CN107957566B - Magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis - Google Patents
Magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis Download PDFInfo
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Abstract
The present invention is a kind of magnetic resonance depth measurement method for extracting signal of singular spectrum analysis based on frequency selection.MRS signal regional known to water instrument acquisition Larmor frequency, which is visited, first with nuclear magnetic resonance depth measurement finds the position of the corresponding MRS signal of Larmor frequency on power spectrum based on power spectrumanalysis after carrying out partial noise inhibition by broadband bandpass filter；Then, the singular spectrum analysis selected based on frequency is carried out to extract MRS signal.Singular spectrum analysis based on frequency selection includes being embedded in, RSVD decomposition, carrying out matrix reconstruction according to the corresponding singular value of MRS signal amplitude selection and diagonally equalize four steps.The present invention is able to solve effectively filtering out for random noise in noisy MRS signal, spike noise and industrial frequency harmonic interference, realize that complicated very noisy interferes effective extraction of lower MRS signal, compared with traditional MRS signal antinoise method, have many advantages, such as that arithmetic speed is fast, signal-to-noise ratio is high, practical.
Description
Technical field
The present invention relates to magnetic resonance depth measurement (also known as ground nuclear magnetic resonance) underground water detectable signal noise filterings and parameter to mention
Technical field is taken, the magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis is specifically utilized.
Background technique
Nuclear magnetic resonance depth measurement (Magnetic Resonance Sounding, MRS) technology is a kind of unique direct quantitative table
The method for levying water content and pore structure, the basic principle is that the MRS generated by Hydrogen Proton resonant transition in Underground water
Signal response carries out underground water detection.The order of magnitude of MRS signal is to receive volt, very faint, easily by environment random noise,
Industrial frequency harmonic and spike are interfered, and the quality of the MRS signal detected is caused to be affected, and then it is special to influence MRS signal
The extraction for levying parameter, reduces the accuracy of inversion result, causes and comment regional water resources content and storage medium ingredient
Fixed inaccuracy.
Currently, in terms of filtering out for magnetic resonance depth measurement signal noise with the research of signal extraction theory and method, both at home and abroad specially
Family scholar has carried out a lot of research work.Annette Hein et al. is in " Symmetry based frequency domain
processing to remove harmonic noise from surface nuclear magnetic resonance
Measurements " (" Geophysical Journal International " the 208th phase in 2017: 724-736 pages) proposition
A kind of feature symmetrical on frequency domain based on MRS signal cannot handle spike noise the method for eliminating industrial frequency noise
And random noise；Tian Baofeng et al. is in " Noise cancellation of a multi-reference full-wave
magnetic resonance sounding signal based on a modified sigmoid variable step
size least mean square algorithm》(《Journal of Central South University of
Technology " the 24th phase in 2017: 900-911 pages) propose it is a kind of based on improve s function variable step- size LMS multichannel it is complete
The reference of wave NMR signal offsets method, but when main channel and poor reference channel correlation, treatment effect is bad.
Sea as et al. " based on Bayes Bootstrap statistics noise-reduction method magnetic resonance depth measurement signal detection " (" Central South University's journal
(natural science edition) " the 9th phase of volume 45 in 2014: 3144-3149 pages) in from each conductive layer MRS signal component extract 2 most
Excellent estimation point is come the signal parameter amplitude e that rebuilds MRS signal, but extract after handling0With mean time of relaxation T2 *Error compared with
Greatly.
CN106772646A discloses " a kind of ground nuclear magnetic resonance method for extracting signal ", and this method can adaptively be found
Fundamental frequency is the industrial frequency harmonic of 49.9Hz~50.1Hz, acquires the auto-correlation expression formula of MRS signal, and fast and effeciently realizes letter
Number and noise separation, but this method just for processing NMR signal in industrial frequency harmonic noise；CN104459809A is public
" a kind of all-wave NMR signal noise filtering method based on independent component analysis " is opened, using independent composition analysis algorithm
Industrial frequency noise is eliminated, virtual input channel signal is constructed using digital quadrature method and solves the problems, such as to owe to determine blind source separating, but
This method is helpless to strong random noise and spike noise interference.CN106226407A discloses " a kind of based on singular spectrum point
Singular spectrum analysis is used for returning in ultrasonic online measuring technique by the online preprocess method of the ultrasound echo signal of analysis ", this method
Wave Signal Pretreatment can realize that the separation of the noise remove of echo-signal and different frequency range signal component in ultrasound detection mentions automatically
It takes；CN106404386A discloses " a method of for acquiring, extracting and diagnosing gear-box fault features signal ", should
Singular spectrum analysis is used in fault diagnosis by method.It can be seen that singular spectrum analysis has been successfully applied each neck of signal processing
Domain, but there is not yet in its noise filtering for being applied to MRS signal.
