CN111650655A - Non-negative matrix factorization supervised transient electromagnetic signal noise reduction method - Google Patents

Non-negative matrix factorization supervised transient electromagnetic signal noise reduction method Download PDF

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CN111650655A
CN111650655A CN202010553227.4A CN202010553227A CN111650655A CN 111650655 A CN111650655 A CN 111650655A CN 202010553227 A CN202010553227 A CN 202010553227A CN 111650655 A CN111650655 A CN 111650655A
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曾庆宁
熊松龄
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Guilin University of Electronic Technology
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Abstract

The invention discloses a non-negative matrix factorization supervised transient electromagnetic signal noise reduction method, which comprises the steps of firstly, carrying out short-time Fourier transform and non-negative matrix factorization processing on a pure signal in a training stage to obtain an atom dictionary representing respective characteristics of the signal, then, processing a noise-containing signal by using the atom dictionary and a noise reduction model in a noise reduction stage to obtain a transient electromagnetic signal preliminarily estimated, finally, repeating the steps for multiple times, respectively accumulating late-stage data of the transient electromagnetic signal preliminarily estimated and original early-and-medium-stage data of the noise-containing signal, solving respective arithmetic mean values, and splicing the late-stage data and the original early-and-medium-stage data to estimate a final complete transient electromagnetic signal. The method can be applied to the work of exploring underground targets such as coal mines, metal mines, oil and gas fields and the like by the transient electromagnetic instrument.

Description

Non-negative matrix factorization supervised transient electromagnetic signal noise reduction method
Technical Field
The invention relates to the field of transient electromagnetic signal processing, in particular to a non-negative matrix factorization supervised transient electromagnetic signal noise reduction method.
Background
The transient electromagnetic method is used as an important geophysical exploration method, and is characterized by that according to the electromagnetic induction principle, an ungrounded return line or grounded line source is used to send a primary field to underground, under the excitation of the primary field a secondary field is excited in the underground geologic body, and the secondary field signal is analyzed and processed so as to attain the goal of detecting underground geologic body. The transient electromagnetic method has higher detection and resolution capability and is widely applied to the exploration work of underground targets such as coal mines, metal mines, oil-gas fields and the like.
During field operation, signals acquired by the transient electromagnetic method are interfered by various noises, such as: the noise of the transient electromagnetic signal is even drowned out when the noise is serious, and the noise seriously affects the subsequent processing work of the transient electromagnetic signal. In the early stage of transient electromagnetic signal processing, people research the characteristics of various noises and provide various noise reduction methods, such as wavelet transformation, Kalman filtering, singular value decomposition, a stacked noise reduction self-encoder and the like, and the methods have the defects of lack of adaptivity, unsatisfactory noise reduction result, complex processing steps, complex model and the like and are not beneficial to subsequent inversion work.
A supervised algorithm of nonnegative matrix factorization is a dictionary learning method, has wide application in the aspects of information source separation, speech enhancement and the like, and can effectively extract the characteristics of transient electromagnetic signals and perform high-quality noise reduction on the transient electromagnetic signals.
Disclosure of Invention
The invention aims to provide a non-negative matrix factorization supervised transient electromagnetic signal noise reduction method aiming at the defects of the current transient electromagnetic signal noise reduction method. The method can effectively remove the noise in the actual transient electromagnetic signal, improve the inversion accuracy of the transient electromagnetic signal and is beneficial to the exploration work of the underground target.
