CN107957566A - Magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis - Google Patents
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Abstract
The present invention is a kind of magnetic resonance depth measurement method for extracting signal of the singular spectrum analysis based on frequency selection.MRS signals regional known to water instrument collection Larmor frequencies are visited first with nuclear magnetic resonance depth measurement, after carrying out partial noise suppression by broadband bandpass filter, find the position of the corresponding MRS signals of Larmor frequencies on power spectrum based on power spectrumanalysis；Then, the singular spectrum analysis based on frequency selection is carried out so as to extract MRS signals.Singular spectrum analysis based on frequency selection includes embedded, RSVD and decomposes, selected corresponding singular value to carry out matrix reconstruction and diagonally four steps of equalization according to MRS signal amplitudes.The present invention can solve effectively filtering out for random noise in noisy MRS signals, spike noise and industrial frequency harmonic interference, realize effective extraction of the lower MRS signals of complicated very noisy interference, compared with traditional MRS signal antinoise methods, have the advantages that arithmetic speed is fast, signal-to-noise ratio is high, highly practical.
Description
Technical Field
The invention relates to the technical field of noise filtering and parameter extraction of underground water detection signals for magnetic resonance sounding (also called ground nuclear magnetic resonance), in particular to a magnetic resonance sounding signal extraction method based on frequency selection singular spectrum analysis.
Background
The nuclear Magnetic Resonance Sounding (MRS) technology is the only method for directly and quantitatively characterizing the water content and the pore structure, and the basic principle is that the underground water is detected by detecting MRS signal response generated by hydrogen proton Resonance transition in the underground water. The MRS signal is in nano-volt, is very weak, and is easily interfered by random noise, power frequency harmonic waves and spike pulses in the environment, so that the quality of the detected MRS signal is influenced, the extraction of characteristic parameters of the MRS signal is further influenced, the accuracy of an inversion result is reduced, and the inaccuracy of the evaluation of regional water resource content and storage medium components is caused.
At present, experts and scholars at home and abroad carry out a great deal of research work aiming at the aspects of magnetic resonance sounding signal noise filtering and signal extraction theory and method research. Annet Hein et al, in Symmetry based on frequency domain processing to remove harmonic noise from surface noise magnetic resonance measures (geographic Journal International 2017, 208: 724-736), proposed a method for eliminating power frequency noise based on the symmetric characteristic of MRS signal in frequency domain, but could not process spike noise and random noise; tian Baofeng et al, in Noise cancellation of multi-reference full-wave magnetic resonance signal base on a modified signal variable step size mean square algorithm (Journal of Central South University of Technology 2017, 24: 900-911), proposed a full-wave nuclear magnetic resonance signal reference cancellation method based on an improved s-function variable step size LMS, but the processing effect is poor when the main channel and the reference channel have poor correlation. Zhang Hairu in magnetic resonance sounding signal detection based on Bayes Bootstrap statistical noise reduction method (university of south China (Nature science), 2014, volume 45, phase 9: 3144-3149) extracts 2 optimal estimation points from MRS signal components of each conductive layer to reconstruct MRS signal, but the processed and extracted signal parameter amplitude e 0 And the mean relaxation time T 2 * The error of (2) is large.
CN106772646A discloses a "ground nuclear magnetic resonance signal extraction method", which can adaptively find power frequency harmonics with a fundamental frequency of 49.9 Hz-50.1 Hz, find an autocorrelation expression of an MRS signal, and quickly and effectively realize separation of the signal and noise, but the method only aims at processing the power frequency harmonic noise in the nuclear magnetic resonance signal; CN104459809A discloses a method for filtering noise of a full-wave nuclear magnetic resonance signal based on independent component analysis, which adopts an independent component analysis algorithm to eliminate power frequency noise, adopts a digital orthogonal method to construct a virtual input channel signal to solve the problem of underdetermined blind source separation, but has no effect on strong random noise and spike noise interference. CN106226407A discloses a singular spectrum analysis-based ultrasonic echo signal online preprocessing method, which uses singular spectrum analysis for echo signal preprocessing in an ultrasonic online detection technology and can automatically realize noise removal of echo signals and separation and extraction of signal components in different frequency bands in ultrasonic detection; CN106404386A discloses a method for collecting, extracting and diagnosing early fault characteristic signals of a gear box, and the method uses singular spectrum analysis in fault diagnosis. It can be seen that the singular spectrum analysis has been successfully applied to various fields of signal processing, but has not been seen to be applied to noise filtering of MRS signals.
