CN113655534B - Nuclear magnetic resonance FID signal noise suppression method based on multi-linear singular value tensor decomposition - Google Patents

Nuclear magnetic resonance FID signal noise suppression method based on multi-linear singular value tensor decomposition Download PDF

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CN113655534B
CN113655534B CN202110794109.7A CN202110794109A CN113655534B CN 113655534 B CN113655534 B CN 113655534B CN 202110794109 A CN202110794109 A CN 202110794109A CN 113655534 B CN113655534 B CN 113655534B
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decomposition
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CN113655534A (en
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刘欢
王泽华
董浩斌
赵昌峰
王晓斌
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China University of Geosciences
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    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
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    • G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
    • G01V3/14—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with electron or nuclear magnetic resonance
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Abstract

The invention provides a nuclear magnetic resonance FID signal noise suppression method based on multi-linear singular value tensor decomposition, which comprises the following steps: acquiring a multichannel signal: enabling one channel to start sampling at intervals of delta t through time delay sampling to obtain a multi-channel signal; converting each channel signal into Hankel matrix to form third-order tensor
Figure DDA0003162185570000011
To third order tensor
Figure DDA0003162185570000012
Performing Tucker decomposition and processing to obtain third order tensor
Figure DDA0003162185570000013
Tensor of third order
Figure DDA0003162185570000014
Recovering the signal into a multi-channel signal, and performing CP tensor decomposition processing on a second-order tensor X formed by the multi-channel signal to finally obtain a high signal-to-noise ratio signal X after multi-channel signal fusionnew. The invention has the beneficial effects that: the method effectively overcomes the limitation of the current algorithm under strong noise interference, simultaneously ensures the real-time property and universality of the algorithm, is applicable to instruments such as a proton magnetometer and a nuclear magnetic resonance water finder, improves the precision of frequency domain measurement and the accuracy of hydrological parameters, and effectively improves the precision and the accuracy of related geoscience instruments.