Summary of the invention
Technical problem to be solved by the present invention lies in provide a kind of magnetic resonance survey based on frequency selection singular spectrum analysis
Deep method for extracting signal solves to influence bring MRS letter due to spike noise complicated in environment, industrial frequency harmonic and random noise etc.
Number extract problem.
The invention is realized in this way selecting singular spectrum analysis (Frequency chosen of based on frequency
Singular-Spectrum-Analysis, F-SSA) magnetic resonance depth measurement method for extracting signal, method includes the following steps:
Step (1): the observation MRS that water instrument collects Larmor frequency known to one group is visited using nuclear magnetic resonance depth measurement (MRS)
Signal X1(t)；
Step (2): by the observation MRS signal X of acquisition1(t) X is obtained by broadband bandpass filter2(t)；
Step (3): the X that will be obtained by broadband bandpass filter2(t) power spectrumanalysis is carried out, by the width of each frequency
Value carries out descending arrangement, finds the sorting position of the corresponding signal amplitude of Larmor frequency；
Step (4): the X that will be obtained by broadband bandpass filter2(t) it carries out singular spectrum analysis and extracts MRS signal, it is odd
Different spectrum analysis includes: insertion, obtains track matrix H；Track matrix H is subjected to RSVD decomposition, what is arranged in descending order is unusual
Value and singular vector U；According to the sorting position that step (3) obtains, corresponding two singular values is selected to carry out matrix reconstruction,
Obtain Matrix C；Matrix C is diagonally equalized, the MRS signal Y (t) extracted；
Further, the specific steps of insertion described in step (4) are as follows:
Signal X2It (t) is one-dimensional real sequence that length is N, X2(t)=(x1,x2,...,xN), positive integer L is sliding window
The value of length, 1 < L < N, L is determined by following formula
Pass through embedding operation original sequence signal X2(t) P vector is constituted, each vector can use hiIt indicates
hi=(xi,xi+1,…,xi+L-1)T
The result of wherein P=N-L+1, i=1,2 ..., P, mapping form track matrix H:
Further, the specific steps that RSVD described in step (4) is decomposed are as follows:
1), parameter k and parameter w, k are set for the k singular value for approximate reconstruction matrix that is taken, w is for ensuring that
The parameter that restructuring matrix condition is set up, wherein w>k, w<L, w<P；
2) the gaussian random matrix G of 0 mean value, 1 variance, is constructedL×w；
3) track matrix H, is calculatedL×PSampling matrix MP×w
4), by sampling matrix MP×wK singular value carries out SVD decomposition before choosing, and obtains the left singular vector of its orthogonal matrix
QP×k, diagonal matrix Zk×k, right singular vector
5) matrix T, is constructedL×k:
TL×k=HL×PQP×k
6), to matrix TL×kSVD decomposition is carried out, its left singular vector U is obtainedL×L, diagonal matrix ΣL×kAnd right singular vector
7), calculating matrix VP×k:
VP×k=QP×kOk×k；
8) H, is calculatedL×PApproximate singular matrix
The approximate singular matrix for acquiring H is decomposed using RSVD, the approximate singular matrix sought need to meet the following conditions:
λk+1For+1 singular value of kth of matrix H；
Diagonal matrix ΣL×kFor L × k rank matrix, main diagonal element is k singular value of MRS signal approximation singular matrix；
K singular value is subjected to descending arrangement (λ1≥λ2≥...≥λk), obtain corresponding orthogonal singular vector set U '=
(u1,u2,...uk), the contribution rate of each singular value are as follows:
Unusual spectrogram is drawn out according to above formula.