Disclosure of Invention
The invention aims to solve the technical problem of providing a magnetic resonance sounding signal extraction method based on frequency selection singular spectrum analysis, and solving the MRS signal extraction problem caused by the influences of complex peak noise, power frequency harmonic, random noise and the like in the environment.
The invention is a magnetic resonance sounding signal extraction method based on Frequency selective Singular-Spectrum Analysis (F-SSA), which comprises the following steps:
step (1): acquiring a group of observed MRS signals X with known Larmor frequency by using a nuclear Magnetic Resonance Sounding (MRS) water detector 1 (t)；
Step (2): will gather the observation MRS signal X 1 (t) obtaining X by means of a wide band bandpass filter 2 (t)；
And (3): x obtained by passing through a wide band-pass filter 2 (t) performing power spectrum analysis, and performing descending order arrangement on the amplitudes of the frequencies to find the ordering position of the signal amplitude corresponding to the Larmor frequency;
and (4): x obtained by passing through a wide band-pass filter 2 (t) performing singular spectrum analysis to extract MRS signals, wherein the singular spectrum analysis comprises the following steps: embedding to obtain a track matrix H; carrying out RSVD decomposition on the track matrix H to obtain singular values and singular vectors U which are arranged in a descending order; selecting two singular values corresponding to the sequencing positions obtained in the step (3) to carry out matrix reconstruction to obtain a matrix C; carrying out diagonal averaging on the matrix C to obtain an extracted MRS signal Y (t);
further, the embedding of the step (4) specifically comprises the following steps:
signal X 2 (t) is a one-dimensional real sequence of length N, X 2 (t)＝(x 1 ,x 2 ,...,x N ) The positive integer L is the length of the sliding window, L is more than 1 and less than N, and the value of L is determined by the following formula
By embedding the operation-primitive sequence signal X 2 (t) forming P vectors, each vector being available h i To represent
h i ＝(x i ,x i+1 ,…,x i+L-1 ) T
Where P = N-L +1, i =1,2, ·, P, the result of the mapping forms a trajectory matrix H:
further, the RSVD decomposition in step (4) specifically comprises the steps of:
1) Setting a parameter k and a parameter w, wherein k is k singular values which are taken for approximating a reconstruction matrix, and w is a parameter for ensuring that the condition of the reconstruction matrix is satisfied, and w is greater than k, w is less than L, and w is less than P;
2) And constructing a Gaussian random matrix G with the mean value of 0 and the variance of 1 L×w ；
3) Calculating a trajectory matrix H L×P Sampling matrix M of P×w
4) Sampling matrix M P×w Selecting the first k singular values to carry out SVD (singular value decomposition) so as to obtain a left singular vector Q of an orthogonal matrix of the first k singular values P×k Diagonal matrix Z k×k Right singular vector
5) Building a matrix T L×k ：
T L×k ＝H L×P Q P×k
6) To matrix T L×k Carrying out SVD to obtain a left singular vector U L×L Diagonal matrix sigma L×k And right singular vectors
7) Calculating matrix V P×k ：
V P×k ＝Q P×k O k×k ；
8) Calculating H L×P Approximate reduced rank matrix of
And (3) solving an approximate reduced rank matrix of H by using RSVD decomposition, wherein the solved approximate reduced rank matrix needs to meet the following conditions:
λ k+1 is the k +1 th singular value of the matrix H;
diagonal matrix sigma L×k The matrix is an L multiplied by k order matrix, and the main diagonal elements of the matrix are k singular values of an MRS signal approximate reduced rank matrix; arranging k singular values in descending order (lambda) 1 ≥λ 2 ≥...≥λ k ) Obtaining the corresponding orthogonal odd-odd vector set U' = (U) 1 ,u 2 ,...u k ) The contribution ratio of each singular value is:
and drawing a singular spectrogram according to the formula.