The technical scheme for realizing the purpose of the invention is as follows:
a non-negative matrix factorization supervised transient electromagnetic signal noise reduction method is different from the prior art in that the method comprises the following steps:
1) acquiring a transient electromagnetic signal y measured by a transient electromagnetic instrument adopting a central loop device, wherein the time domain of the transient electromagnetic signal y containing noise is represented by y (M) ═ v (M) + n (M), M ═ 1,2, … … M, wherein M represents the size of acquired data, v (M) is a pure transient electromagnetic signal, and n (M) is additive noise;
2) discarding the late data of the transient electromagnetic signal y containing noise and keeping the early and middle dataAccording to
Figure BDA0002543341660000011
For later use;
3) constructing a signal feature extractor: respectively carrying out short-time Fourier transform on a transient electromagnetic signal y containing noise, a pure transient electromagnetic signal V (m) and a noise signal N (m) to obtain respective amplitude spectrums and phase spectrums, taking the amplitude spectrums to obtain non-negative matrixes Y, V and N of signals corresponding to the signals, carrying out non-negative matrix decomposition on the non-negative matrixes V and N, extracting the characteristics of the corresponding signals, and finally splicing atom dictionaries representing the characteristics of the corresponding signals into an overall dictionary W, wherein the specific process is as follows:
3-1): carrying out short-time Fourier transform on the clean transient electromagnetic signal v (m), the additive noise n (m) and the noisy transient electromagnetic signal y (m) and obtaining the amplitude spectrums of the signals to obtain corresponding non-negative matrixes shown in formula (1), formula (2) and formula (3):
Figure BDA0002543341660000021
Figure BDA0002543341660000022
Figure BDA0002543341660000023
where w (m) is a real window sequence, and k represents the frame shift, the amplitude spectra of the corresponding clean transient electromagnetic signal and noise signal are V ═ Vk(f, t) | and N ═ Nk(f, t) |, the phase spectrum of the noisy transient electromagnetic signal is arg { Y |k(f,t)}；
3-2) carrying out non-negative matrix decomposition on the amplitude spectrum obtained in the step 3-1) to obtain an atom dictionary representing corresponding signal characteristics, wherein the process can be completed by minimizing the following objective function:
Figure BDA0002543341660000024
Figure BDA0002543341660000025
wherein, the atom dictionary WvRepresenting features of clean, transient electromagnetic signals, atomic dictionary WnCharacteristic of noise signal, HvAnd HnCoefficient matrixes respectively representing V and N, | · | | non-woven phosphorFIs the Frobenius norm,
to minimize the above objective function, a multiplicative iterative rule shown by the following formula is used to solve:
Figure BDA0002543341660000026
Figure BDA0002543341660000027
wherein S represents the target matrix to be subjected to non-negative matrix factorization, corresponding to V and N, W in formula (4) and formula (5)bjAnd HbjRepresent elements in the matrices W and H, respectively;
3-3) splicing the atom dictionaries which are obtained in the step 3-2) and represent the signal features of the atom dictionaries to obtain a total dictionary W ═ WvWn]；
4) After a general dictionary W is obtained, a non-negative matrix Y representing a noisy signal is subjected to non-negative matrix decomposition to obtain a coefficient matrix H, and a matrix representing pure transient electromagnetic signals is estimated by adopting a noise reduction model
Figure BDA0002543341660000031
Finally, the phase spectrum of the noisy signal y obtained in the step 3) and the estimated matrix which represents the pure transient electromagnetic signal are combined
Figure BDA0002543341660000032
Carrying out short-time Fourier inverse transformation to obtain a transient electromagnetic signal of preliminary estimation
Figure BDA0002543341660000033
The specific process is as follows:
4-1) after obtaining the total dictionary W, carrying out non-negative matrix decomposition on a non-negative matrix Y representing a noisy signal to obtain a coefficient matrix H, wherein the process can be expressed as the following optimization process:
Figure BDA0002543341660000034
wherein arg represents H taking the minimum of the norm of the above formula;
4-2) for step 4-1) obtaining the coefficient matrix H, can be written as
Figure BDA0002543341660000035
Weights representing the features of the atoms in the global dictionary W;
4-3) estimating a pure transient electromagnetic signal matrix by adopting a noise reduction model shown in the following formula (8) and formula (9)
Figure BDA0002543341660000036
Figure BDA0002543341660000037
Figure BDA0002543341660000038
4-4) matrix of the estimated pure transient electromagnetic signals obtained in step 4-3)
Figure BDA0002543341660000039
Comparing the phase spectrum arg { Y) of the transient electromagnetic signal containing noise obtained in the step 3) with the phase spectrum arg { Y of the transient electromagnetic signal containing noise obtained in the step 3)k(f, t) } carrying out short-time Fourier inverse transformation to obtain the preliminarily estimated transient electromagnetic signal
Figure BDA00025433416600000310
5) Repeating the steps 1) and 2) at least 50 times, and generating early-middle data of noise-containing signals with different values each time
Figure BDA00025433416600000311
And calculate these early and middle data
Figure BDA00025433416600000312
Is arithmetic mean of
Figure BDA00025433416600000313
Repeating the steps 3) to 4) at least 50 times to obtain
Figure BDA00025433416600000314
And discarding early and middle data and retaining late data to obtain preliminarily estimated late data of the transient electromagnetic signal
Figure BDA00025433416600000315
6) The obtained early and medium term data
Figure BDA00025433416600000316
And late stage data
Figure BDA00025433416600000317
Splicing to estimate the final pure transient electromagnetic signal
Figure BDA00025433416600000318
The technical scheme includes that a transient electromagnetic signal containing noise is divided into an early-middle part and a late part, the signal containing noise is processed by adopting a non-negative matrix factorization supervised algorithm, the steps are repeated for many times, late data of a processing result and original early-middle data of the signal containing noise are accumulated respectively to calculate an arithmetic mean value, and finally a complete noise reduction signal is spliced.