Further, corresponding two singular values are selected to carry out matrix weight according to sorting position described in step (4)
The specific steps of structure are as follows:
The sequence v that MRS signal amplitude size is found according to step (3) selects 2v-1 and 2v inside singular spectrum
Singular value；
According to selected singular value restructuring matrix, steps are as follows for reconstruct:
1) the right singular vector W of reconstruction signal matrix, is calculated:
Wherein, j=2v-1,2v；
2), reconstruction signal Matrix C
Further, the specific steps diagonally equalized in the step (4) are as follows:
By diagonally equalizing singular spectrum analysis reconstruction signal matrix { c1,c2,…,cq,…,cPBe converted into it is corresponding
Reproducing sequence { g1,g2,…,gq,…,gP, wherein sequence gqIndicate q-th of singular spectrum analysis reproducing sequence,Process is as follows:
Wherein, cqIndicate q-th of singular spectrum analysis reconstruction signal matrix, For matrix cqIn m row
N column element,Indicate reproducing sequence gqD-th of element, q=1,2 ..., P, d=1,2 ..., N；By reproducing sequence { g1,
g2,…,gPAdd up summation, the MRS signal sequence after being denoisedWherein Y (t)={ y (t1),y(t2),…,y
(tN)={ y1,y2,…,yN}。
Compared with prior art, the present invention beneficial effect is that the invention proposes the singular spectrum analysis selected based on frequency
Magnetic resonance depth measurement signal extracting method, for single channel acquisition detection data, by find MRS signal amplitude in power
Name placement in spectrum carries out matrix reconstruction using corresponding singular value and signal restores, can disposably remove spike and make an uproar
The interference of sound, industrial frequency harmonic and random noise realizes effective extraction of MRS signal.The method of the present invention solves magnetic resonance survey
The signal as caused by spike noise, industrial frequency harmonic and random noise is difficult to the problem effectively extracted in deep water detection work, simultaneously
The present invention, which breaches classical noise-eliminating method, needs the limitation of the other conditions such as multi-channel detection, saves a large amount of financial resource and material resource, opens
Singular spectrum analysis has been warded off in the new world in NMR signal de-noising field.
Detailed description of the invention
Fig. 1 is the flow chart element of the extracting method of the magnetic resonance depth measurement signal of the singular spectrum analysis selected the present invention is based on frequency
Figure；
Fig. 2 is RSVD decomposition algorithm flow diagram of the present invention；
Fig. 3 is the noisy MRS signal of the present invention and pure MRS signal time domain and its power spectrum, wherein (a) is Time Domain Spectrum, (b)
For power spectrum；
Fig. 4 is the noisy MRS signal bandpass filter of present invention time domain and its power spectrum before and after the processing, wherein (a) is time domain
Spectrum (b) is power spectrum；
Fig. 5 is that present example 1 selects bandpass filter curve；
Fig. 6 is the unusual spectrogram of present example 1；
Fig. 7 is present invention emulation MRS signal F-SSA time domain and its power spectrum before and after the processing, wherein (a) is Time Domain Spectrum, (b)
For power spectrum；
Fig. 8 is present invention actual measurement MRS signal bandpass filter time domain and its power spectrum before and after the processing, wherein (a) is time domain
Spectrum (b) is power spectrum；
Fig. 9 is that present example 2 selects bandpass filter curve；
Figure 10 is the unusual spectrogram of present example 2；
Figure 11 is present invention actual measurement MRS signal F-SSA time domain and its power spectrum before and after the processing, wherein (a) is Time Domain Spectrum,
It (b) is power spectrum.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
As shown in Figure 1, the magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis, including following step
It is rapid:
Step (1): the observation MRS that water instrument collects Larmor frequency known to one group is visited using nuclear magnetic resonance depth measurement (MRS)
Signal X1(t)；
Step (2): by the observation MRS signal X of acquisition1(t) X is obtained by broadband bandpass filter2(t)；
Step (3): the X that will be obtained by broadband bandpass filter2(t) power spectrumanalysis is carried out, by the width of each frequency
Value carries out descending arrangement, finds the sorting position of the corresponding signal amplitude of Larmor frequency；
Step (4): the X that will be obtained by broadband bandpass filter2(t) it carries out singular spectrum analysis and extracts MRS signal.It is odd
Different spectrum analysis includes: insertion, obtains track matrix H；Track matrix H is subjected to RSVD decomposition, what is arranged in descending order is unusual
Value and singular vector U；According to the sorting position that step (3) obtains, corresponding two singular values is selected to carry out matrix reconstruction,
Obtain Matrix C；Matrix C is diagonally equalized, the MRS signal Y (t) extracted；