Further, the specific step of selecting two singular values corresponding to the sorting positions according to the sorting positions to perform matrix reconstruction in step (4) is:
finding the sorting v of the MRS signal amplitude according to the step (3), and selecting the 2v-1 nd singular value and the 2 v-th singular value in a singular spectrum;
reconstructing the matrix according to the selected singular values, wherein the reconstruction steps are as follows:
1) Calculating a right singular vector W of the reconstructed signal matrix:
wherein j =2v-1,2v;
2) Reconstructed signal matrix C
Further, the specific steps of diagonal averaging in step (4) are as follows:
reconstruction of the singular spectral analysis Signal matrix c by diagonal averaging 1 ,c 2 ,…,c q ,…,c P Converts into the corresponding reconstructed sequence g 1 ,g 2 ,…,g q ,…,g P In which the sequence g q Representing the qth singular spectral analysis reconstruction sequence,the procedure is as follows:
wherein, c q Representing the qth singular spectral analysis reconstructed signal matrix, is a matrix c q The m-th row and the n-th column,represents a reconstructed sequence g q Q =1,2,.., P, d =1,2,.., N; will reconstruct the sequence g 1 ,g 2 ,…,g P Summating to obtain denoised MRS signal sequenceWherein Y (t) = { Y (t) 1 ),y(t 2 ),…,y(t N )}＝{y 1 ,y 2 ,…,y N }。
Compared with the prior art, the method has the advantages that the method for extracting the magnetic resonance sounding signal based on the frequency-selective singular spectrum analysis is provided, the position sequence of the MRS signal amplitude in the power spectrum is searched for aiming at the detection data acquired by a single channel, the corresponding singular value is adopted for matrix reconstruction and signal recovery, the interference of spike noise, power frequency harmonic and random noise can be removed at one time, and the effective extraction of the MRS signal is realized. The method solves the problem that signals are difficult to effectively extract due to peak noise, power frequency harmonic and random noise in the magnetic resonance sounding water exploration work, breaks through the limitation that a classical noise elimination method needs other conditions such as multi-channel detection and the like, saves a large amount of financial resources and material resources, and opens up a new place of singular spectrum analysis in the field of nuclear magnetic resonance signal noise elimination.
Drawings
FIG. 1 is a flow chart of the method for extracting a magnetic resonance sounding signal based on frequency selective singular spectrum analysis according to the present invention;
FIG. 2 is a block diagram of the RSVD decomposition algorithm of the present invention;
FIG. 3 is a time domain and power spectrum of a noisy MRS signal and a clean MRS signal according to the present invention, wherein (a) is the time domain spectrum and (b) is the power spectrum;
FIG. 4 shows the time domain and its power spectrum before and after processing by the band-pass filter for noisy MRS signals according to the present invention, wherein (a) is the time domain spectrum and (b) is the power spectrum;
FIG. 5 is a graph of an alternative bandpass filter of example 1 of the present invention;
FIG. 6 is a graph of a singular spectrogram of example 1 of the present invention;
FIG. 7 is the time domain and its power spectrum before and after the F-SSA processing of the simulated MRS signal of the present invention, wherein (a) is the time domain spectrum and (b) is the power spectrum;
FIG. 8 shows the time domain and its power spectrum before and after the actual measurement of MRS signal band-pass filter, wherein (a) is the time domain spectrum and (b) is the power spectrum;
FIG. 9 is a graph of an alternative bandpass filter of example 2 of the present invention;
FIG. 10 is a strange spectrum of example 2 of the present invention;