Description

Nuclear magnetic resonance FID signal noise suppression method based on multi-linear singular value tensor decomposition
Technical Field
The invention relates to the field of signal processing, in particular to a nuclear magnetic resonance (FID) signal noise suppression method and method based on multi-linear singular value tensor decomposition.
Background
Free Induction Decay (FID) signals are signals generated in nuclear magnetic resonance technology, and in related instruments (such as proton precession magnetometers, nuclear magnetic resonance water detectors and the like) in the field of geophysical exploration by using the nuclear magnetic resonance technology, required geomagnetic field values, hydrological parameters and the like are obtained by means of extracting parameters of the nuclear magnetic resonance FID signals, measuring frequencies, inverting hydrological parameters and the like, but the obtained FID signals are very weak, and the FID signals are easily submerged in environmental noise and artificial noise. How to suppress various types of noise becomes a major limitation of nmr techniques in related geosciences. Therefore, in order to improve the measurement accuracy and accuracy of the geoscience instrument, it is necessary to perform noise suppression on the acquired FID signal to obtain more accurate information such as frequency, hydrological parameters, and the like.
The FID signal noise suppression means in the current stage mainly performs noise suppression through algorithms, and commonly used algorithms include SVD, wavelet transform, PCA, EMD, and the like, but the algorithms still have the following limitations in practical application: 1) the requirement on the data volume is high, and the noise suppression effect is greatly reduced under the condition of few sampling points; 2) the analysis processing is carried out in a time-frequency domain, the calculation amount is large, and the real-time performance cannot be guaranteed; 3) the universality is weak, and the algorithms perform noise suppression on specific types of noise, but in a practical situation, a plurality of types of noise exist simultaneously. Therefore, when the obtained FID signal is noisy and the noise category is high, these algorithms are not capable of performing effective noise suppression, so that the instrument cannot work normally.
Disclosure of Invention
In view of the above, aiming at the technical defects, the invention provides a method for suppressing noise of an FID signal based on nonlinear singular value tensor decomposition, which comprises the following steps:
s101: acquiring a multichannel signal: enabling one channel to start sampling at intervals of delta t through time delay sampling to obtain a multi-channel signal;
s102: noise suppression based on multilinear singular value tensor decomposition:
converting each channel signal into Hankel matrix to form third-order tensor
Figure GDA0003570419470000021
To third order tensor
Figure GDA0003570419470000022
Performing Tucker decomposition and processing to obtain third order tensor
Figure GDA0003570419470000023
Tensor of third order
Figure GDA0003570419470000024
Recovering the signal into a multi-channel signal, and performing CP tensor decomposition processing on a second-order tensor X formed by the multi-channel signal to finally obtain a high signal-to-noise ratio signal X after multi-channel signal fusionnew。
Further, the third order tensor obtained in step S102
Figure GDA00035704194700000214
The specific process of performing the Tucker decomposition treatment comprises the following steps:
to tensor
Figure GDA0003570419470000025
Performing Tucker decomposition to obtain a core tensor
Figure GDA0003570419470000026
With a plurality of adjoint matrices U(n)；
To core tensor
Figure GDA0003570419470000027
Carrying out zero setting processing on singular values with relatively small median values to obtain a processed core tensor
Figure GDA0003570419470000028
The processed core tensor
Figure GDA0003570419470000029
A plurality of adjoint matrixes U obtained in the last step(n)Carrying out tensor modular multiplication operation to obtain third-order tensor
Figure GDA00035704194700000210
I.e. a part of the noise suppression is done.
Further, for the third order tensor
Figure GDA00035704194700000211
The restoration is a multichannel signal X, and the specific process of CP tensor decomposition is as follows:
tensor of third order
Figure GDA00035704194700000212
Transforming into a multi-channel signal matrix X (namely a second-order tensor) through a Hankel inverter; and decomposing the second-order tensor X into a form of two groups of one-dimensional vector outer products by using CP tensor decomposition to obtain a vector a and a vector b, and calculating the vector a and the vector b to obtain a fused denoising FID signal so as to complete all noise suppression.
Further, the operation process of the a, b vector is as follows:
Figure GDA00035704194700000213
wherein mean (a) x b represents that the mean value of the vector a is multiplied by the vector b to obtain a fused signal xnew。
The invention has the beneficial effects that: the method effectively overcomes the limitation of the current algorithm under strong noise interference, simultaneously ensures the real-time property and universality of the algorithm, is applicable to instruments such as a proton magnetometer and a nuclear magnetic resonance water finder, improves the precision of frequency domain measurement and the accuracy of hydrological parameters, and effectively improves the precision and the accuracy of related geoscience instruments.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a multi-channel equal delay sampling method;
fig. 3 is a comparison of the effect of the FID signal measured in the extreme environment after noise suppression by SVD, PCA, and multi-linear singular value tensor decomposition (MLSVD).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, a method for suppressing noise of a nuclear magnetic resonance FID signal based on nonlinear singular value tensor decomposition includes the following steps:
s101: acquiring a multichannel signal: enabling one channel to start sampling at intervals of delta t through time delay sampling to obtain a multi-channel signal;
in the embodiment of the invention, a multi-channel equal delay sampling method is adopted to obtain a plurality of related FID signals, one channel is enabled to start sampling every time delta t through delay sampling, and the sampling time is equal, so that a plurality of signals related to the original signals can be obtained.
For example, when the number of channels is 5, 5 FID signals x are obtained1,x2,x3,x4,x5A schematic diagram of the multi-channel equal delay sampling method is shown in fig. 2.
The method actually yields 5 vectors x1,x2,x3,x4,x5There are different signal and noise components:
Figure GDA0003570419470000041
wherein xsRepresenting a signal component, xnRepresenting the noise component. The correlation among signal components of multi-channel data acquired by a multi-channel equal delay sampling method is strong, the correlation among noise components is low, and compared with multi-channel sampling, the correlation of noise data is reduced.
S102: noise suppression based on multilinear singular value tensor decomposition:
converting each channel signal into Hankel matrix to form third-order tensor
Figure GDA0003570419470000042
To third order tensor
Figure GDA0003570419470000043
And performing Tucker decomposition processing and Hankel inverse transformation to obtain a multichannel signal X, performing CP tensor decomposition on the X to complete signal fusion, and completing noise suppression.
In the invention, after acquiring multichannel data, the multichannel data is constructed into a third-order tensor, and the noise processing is carried out by utilizing the decomposition of a multilinear singular value tensor:
1) and transforming the signals of each channel into a Hankel matrix, wherein a three-dimensional array formed by a plurality of Hankel matrices is a third-order tensor. After the third-order tensor is constructed, the tensor needs to be subjected to multi-linear singular value tensor decomposition. Assuming a third order tensor is derived:
Figure GDA0003570419470000044
2) to tensor
Figure GDA0003570419470000045
Performing Tucker decomposition: tensor
Figure GDA0003570419470000046
Decomposed into a core tensor
Figure GDA0003570419470000047
With N adjoint matrices
Figure GDA0003570419470000048
The result of successive modulo n multiplications.
3) Tensor
Figure GDA0003570419470000049
Obtaining a core tensor after Tucker decomposition
Figure GDA00035704194700000410
The values also represent the signal and noise components of the data. The smaller value representing noise is set to zero and restored to new tensor
Figure GDA00035704194700000411
The effect of noise processing can be obtained.
4) Will tensor
Figure GDA00035704194700000412
Obtaining a second-order tensor (matrix) X through Hankel inverse transformation, decomposing the second-order tensor (matrix) X through a CP tensor to obtain two vectors a and b, and calculating the vectors a and b:
Figure GDA0003570419470000051
mean (a) x b denotes multiplying the mean of vector a by vector b to obtain the fused signal xnewNamely the fused FID signal.
The present invention provides an embodiment as follows:
fig. 3 is a comparison of the effect of the FID signal measured in the extreme environment after noise suppression by SVD, PCA and multi-linear singular value tensor decomposition (MLSVD), and it can be seen from the time domain diagram (SVD is the uppermost and lowermost part on the left side of fig. 3, MLSVD is the middle trapezoidal part on the left side of fig. 3, and PCA is the part between the two) and the frequency domain diagram that the noise reduction effect of the FID signal noise suppression algorithm based on the multi-linear singular value decomposition is obvious, and the useful information of the FID signal can still be recovered under the condition that other algorithms cannot work. The signal envelope is clearer and the attenuation characteristic is more obvious in the time domain; the frequency spectrum curve is smoother and more approximate to the real FID signal frequency spectrum in the frequency domain.
The noise suppression effects of the SVD, PCA and the multi-linear singular value tensor decomposition algorithms at different sampling points are sorted, the comparison results are shown in Table 1, and it can be seen that the multi-linear singular value tensor decomposition algorithms have obvious noise suppression effects compared with other algorithms at different sampling points, and when the noise is large, the SVD and the PCA cannot work, and the multi-linear singular value tensor decomposition algorithms can still effectively perform noise suppression.
Table 1: and decomposing the noise reduction effect of the SVD, the PCA and the multi-linear singular value tensor under different conditions.
Figure GDA0003570419470000052
Figure GDA0003570419470000061
Compared with the existing FID signal noise suppression algorithm, the method has the following characteristics:
(1) a multi-channel signal acquisition method based on time delay is adopted to acquire more signal noise characteristic information;
(2) the noise singular value is calculated and processed by using the multi-linear singular value tensor decomposition, and the real-time performance of the algorithm is ensured while the noise suppression effect is ensured;
(3) information fusion of multi-channel signals is realized through CP tensor decomposition, and the noise suppression effect of the invention is further improved.
The invention provides a nuclear magnetic resonance signal noise suppression method based on multi-linear singular value tensor decomposition, which effectively overcomes the limitation of the current algorithm under strong noise interference, ensures the real-time property and universality of the algorithm, is suitable for instruments such as a proton magnetometer and a nuclear magnetic resonance water finder, improves the precision of frequency domain measurement and the accuracy of hydrological parameters, and effectively improves the precision and the accuracy of related geoscience instruments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (4)