The method can effectively remove the noise in the actual transient electromagnetic signal, improve the inversion accuracy of the transient electromagnetic signal and is beneficial to the exploration work of the underground target.
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FIG. 1 is a functional block diagram of an embodiment method;
FIG. 2 is a schematic block diagram of a signal feature extractor in an embodiment;
FIG. 3 is a time domain diagram of a noisy transient electromagnetic signal under the condition of the natural electrical noise and the signal-to-noise ratio of 15dB in the embodiment;
FIG. 4 is a time domain diagram of a noisy transient electromagnetic signal with a signal-to-noise ratio of 15dB and a sky-electric noise in an embodiment after noise reduction by the method of the present embodiment.
Detailed Description
The invention will be further elucidated with reference to the drawings and examples, without however being limited thereto.
Example (b):
referring to fig. 1, a non-negative matrix factorization supervised transient electromagnetic signal noise reduction method includes the following steps:
1) acquiring a transient electromagnetic signal y measured by a transient electromagnetic instrument adopting a central loop device, wherein the time domain of the transient electromagnetic signal y containing noise is represented by y (M) ═ v (M) + n (M), M ═ 1,2, … … M, wherein M represents the size of acquired data, v (M) is a pure transient electromagnetic signal, and n (M) is additive noise;
2) discarding the late data of the transient electromagnetic signal y containing noise and retaining the early and middle data
Figure BDA0002543341660000041
For later use;
3) constructing a signal feature extractor: respectively carrying out short-time Fourier transform on a transient electromagnetic signal y containing noise, a pure transient electromagnetic signal V (m) and a noise signal N (m) to obtain respective amplitude spectrums and phase spectrums, taking the amplitude spectrums to obtain non-negative matrixes Y, V and N of signals corresponding to the signals, carrying out non-negative matrix decomposition on the non-negative matrixes V and N, extracting the characteristics of the corresponding signals, and finally splicing atom dictionaries representing the characteristics of the corresponding signals into an overall dictionary W, wherein the specific process is shown in FIG. 2:
3-1): carrying out short-time Fourier transform on the clean transient electromagnetic signal v (m), the additive noise n (m) and the noisy transient electromagnetic signal y (m) and obtaining the amplitude spectrums of the signals to obtain corresponding non-negative matrixes shown in formula (1), formula (2) and formula (3):
Figure BDA0002543341660000042
Figure BDA0002543341660000043
Figure BDA0002543341660000044
where w (m) is a real window sequence, and k represents the frame shift, the amplitude spectra of the corresponding clean transient electromagnetic signal and noise signal are V ═ Vk(f, t) | and N ═ Nk(f, t) |, the phase spectrum of the noisy transient electromagnetic signal is arg { Y |k(f,t)}；
3-2) carrying out non-negative matrix decomposition on the amplitude spectrum obtained in the step 3-1) to obtain an atom dictionary representing corresponding signal characteristics, wherein the process can be completed by minimizing the following objective function:
Figure BDA0002543341660000051
Figure BDA0002543341660000052
wherein, the atom dictionary WvRepresenting features of clean, transient electromagnetic signals, atomic dictionary WnCharacteristic of noise signal, HvAnd HnCoefficient matrixes respectively representing V and N, | · | | non-woven phosphorFIs the Frobenius norm,
to minimize the above objective function, a multiplicative iterative rule shown by the following formula is used to solve:
Figure BDA0002543341660000053
Figure BDA0002543341660000054
wherein S represents the target matrix to be subjected to non-negative matrix factorization, corresponding to V and N, W in formula (4) and formula (5)bjAnd HbjRepresent elements in the matrices W and H, respectively;
3-3) splicing the atom dictionaries which are obtained in the step 3-2) and represent the signal features of the atom dictionaries to obtain a total dictionary W ═ WvWn]；