FIG. 11 shows the time domain and the power spectrum before and after the F-SSA processing of the actually measured MRS signal according to the present invention, wherein (a) is the time domain spectrum and (b) is the power spectrum.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, the magnetic resonance sounding signal extraction method based on frequency selective singular spectrum analysis includes the following steps:
step (1): acquiring a group of observed MRS signals X with known Larmor frequency by using a nuclear Magnetic Resonance Sounding (MRS) water detector 1 (t)；
Step (2): will gather the observation MRS signal X 1 (t) obtaining X by means of a wide band bandpass filter 2 (t)；
And (3): x obtained by passing through a wide band-pass filter 2 (t) performing power spectrum analysis, and performing descending order arrangement on the amplitudes of the frequencies to find the ordering position of the signal amplitude corresponding to the Larmor frequency;
and (4): x obtained by passing through a wide band-pass filter 2 And (t) performing singular spectrum analysis to extract MRS signals. The singular spectrum analysis comprises: embedding to obtain a track matrix H; carrying out RSVD decomposition on the track matrix H to obtain singular values and singular vectors U which are arranged in a descending order; selecting two singular values corresponding to the sequencing positions obtained in the step (3) to carry out matrix reconstruction to obtain a matrix C; carrying out diagonal averaging on the matrix C to obtain an extracted MRS signal Y (t);
a magnetic resonance sounding signal extraction method based on frequency selection singular spectrum analysis specifically comprises the following embedding steps:
signal X 2 (t) is a one-dimensional real sequence of length N, X 2 (t)＝(x 1 ,x 2 ,...,x N ) The positive integer L is the length of the sliding window, L is more than 1 and less than N, and the value of L is determined by the following formula
By embedding the operation-primitive sequence signal X 2 (t) forming P vectors, each vector being available h i To represent
h i ＝(x i ,x i+1 ,…,x i+L-1 ) T
Where P = N-L +1, i =1,2, ·, P, the result of the mapping forms a trajectory matrix H:
as shown in fig. 2, the RSVD decomposition provided by the present invention specifically comprises the following steps:
1) Setting a parameter k and a parameter w, wherein k is k singular values which are taken for approximating a reconstruction matrix, and w is a parameter for ensuring that the condition of the reconstruction matrix is satisfied, and w is greater than k, w is less than L, and w is less than P;
2) And constructing a Gaussian random matrix G with 0 mean value and 1 variance L×w ；
3) Calculating a trajectory matrix H L×P Sampling matrix M of P×w
4) Sampling matrix M P×w Selecting the first k singular values to carry out SVD (singular value decomposition) to obtain a left singular vector Q of an orthogonal matrix of the first k singular values P×k Diagonal matrix Z k×k Right singular vector
5) Building a matrix T L×k ：
T L×k ＝H L×P Q P×k
6) To matrix T L×k Carrying out SVD to obtain a left singular vector U L×L Diagonal matrix sigma L×k And right singular vectors
7) Calculating matrix V P×k ：
V P×k ＝Q P×k O k×k ；
8) Calculating H L×P Approximate rank reduction matrix H E L×P ：
And (3) solving an approximate reduced rank matrix of H by using RSVD decomposition, wherein the solved approximate reduced rank matrix needs to meet the following conditions:
λ k+1 is the (k + 1) th singular value of the matrix H;
diagonal matrix sigma L×k The matrix is an L multiplied by k order matrix, and the main diagonal elements of the matrix are k singular values of an MRS signal approximate reduced rank matrix; arranging k singular values in descending order (lambda) 1 ≥λ 2 ≥...≥λ k ) Obtaining the corresponding orthogonal singular vector setAnd then U' = (U) 1 ,u 2 ,...u k ) The contribution ratio of each singular value is:
and drawing a singular spectrogram according to the formula.