A kind of specific step selecting insertion described in the magnetic resonance depth measurement method for extracting signal of singular spectrum analysis based on frequency
Suddenly are as follows:
Signal X2It (t) is one-dimensional real sequence that length is N, X2(t)=(x1,x2,...,xN), positive integer L is sliding window
The value of length, 1 < L < N, L is determined by following formula
Pass through embedding operation original sequence signal X2(t) P vector is constituted, each vector can use hiIt indicates
hi=(xi,xi+1,…,xi+L-1)T
The result of wherein P=N-L+1, i=1,2 ..., P, mapping form track matrix H:
As shown in Fig. 2, the specific steps that RSVD provided by the invention is decomposed are as follows:
1), parameter k and parameter w, k are set for the k singular value for approximate reconstruction matrix that is taken, w is for ensuring that
The parameter that restructuring matrix condition is set up, wherein w>k, w<L, w<P；
2) the gaussian random matrix G of 0 mean value, 1 variance, is constructedL×w；
3) track matrix H, is calculatedL×PSampling matrix MP×w
4), by sampling matrix MP×wK singular value carries out SVD decomposition before choosing, and obtains the left singular vector of its orthogonal matrix
QP×k, diagonal matrix Zk×k, right singular vector
5) matrix T, is constructedL×k:
TL×k=HL×PQP×k
6), to matrix TL×kSVD decomposition is carried out, its left singular vector U is obtainedL×L, diagonal matrix ΣL×kAnd right singular vector
7), calculating matrix VP×k:
VP×k=QP×kOk×k；
8) H, is calculatedL×PApproximate singular matrix H~L×P:
The approximate singular matrix for acquiring H is decomposed using RSVD, the approximate singular matrix sought need to meet the following conditions:
λk+1For (k+1) a singular value of matrix H；
Diagonal matrix ΣL×kFor L × k rank matrix, main diagonal element is k singular value of MRS signal approximation singular matrix；
K singular value is subjected to descending arrangement (λ1≥λ2≥...≥λk), obtain corresponding orthogonal singular vector set U '=
(u1,u2,...uk), the contribution rate of each singular value are as follows:
Unusual spectrogram is drawn out according to above formula.
It is a kind of that matrix reconstruction described in the all-wave NMR signal extracting method of singular spectrum analysis is selected based on frequency
Specific steps are as follows:
The sequence v that MRS signal amplitude size is found according to step (3) selects 2v-1 and 2v inside singular spectrum
Singular value；
According to selected singular value restructuring matrix, steps are as follows for reconstruct:
1) the right singular vector W of reconstruction signal matrix, is calculated
Wherein, j=2v-1,2v；
2), reconstruction signal Matrix C
It is a kind of that diagonal described in the all-wave NMR signal extracting method of singular spectrum analysis be averaged is selected based on frequency
The specific steps of change are as follows:
By diagonally equalizing singular spectrum analysis reconstruction signal matrix { c1,c2,…,cq,…,cPBe converted into it is corresponding
Reproducing sequence { g1,g2,…,gq,…,gP, wherein sequence gqIndicate q-th of singular spectrum analysis reproducing sequence,Process is as follows:
Wherein, cqIndicate q-th of singular spectrum analysis reconstruction signal matrix, For matrix cqIn m row
N-th column element,Indicate reproducing sequence gqD-th of element, q=1,2 ..., P, d=1,2 ..., N.By reproducing sequence
{g1,g2,…,gPAdd up summation, the MRS signal sequence after being denoisedWherein Y (t)={ y (t1),y
(t2),…,y(tN)={ y1,y2,…,yN}。
Embodiment 1
The present embodiment is the emulation experiment of the method for the present invention carried out under MATLAB 2015a programmed environment.Based on frequency
The simulation algorithm of the magnetic resonance depth measurement method for extracting signal of singular spectrum analysis is selected, referring to Fig.1, comprising the following steps:
Step (1): construction Larmor frequency is 2114Hz, amplitude e0For 180nV, relaxation time T2 *For 0.1s, phase is
1.03 pure MRS signal, signal sampling rate 10kHz, signal length 500ms, data points are 5000, such as Fig. 3 (a) and
Shown in Fig. 3 (b).On the basis of the signal, 16 groups of signals and associated noises are emulated, every group of signal adds 100 between 0Hz~5000Hz
A amplitude is 100nV, and phase is random, and frequency is the Hz noise of 50Hz integral multiple；Amplitude is 100nV, duration 10ms
Spike noise and amplitude be 60nV random noise.16 groups of noises are carried out statistical stacking to form signal-to-noise ratio being -13.3930dB
Observation MRS signal X1(t) (for row vector), shown in time-domain diagram such as Fig. 3 (a), shown in power spectrum chart such as Fig. 3 (b)；
Step (2): MRS signal X will be observed1(t) pass through bandpass filter as shown in Figure 5, used bandpass filtering
Device is Chebyshev filter, and passband left margin is 1900Hz, and passband right margin is 2300Hz, and stopband left margin is 1700Hz,
Stopband right margin is 2500Hz, and decay 0.1dB for passband sideband region, and stopband cut-off region decaying 30dB obtains signal X2(t), such as Fig. 4
(a) shown in.