4) After a general dictionary W is obtained, a non-negative matrix Y representing a noisy signal is subjected to non-negative matrix decomposition to obtain a coefficient matrix H, and a matrix representing pure transient electromagnetic signals is estimated by adopting a noise reduction model
Figure BDA0002543341660000055
Finally, the phase spectrum of the noisy signal y obtained in the step 3) and the estimated matrix which represents the pure transient electromagnetic signal are combined
Figure BDA0002543341660000056
Carrying out short-time Fourier inverse transformation to obtain a transient electromagnetic signal of preliminary estimation
Figure BDA0002543341660000057
The specific process is as follows:
4-1) after obtaining the total dictionary W, carrying out non-negative matrix decomposition on a non-negative matrix Y representing a noisy signal to obtain a coefficient matrix H, wherein the process can be expressed as the following optimization process:
Figure BDA0002543341660000058
wherein arg represents H taking the minimum of the norm of the above formula;
4-2) for step 4-1) obtaining the coefficient matrix H, can be written as
Figure BDA0002543341660000059
Weights representing the features of the atoms in the global dictionary W;
4-3) estimating a pure transient electromagnetic signal matrix by adopting a noise reduction model shown in the following formula (8) and formula (9)
Figure BDA00025433416600000510
Figure BDA00025433416600000511
Figure BDA0002543341660000061
4-4) matrix of the estimated pure transient electromagnetic signals obtained in step 4-3)
Figure BDA0002543341660000062
Comparing the phase spectrum arg { Y) of the transient electromagnetic signal containing noise obtained in the step 3) with the phase spectrum arg { Y of the transient electromagnetic signal containing noise obtained in the step 3)k(f, t) } carrying out short-time Fourier inverse transformation to obtain the preliminarily estimated transient electromagnetic signal
Figure BDA0002543341660000063
5) Repeating the steps 1) and 2) at least 50 times, and generating early-middle data of noise-containing signals with different values each time
Figure BDA0002543341660000064
And calculate these early and middle data
Figure BDA0002543341660000065
Is arithmetic mean of
Figure BDA0002543341660000066
Repeating the steps 3) to 4) at least 50 times to obtain
Figure BDA0002543341660000067
And discarding early and middle data and retaining late data to obtain preliminarily estimated late data of the transient electromagnetic signal
Figure BDA0002543341660000068
6) The obtained early and medium term data
Figure BDA0002543341660000069
And late stage data
Figure BDA00025433416600000610
Splicing to estimate the final pure transient electromagnetic signal
Figure BDA00025433416600000611
The method can effectively inhibit noise, the processed waveform is smooth, the noise is suppressed to be clean, in addition, in terms of two noise reduction performance evaluation indexes of the output signal-to-noise ratio and the root-mean-square error, the method can greatly improve the output signal-to-noise ratio and reduce the root-mean-square error even under the condition of low signal-to-noise ratio, can obtain better noise reduction effect, improves the data quality, and is beneficial to the subsequent inversion processing of transient electromagnetic signals.
As shown in fig. 3 and 4, fig. 3 is a time domain schematic diagram of a section of noisy transient electromagnetic signal under the condition of a sky electric noise and a signal-to-noise ratio of 15dB, fig. 4 is a time domain schematic diagram of the noisy transient electromagnetic signal under the condition of the sky electric noise in the present example, and the noise reduction of the noisy transient electromagnetic signal under the condition of the signal-to-noise ratio of 15dB according to the method of the present example, as is apparent from fig. 3 and 4, the sky electric noise is substantially eliminated after the noise reduction of the noisy transient electromagnetic signal according to the present example, no obvious burr is seen, the noise reduction effect is good, and experimental results show that the noise in the transient electromagnetic signal can be effectively reduced according.