A full-wave nuclear magnetic resonance signal extraction method based on frequency selection singular spectrum analysis specifically comprises the following steps:
finding the sorting v of the MRS signal amplitude according to the step (3), and selecting the 2v-1 nd singular value and the 2 v-th singular value in a singular spectrum;
reconstructing the matrix according to the selected singular values, wherein the reconstruction steps are as follows:
1) Calculating a right singular vector W of the reconstructed signal matrix
Wherein j =2v-1,2v;
2) Reconstructed signal matrix C
A full-wave nuclear magnetic resonance signal extraction method based on frequency selection singular spectrum analysis specifically comprises the following steps:
reconstruction of the singular spectral analysis Signal matrix c by diagonal averaging 1 ,c 2 ,…,c q ,…,c P Is converted into a corresponding reconstruction sequence g 1 ,g 2 ,…,g q ,…,g P In which the sequence g q Representing the qth singular spectral analysis reconstruction sequence,the procedure is as follows:
wherein, c q Representing the qth singular spectral analysis reconstructed signal matrix, is a matrix c q The m-th row and the n-th column,represents a reconstructed sequence g q Q =1,2,.. P, d =1,2,. Ann, N. Will reconstruct the sequence g 1 ,g 2 ,…,g P Summating to obtain denoised MRS signal sequenceWherein Y (t) = { Y (t) 1 ),y(t 2 ),…,y(t N )}＝{y 1 ,y 2 ,…,y N }。
Example 1
This example is a simulation experiment of the method of the present invention conducted in the MATLAB 2015a programming environment. The simulation algorithm of the magnetic resonance sounding signal extraction method based on frequency selection singular spectrum analysis, referring to fig. 1, comprises the following steps:
step (1): constructing Larmor frequency of 2114Hz and amplitude e 0 At 180nV, relaxation time T 2 * The signal sampling rate is 10kHz, the signal length is 500ms, and the number of data points is 5000, as shown in fig. 3 (a) and 3 (b), for a clean MRS signal with 0.1s and 1.03 phase. On the basis of the signals, 16 groups of noisy signals are simulated, 100 power frequency interferences with amplitude of 100nV, random phase and frequency of integral multiple of 50Hz are added between 0Hz and 5000Hz in each group of signals; spike amplitude of 100nV and duration of 10msNoise and random noise of 60nV amplitude. Carrying out statistical superposition on 16 groups of noises to form an observed MRS signal X with the signal-to-noise ratio of-13.3930 dB 1 (t) (row vector), time domain diagram as shown in fig. 3 (a), power spectrum diagram as shown in fig. 3 (b);
step (2): will observe MRS signal X 1 (t) passing through the band-pass filter shown in FIG. 5, the adopted band-pass filter is a Chebyshev filter, the left boundary of the pass band is 1900Hz, the right boundary of the pass band is 2300Hz, the left boundary of the stop band is 1700Hz, the right boundary of the stop band is 2500Hz, the attenuation of the side band region of the pass band is 0.1dB, the attenuation of the cut-off region of the stop band is 30dB, and a signal X is obtained 2 (t) as shown in FIG. 4 (a).
And (3): evaluating and observing MRS signal X 2 The power spectrum of (t) is shown in FIG. 4 (b). Determining that the amplitude of the Larmor signal in the noisy signal is arranged at a first position;
and (4): x obtained by passing through a wide band-pass filter 2 (t) embedding is performed with a window length selected to beObtaining a track matrix H;
the track matrix H is RSVD decomposed, let k =20, w =200, satisfying the approximate condition, obtaining singular values and singular vectors U arranged in descending order, and drawing a singular spectrum as shown in figure 6;
according to the sequencing position obtained in the step (3), the Larmor signal amplitude is arranged at the first position, so that a first singular value and a second singular value are selected for matrix reconstruction, and a matrix X is obtained;
carrying out diagonal averaging on the matrix X to obtain an extracted MRS signal Y (t), wherein a time domain diagram and a power spectrum are shown in fig. 7 (a) and fig. 7 (b);
in order to verify the practicability of the method, the denoised MRS signal Y (t) is subjected to signal-to-noise ratio (SNR) estimation. Calculated, its SNR =9.2147dB, which is 22.6076dB higher than SNR before separation; then, envelope extraction and data fitting are carried out on Y (t) to obtain the initial amplitude e of the key parameter of the separation signal 0 And relaxation time T 2 * And the calculation can be carried out to obtain,the relative errors are 1.6024% and 3.0142% respectively, and are controlled within +/-5%, so that the application requirements are met.