Step (3): observation MRS signal X is sought2(t) power spectrum, as shown in Fig. 4 (b).It determines in signals and associated noises
Larmor signal amplitude makes number one；
Step (4): the X that will be obtained by broadband bandpass filter2(t) be embedded in, the length of window selected forObtain track matrix H；
Track matrix H is subjected to RSVD decomposition, enables k=20, w=200, Meet approximate condition, the singular values and singular vectors U arranged in descending order draws out singular spectrum
Such as Fig. 6；
According to the sorting position that step (3) obtains, Larmor signal amplitude makes number one, therefore selects first and the
Two two singular values carry out matrix reconstruction, obtain matrix X；
Matrix X is diagonally equalized, the MRS signal Y (t) extracted, time-domain diagram and power spectrum such as Fig. 7 (a) and
Shown in Fig. 7 (b)；
In order to verify the practicability of the method for the present invention, MRS signal Y (t) after denoising signal-to-noise ratio (SNR) estimation has been subjected to.
It is computed, SNR=9.2147dB, the SNR before relatively separating improves 22.6076dB；Then envelope extraction has been carried out to Y (t)
It is fitted with data, to obtain the key parameter initial amplitude e of separation signal0With relaxation time T2 *, it can be calculated,Relative error is respectively 1.6024%, 3.0142%, control ± 5% with
It is interior, meet application requirement.
Embodiment 2
The present embodiment is using the MRS signal that Changchun enamelware pot town (the ground Larmor frequency is about 2332.5Hz) acquires as originally
The process object of inventive method.As shown in Figure 1, the magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis,
The following steps are included:
Step (1): water instrument is visited using nuclear magnetic resonance depth measurement (MRS) and collects one group of observation MRS signal X1(t) (for row to
Amount), as shown in Fig. 8 (a) and Fig. 8 (b), sample rate 25kHz, data points are 12476, and calculating its signal-to-noise ratio is SNR=-
7.1453dB；
Step (2): MRS signal X will be observed1(t) pass through bandpass filter as shown in Figure 9, used bandpass filtering
Device is Chebyshev filter, and passband left margin is 2100Hz, and passband right margin is 2500Hz, and stopband left margin is 1800Hz,
Stopband right margin is 2800Hz, and decay 0.1dB for passband sideband region, and stopband cut-off region decaying 30dB obtains signal X2(t), such as Fig. 8
(a) shown in.
Step (3): observation MRS signal X is sought2(t) power spectrum, as shown in Fig. 8 (b) blue.It determines in signals and associated noises
Larmor signal amplitude comes second；
Step (4): the X that will be obtained by broadband bandpass filter2(t) be embedded in, the length of window selected forObtain track matrix H；
Track matrix H is subjected to RSVD decomposition, enables k=20, w=200, Meet approximate condition, the singular values and singular vectors U arranged in descending order draws out singular spectrum
Such as Figure 10；
According to the sorting position that step (3) obtains, Larmor signal amplitude comes second, therefore selects third and the
Four two singular values carry out matrix reconstruction, obtain matrix X；
Matrix X is diagonally equalized, the MRS signal Y (t) extracted, time-domain diagram and power spectrum such as Figure 11 (a) and
Shown in Figure 11 (b)；
In order to verify the practicability of the method for the present invention, MRS signal Y (t) after denoising signal-to-noise ratio (SNR) estimation has been subjected to.
It is computed, SNR=11.9542dB, the SNR before relatively separating improves 19.0995dB；Then envelope extraction has been carried out to Y (t)
It is fitted with data, to obtain the key parameter initial amplitude e of separation signal0With relaxation time T2 *, can be calculated, e0=
63.7791nV T2 *=0.1890s is consistent with practical Geology Drilling data results.