1. A nuclear magnetic resonance FID signal noise suppression method based on multi-linear singular value tensor decomposition is characterized by comprising the following steps: the method comprises the following steps:
s101: acquiring a multichannel signal: enabling one channel to start sampling at intervals of delta t through time delay sampling to obtain a multi-channel signal;
s102: noise suppression based on multilinear singular value tensor decomposition:
converting each channel signal into Hankel matrix to form third-order tensor
Figure FDA0003570419460000011
To third order tensor
Figure FDA0003570419460000012
Performing Tucker decomposition and processing to obtain third order tensor
Figure FDA0003570419460000013
Tensor of third order
Figure FDA0003570419460000014
Recovering the signal into a multi-channel signal, and performing CP tensor decomposition processing on a second-order tensor X formed by the multi-channel signal to finally obtain a high signal-to-noise ratio signal X after the multi-channel signal is fusednew。
2. The method for suppressing noise of nuclear magnetic resonance (FID) signals based on the nonlinear singular value tensor decomposition as claimed in claim 1, wherein the method comprises the following steps: the third order tensor obtained in step S102
Figure FDA0003570419460000015
The specific process of performing the Tucker decomposition treatment comprises the following steps:
to tensor
Figure FDA0003570419460000016
Performing Tucker decomposition to obtainTo a core tensor
Figure FDA0003570419460000017
Multiple adjoint matrixes U(n)；
To core tensor
Figure FDA0003570419460000018
The singular value with relatively small numerical value is subjected to zero setting processing to obtain a processed core tensor
Figure FDA0003570419460000019
The processed core tensor
Figure FDA00035704194600000110
A plurality of adjoint matrixes U obtained in the last step(n)Carrying out tensor modular multiplication operation to obtain third-order tensor
Figure FDA00035704194600000111
I.e. a part of the noise suppression is done.
3. The method for suppressing noise of nuclear magnetic resonance (FID) signals based on the nonlinear singular value tensor decomposition as claimed in claim 1, wherein the method comprises the following steps: to third order tensor
Figure FDA00035704194600000112
The restoration is a multichannel signal X, and the specific process of CP tensor decomposition is as follows:
tensor of third order
Figure FDA00035704194600000113
Transforming into a second-order tensor X through Hankel inverse transformation; and decomposing the second-order tensor X into a form of two groups of one-dimensional vector outer products by using CP tensor decomposition to obtain a vector a and a vector b, and calculating the vector a and the vector b to obtain a fused denoising FID signal so as to complete all noise suppression.
4. The FID signal noise suppression method based on the nonlinear singular value tensor decomposition as claimed in claim 3, wherein the FID signal noise suppression method comprises the following steps: the operation process of the a and b vectors is as follows:
Figure FDA0003570419460000021
wherein mean (a) x b represents that the mean value of the vector a is multiplied by the vector b to obtain a fused signal xnew。
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