Example 2
In the embodiment, an MRS signal collected from a burning town in Changchun city (the Dellarmor frequency is about 2332.5 Hz) is taken as a processing object of the method. As shown in fig. 1, the magnetic resonance sounding signal extraction method based on frequency selective singular spectrum analysis includes the following steps:
step (1): acquiring a group of observed MRS signals X by using a nuclear Magnetic Resonance Sounding (MRS) water detector 1 (t) (row vector), as shown in fig. 8 (a) and 8 (b), the sampling rate is 25kHz, the number of data points is 12476, and the SNR is calculated as SNR = -7.1453dB;
step (2): will observe MRS signal X 1 (t) passing through the band pass filter as shown in FIG. 9, the adopted band pass filter is a Chebyshev filter, the left boundary of the pass band is 2100Hz, the right boundary of the pass band is 2500Hz, the left boundary of the stop band is 1800Hz, the right boundary of the stop band is 2800Hz, the attenuation of the sideband area of the pass band is 0.1dB, the attenuation of the cut-off area of the stop band is 30dB, and a signal X is obtained 2 (t) as shown in FIG. 8 (a).
And (3): finding observed MRS signal X 2 The power spectrum of (t) is shown in blue in FIG. 8 (b). Determining that the amplitude of the Larmor signal in the noise-containing signal is arranged at the second position;
and (4): x obtained by passing through a wide band-pass filter 2 (t) embedding, the window length selected beingObtaining a track matrix H;
subjecting the track matrix H to RSVD decomposition, let k =20, w =200, satisfying approximate conditions, obtaining singular values and singular vectors U arranged in descending order, and drawing a singular spectrum as shown in figure 10;
arranging the Larmor signal amplitude at the second position according to the sequencing position obtained in the step (3), and therefore selecting the third singular value and the fourth singular value to carry out matrix reconstruction to obtain a matrix X;
performing diagonal averaging on the matrix X to obtain an extracted MRS signal Y (t), where a time domain diagram and a power spectrum are shown in fig. 11 (a) and 11 (b);
in order to verify the practicability of the method, the denoised MRS signal Y (t) is subjected to signal-to-noise ratio (SNR) estimation. Calculated, the SNR =11.9542dB is improved by 19.0995dB compared with the SNR before separation; then, envelope extraction and data fitting are carried out on Y (t) to obtain the initial amplitude e of the key parameter of the separation signal 0 And relaxation time T 2 * Calculated to obtain e 0 ＝63.7791nV，T 2 * =0.1890s, corresponding to the actual hydrogeological drilling data results.
Claims (5)
1. A magnetic resonance sounding signal extraction method based on frequency selection singular spectrum analysis is characterized by comprising the following steps:
step (1): acquiring a group of observed MRS signals X with known Larmor frequency by utilizing a nuclear magnetic resonance depth sounding water detector 1 (t)；
Step (2): will gather the observation MRS signal X 1 (t) obtaining the signal X through a wide band bandpass filter 2 (t)；
And (3): the signal X obtained by the broadband band-pass filter 2 (t) performing power spectrum analysis, and performing descending order arrangement on the amplitudes of the frequencies to find the ordering position of the signal amplitude corresponding to the Larmor frequency;
and (4): signal X obtained by passing through a wide band-pass filter 2 (t) performing singular spectrum analysis to extract MRS signals, wherein: the singular spectrum analysis comprises:
embedding to obtain a track matrix H;
carrying out RSVD decomposition on the track matrix H to obtain singular values and singular vectors U which are arranged in a descending order;
selecting two singular values corresponding to the sequencing positions obtained in the step (3) to carry out matrix reconstruction to obtain a matrix C;
and carrying out diagonal averaging on the matrix C to obtain the extracted MRS signal Y (t).
