelet sound denoising method based on robust principal component analysis of claim 2, wherein the expression of the threshold function is:
y(x,λ)＝(1-μ1)·x+μ1·sign(x)·(|x|-λ·μ2)
wherein y (x, lambda) is the value of the high-frequency wavelet coefficient after threshold filtering, x is the high-frequency wavelet coefficient, lambda is the threshold, mu1＝exp[-(|x|-λ)2]，μ1Sign (x) is a sign function for the weighting factors,
Figure FDA0003498031210000021
Figure FDA0003498031210000022
μ2is a regulatory factor.
5. The wavelet sound denoising method based on robust principal component analysis according to claim 2, wherein the high frequency wavelet coefficient set thresholds comprise a first layer high frequency wavelet coefficient set threshold and other layer high frequency wavelet coefficient set thresholds;
the expression of the threshold setting of the first-layer high-frequency wavelet coefficient is as follows:
Figure FDA0003498031210000023
wherein λ is1Setting a threshold value for the high-frequency wavelet coefficient of the first layer, wherein me is the median value of the high-frequency wavelet coefficient of the jth layer, N1The length of the first layer high-frequency wavelet coefficient;
the expression of the set threshold of the high-frequency wavelet coefficients of other layers is as follows:
Figure FDA0003498031210000024
wherein λ isjIs the threshold value of the high-frequency wavelet coefficient of the j-th layer, and j is the layer number of the high-frequency wavelet coefficient.
6. A wavelet sound denoising system based on robust principal component analysis, comprising:
the acquisition module is used for acquiring a noise-containing sound signal;
the separation module is used for separating the noise-containing sound signals by adopting a robustness principal component analysis method to obtain the separated noise-containing sound signals;
a wavelet threshold denoising module, configured to filter the separated noisy sound signal by using a wavelet threshold denoising algorithm to obtain a filtered noisy sound signal;
and the low-pass filtering module is used for performing low-pass filtering on the filtered sound signal containing the noise to obtain the sound signal subjected to noise reduction.
7. The wavelet sound denoising system based on robust principal component analysis according to claim 6, wherein the wavelet threshold denoising module specifically comprises:
the wavelet decomposition unit is used for performing wavelet decomposition on the separated noise-containing sound signals to obtain high-frequency wavelet coefficients with different layers and a last layer of low-frequency wavelet coefficient;
the threshold filtering unit is used for performing threshold filtering on the high-frequency wavelet coefficients with different layers according to a threshold value and a threshold function set by the high-frequency wavelet coefficients to obtain the filtered high-frequency wavelet coefficients with different layers;
and the reconstruction unit is used for reconstructing the filtered high-frequency wavelet coefficients with different layers and the last low-frequency wavelet coefficient to obtain the filtered noise-containing sound signal.
8. The wavelet sound denoising system based on robust principal component analysis according to claim 7, wherein the threshold filtering unit specifically comprises:
the judgment subunit is used for judging whether the absolute value of the high-frequency wavelet coefficient of each layer is greater than the set threshold of the high-frequency wavelet coefficient; if yes, carrying out zero setting processing on the high-frequency wavelet coefficient; if not, processing the high-frequency wavelet coefficients of each layer by using the threshold function to obtain the filtered high-frequency wavelet coefficients of different layers.
9. The wavelet sound denoising system based on robust principal component analysis of claim 7, wherein the expression of the threshold function is:
y(x,λ)＝(1-μ1)·x+μ1·sign(x)·(|x|-λ·μ2)
wherein y (x, lambda) is the value of the high-frequency wavelet coefficient after threshold filtering, x is the high-frequency wavelet coefficient, lambda is the threshold, mu1＝exp[-(|x|-λ)2]，μ1Sign (x) is a sign function for the weighting factors,
Figure FDA0003498031210000031
Figure FDA0003498031210000032
μ2is a regulatory factor.
10. The wavelet sound denoising system based on robust principal component analysis according to claim 7, wherein the high frequency wavelet coefficient set thresholds comprise a first layer high frequency wavelet coefficient set threshold and other layer high frequency wavelet coefficient set thresholds;
the expression of the threshold setting of the first-layer high-frequency wavelet coefficient is as follows:
Figure FDA0003498031210000033
wherein λ is1Setting a threshold value for the high-frequency wavelet coefficient of the first layer, wherein me is the median value of the high-frequency wavelet coefficient of the jth layer, N1The length of the first layer high-frequency wavelet coefficient;
the expression of the set threshold of the high-frequency wavelet coefficients of other layers is as follows:
Figure FDA0003498031210000034
wherein λ isjIs the threshold value of the high-frequency wavelet coefficient of the j-th layer, and j is the layer number of the high-frequency wavelet coefficient.
CN202210119888.5A 2022-02-09 2022-02-09 Wavelet sound denoising method and system based on robustness principal component analysis Pending CN114444548A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114722885A (en) * 2022-06-09 2022-07-08 山东山矿机械有限公司 Intelligent detection method and system for abnormal operation of carrier roller carrying trolley
CN114722885B (en) * 2022-06-09 2022-08-16 山东山矿机械有限公司 Intelligent detection method and system for abnormal operation of carrier roller carrying trolley

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