Claims (1)

1. A non-negative matrix factorization supervised transient electromagnetic signal noise reduction method is characterized by comprising the following steps:
1) acquiring a transient electromagnetic signal y measured by a transient electromagnetic instrument of a central loop device, wherein the time domain of the transient electromagnetic signal y containing noise is represented by y (M) ═ v (M) + n (M), M ═ 1,2, … … M, wherein M represents the size of acquired data, v (M) is a pure transient electromagnetic signal, and n (M) is additive noise;
2) discarding the late data of the transient electromagnetic signal y containing noise and retaining the early and middle data
Figure FDA0002543341650000016
3) Constructing a signal feature extractor: respectively carrying out short-time Fourier transform on a transient electromagnetic signal y containing noise, a pure transient electromagnetic signal V (m) and additive noise N (m) to obtain respective amplitude spectrums and phase spectrums, taking the amplitude spectrums to obtain non-negative matrixes Y, V and N of signals corresponding to the signals, carrying out non-negative matrix decomposition on the non-negative matrixes V and N, extracting the characteristics of the corresponding signals, and finally splicing atom dictionaries representing the characteristics of the corresponding signals into an overall dictionary W, wherein the specific process is as follows:
3-1): carrying out short-time Fourier transform on the clean transient electromagnetic signal v (m), the additive noise n (m) and the noisy transient electromagnetic signal y (m) and obtaining the amplitude spectrums of the signals to obtain corresponding non-negative matrixes shown in formula (1), formula (2) and formula (3):
Figure FDA0002543341650000011
Figure FDA0002543341650000012
Figure FDA0002543341650000013
where w (m) is a real window sequence, and k represents the frame shift, the amplitude spectra of the corresponding clean transient electromagnetic signal and noise signal are V ═ Vk(f, t) | and N ═ Nk(f, t) |, the phase spectrum of the noisy transient electromagnetic signal is arg { Y |k(f,t)}；
3-2) carrying out non-negative matrix decomposition on the amplitude spectrum obtained in the step 3-1) to obtain an atom dictionary representing corresponding signal characteristics, wherein the process can be completed by minimizing the following objective function:
Figure FDA0002543341650000014
Figure FDA0002543341650000015
wherein, the atom dictionary WvRepresenting features of clean, transient electromagnetic signals, atomic dictionary WnCharacteristic of noise signal, HvAnd HnCoefficient matrixes respectively representing V and N, | · | | non-woven phosphorFIs the Frobenius norm,
to minimize the above objective function, a multiplicative iterative rule shown by the following formula is used to solve:
Figure FDA0002543341650000021
Figure FDA0002543341650000022
wherein S represents the target matrix to be subjected to non-negative matrix factorization, corresponding to V and N, W in formula (4) and formula (5)bjAnd HbjRepresent elements in the matrices W and H, respectively;
3-3) splicing the atom dictionaries which are obtained in the step 3-2) and represent the signal features of the atom dictionaries to obtain a total dictionary W ═ WvWn]；
4) After a general dictionary W is obtained, a non-negative matrix Y representing a noisy signal is subjected to non-negative matrix decomposition to obtain a coefficient matrix H, and a matrix representing pure transient electromagnetic signals is estimated by adopting a noise reduction model
Figure FDA0002543341650000023
Finally, the phase spectrum of the noisy signal y obtained in the step 3) and the estimated matrix which represents the pure transient electromagnetic signal are combined
Figure FDA0002543341650000024
Carrying out short-time Fourier inverse transformation to obtain a transient electromagnetic signal of preliminary estimation
Figure FDA0002543341650000025
The specific process is as follows:
4-1) after obtaining the total dictionary W, carrying out non-negative matrix decomposition on a non-negative matrix Y representing a noisy signal to obtain a coefficient matrix H, wherein the process can be expressed as the following optimization process:
Figure FDA0002543341650000026
wherein arg represents H taking the minimum of the norm of the above formula;
4-2) for step 4-1) obtaining the coefficient matrix H, can be written as
Figure FDA0002543341650000027
Weights representing the features of the atoms in the global dictionary W;
4-3) estimating a pure transient electromagnetic signal matrix by adopting a noise reduction model shown in the following formula (8) and formula (9)
Figure FDA0002543341650000028
Figure FDA0002543341650000029
Figure FDA00025433416500000210
4-4) matrix of the estimated pure transient electromagnetic signals obtained in step 4-3)
Figure FDA00025433416500000211
Comparing the phase spectrum arg { Y) of the transient electromagnetic signal containing noise obtained in the step 3) with the phase spectrum arg { Y of the transient electromagnetic signal containing noise obtained in the step 3)k(f, t) } carrying out short-time Fourier inverse transformation to obtain the preliminarily estimated transient electromagnetic signal
Figure FDA00025433416500000212
5) Repetition ofExecuting step 1) -step 2) at least 50 times, and generating early-middle data of noise-containing signals with different values each time
Figure FDA00025433416500000213
And calculate these early and middle data
Figure FDA00025433416500000214
Is arithmetic mean of
Figure FDA00025433416500000215
Repeating the steps 3) to 4) at least 50 times to obtain
Figure FDA00025433416500000216
And discarding early and middle data and retaining late data to obtain preliminarily estimated late data of the transient electromagnetic signal
Figure FDA0002543341650000031
6) The obtained early and medium term data
Figure FDA0002543341650000032
And late stage data
Figure FDA0002543341650000033
Splicing to estimate the final pure transient electromagnetic signal
Figure FDA0002543341650000034
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CN116756637A (en) * 2023-08-10 2023-09-15 暨南大学 Wireless signal intelligent detection and identification method and computer readable storage medium
CN116756637B (en) * 2023-08-10 2023-12-05 暨南大学 Wireless signal intelligent detection and identification method and computer readable storage medium

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