2. The method for extracting the magnetic resonance sounding signal based on the frequency selective singular spectrum analysis according to claim 1, wherein the embedding in the step (4) comprises the following specific steps:
signal X 2 (t) is a one-dimensional real sequence of length N: x 2 (t)＝(x 1 ,x 2 ,...,x N ) The positive integer L is the length of the sliding window, L is more than 1 and less than N, and the value of L is determined by the following formula:
by embedding the operation-primitive sequence signal X 2 (t) forming P vectors, each vector using h i Represent
h i ＝(x i ,x i+1 ,…,x i+L-1 ) T
Where P = N-L +1, i =1,2, ·, P, the result of the mapping forms a trajectory matrix H:
3. the method for extracting the magnetic resonance sounding signal based on the frequency selective singular spectrum analysis as claimed in claim 1, wherein the RSVD decomposition in the step (4) comprises the following specific steps:
1) Setting a parameter k and a parameter w, wherein k is k singular values which are taken for approximating a reconstruction matrix, and w is a parameter for ensuring that the condition of the reconstruction matrix is satisfied, and w is greater than k, w is less than L, and w is less than P;
2) And constructing a Gaussian random matrix G with 0 mean value and 1 variance L×w ；
3) Calculating a trajectory matrix H L×P Sampling matrix M of P×w ：
4) Sampling matrix M P×w Selecting the first k singular values to carry out SVD (singular value decomposition) to obtain a left singular vector Q of an orthogonal matrix of the first k singular values P×k Diagonal matrix Z k×k Right singular vectorExpressed as:
5) Building a matrix T L×k ：
T L×k ＝H L×P Q P×k ；
6) To matrix T L×k Carrying out SVD to obtain a left singular vector U L×L Diagonal matrix sigma L×k And right singular vectorsExpressed as:
7) Calculating matrix V P×k ：
V P×k ＝Q P×k O k×k ；
8) Calculating H L×P Approximate reduced rank matrix of
And (3) solving an approximate reduced rank matrix of H by using RSVD decomposition, wherein the solved approximate reduced rank matrix needs to meet the following conditions:
λ k+1 is the k +1 th singular value of the matrix H;
diagonal matrix sigma L×k The matrix is an L multiplied by k order matrix, and the main diagonal elements of the matrix are k singular values of an MRS signal approximate reduced rank matrix; arranging k singular values in descending order (lambda) 1 ≥λ 2 ≥...≥λ k ) Obtaining the corresponding orthogonal odd-odd vector set U' = (U) 1 ,u 2 ,...u k ) The contribution ratio of each singular value is:
and drawing a singular spectrogram according to the formula.
4. The method for extracting magnetic resonance sounding signal based on frequency selective singular spectrum analysis according to claim 1, wherein the selecting two singular values corresponding to the sorted positions for matrix reconstruction in the step (4) comprises:
finding the sorting v of the MRS signal amplitude according to the step (3), and selecting the 2v-1 nd singular value and the 2 v-th singular value in a singular spectrum;
reconstructing the matrix according to the selected singular value, wherein the reconstruction steps are as follows:
1) Calculating a right singular vector W of the reconstructed signal matrix
Wherein j =2v-1,2v;
2) Reconstructed signal matrix C
5. The method for extracting magnetic resonance sounding signal based on frequency selective singular spectrum analysis according to claim 1, wherein the diagonal averaging in the step (4) comprises the following specific steps:
reconstruction of the Signal matrix c from the singular spectral analysis by diagonal averaging 1 ,c 2 ,…,c q ,…,c P Is converted into a corresponding reconstruction sequence g 1 ,g 2 ,…,g q ,…,g P In which sequence g q Representing the qth singular spectral analysis reconstruction sequence,the procedure is as follows:
wherein, c q Representing the qth singular spectral analysis reconstructed signal matrix, is a matrix c q The m-th row and the n-th column,represents the reconstructed sequence g q Q =1,2,.. P, d =1,2,.., N; will reconstruct the sequence g 1 ,g 2 ,…,g P Summating to obtain denoised MRS signal sequenceWherein Y (t) = { Y (t) 1 ),y(t 2 ),…,y(t N )}＝{y 1 ,y 2 ,…,y N }。
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| CN109100813A (en) * | 2018-08-14 | 2018-12-28 | 吉林大学 | A method of it is filtered based on collaboration and eliminates spike noise in ground nuclear magnetic resonance data |
| CN109765629A (en) * | 2019-01-30 | 2019-05-17 | 吉林大学 | A kind of ground magnetic resonance signal extracting method that can suppress same frequency noise jamming |
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| CN109100813A (en) * | 2018-08-14 | 2018-12-28 | 吉林大学 | A method of it is filtered based on collaboration and eliminates spike noise in ground nuclear magnetic resonance data |
| CN109858356A (en) * | 2018-12-27 | 2019-06-07 | 北京邮电大学 | A kind of detection method and device of unknown complex system input signal |
| CN109828318A (en) * | 2019-01-25 | 2019-05-31 | 吉林大学 | A kind of magnetic resonance depth measurement signal noise filtering method based on variation mode decomposition |
| CN109885903A (en) * | 2019-01-29 | 2019-06-14 | 吉林大学 | A kind of ground nuclear magnetic resonance signal peaks noise remove method based on model |
| CN109765629A (en) * | 2019-01-30 | 2019-05-17 | 吉林大学 | A kind of ground magnetic resonance signal extracting method that can suppress same frequency noise jamming |
| CN109885906A (en) * | 2019-01-30 | 2019-06-14 | 吉林大学 | Magnetic resonance sounding signal sparse noise elimination method based on particle swarm optimization |
| CN109765629B (en) * | 2019-01-30 | 2021-06-01 | 吉林大学 | Ground magnetic resonance signal extraction method capable of suppressing same frequency noise interference |
| CN110133559B (en) * | 2019-05-21 | 2021-05-11 | 辽宁开普医疗系统有限公司 | Magnetic resonance B0 field disturbance compensation system and method |
| CN110133559A (en) * | 2019-05-21 | 2019-08-16 | 辽宁开普医疗系统有限公司 | A kind of magnetic resonance B0 disturbance compensation systems and method |
| CN110285970B (en) * | 2019-07-18 | 2020-05-12 | 东北大学 | Matrix recovery-based weak fault enhancement method for rolling bearing |
| CN110285970A (en) * | 2019-07-18 | 2019-09-27 | 东北大学 | The rolling bearing Weak fault Enhancement Method restored based on matrix |
| CN113180636A (en) * | 2021-04-29 | 2021-07-30 | 杭州微影医疗科技有限公司 | Interference cancellation method, medium, and apparatus |
| CN113180636B (en) * | 2021-04-29 | 2022-09-16 | 杭州微影医疗科技有限公司 | Interference cancellation method, medium, and apparatus |
| CN113640891A (en) * | 2021-08-11 | 2021-11-12 | 吉林大学 | Singular spectrum analysis-based transient electromagnetic detection data noise filtering method |
| CN113640891B (en) * | 2021-08-11 | 2022-11-08 | 吉林大学 | Singular spectrum analysis-based transient electromagnetic detection data noise filtering method |
| CN117111155A (en) * | 2023-10-25 | 2023-11-24 | 东北石油大学三亚海洋油气研究院 | Microseism data denoising method based on integrated framework |
| CN117111155B (en) * | 2023-10-25 | 2023-12-26 | 东北石油大学三亚海洋油气研究院 | Microseism data denoising method based on integrated framework |
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