Claims (5)
1. a kind of magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis, which is characterized in that including following
Step:
Step (1): the observation MRS signal X that water instrument collects Larmor frequency known to one group is visited using nuclear magnetic resonance depth measurement1(t)；
Step (2): by the observation MRS signal X of acquisition1(t) signal X is obtained by broadband bandpass filter2(t)；
Step (3): the signal X that will be obtained by broadband bandpass filter2(t) power spectrumanalysis is carried out, by the amplitude of each frequency
Descending arrangement is carried out, the sorting position of the corresponding signal amplitude of Larmor frequency is found；
Step (4): the signal X that will be obtained by broadband bandpass filter2(t) it carries out singular spectrum analysis and extracts MRS signal,
In: singular spectrum analysis includes:
Insertion, obtains track matrix H；
Track matrix H is subjected to RSVD decomposition, the singular values and singular vectors U arranged in descending order；
According to the sorting position that step (3) obtains, selects corresponding two singular values to carry out matrix reconstruction, obtain Matrix C；
Matrix C is diagonally equalized, the MRS signal Y (t) extracted.
2. a kind of magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis described in accordance with the claim 1,
It is characterized in that, the specific steps of the insertion in the step (4) are as follows:
Signal X2(t) it is one-dimensional real sequence that length is N: X2(t)=(x1,x2,...,xN), positive integer L is sliding window length,
The value of 1 < L < N, L is determined by following formula:
Pass through embedding operation original sequence signal X2(t) P vector, each vector h are constitutediIt indicates
hi=(xi,xi+1,…,xi+L-1)T
The result of wherein P=N-L+1, i=1,2 ..., P, mapping form track matrix H:
3. a kind of magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis described in accordance with the claim 1,
It is characterized in that, the specific steps that the RSVD in the step (4) is decomposed are as follows:
1), parameter k and parameter w, k are set for the k singular value for approximate reconstruction matrix that is taken, w is for ensuring that reconstruct
The parameter that conditioned matrix is set up, wherein w>k, w<L, w<P；
2) the gaussian random matrix G of 0 mean value, 1 variance, is constructedL×w；
3) track matrix H, is calculatedL×PSampling matrix MP×w:
4), by sampling matrix MP×wK singular value carries out SVD decomposition before choosing, and obtains the left singular vector Q of its orthogonal matrixP×k, it is right
Angular moment battle array Zk×k, right singular vectorIt indicates are as follows:
5) matrix T, is constructedL×k:
TL×k=HL×PQP×k；
6), to matrix TL×kSVD decomposition is carried out, its left singular vector U is obtainedL×L, diagonal matrix ΣL×kAnd right singular vector
It indicates are as follows:
7), calculating matrix VP×k:
VP×k=QP×kOk×k；
8) H, is calculatedL×PApproximate singular matrix
The approximate singular matrix for acquiring H is decomposed using RSVD, the approximate singular matrix sought need to meet the following conditions:
λk+1For+1 singular value of kth of track matrix H；
Diagonal matrix ΣL×kFor L × k rank matrix, main diagonal element is k singular value of MRS signal approximation singular matrix；By k
A singular value carries out descending arrangement (λ1≥λ2≥...≥λk), obtain corresponding orthogonal singular vector set U '=(u1,
u2,...uk), the contribution rate of each singular value are as follows:
Unusual spectrogram is drawn out according to above formula.
4. a kind of magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis described in accordance with the claim 3,
It is characterized in that, in the step (4) according to sorting position, select corresponding two singular values to carry out matrix reconstruction
Include:
The sequence v that MRS signal amplitude size is found according to step (3) selects 2v-1 and 2v a unusual inside singular spectrum
Value；
According to selected singular value restructuring matrix, steps are as follows for reconstruct:
1) the right singular vector W of reconstruction signal matrix, is calculated
Wherein, j=2v-1,2v；
2), reconstruction signal Matrix C
5. a kind of magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis described in accordance with the claim 1,
It is characterized in that, the specific steps diagonally equalized in the step (4) are as follows:
By diagonally equalizing singular spectrum analysis reconstruction signal matrix { c1,c2,…,cq,…,cPIt is converted into corresponding reconstruct sequence
Arrange { g1,g2,…,gq,…,gP, wherein sequence gqIndicate q-th of singular spectrum analysis reproducing sequence,Process is as follows:
Wherein, cqIndicate q-th of singular spectrum analysis reconstruction signal matrix, For matrix cqIn m row n-th arrange
Element,Indicate reproducing sequence gqD-th of element, q=1,2 ..., P, d=1,2 ..., N；By reproducing sequence { g1,
g2,…,gPAdd up summation, the MRS signal sequence after being denoisedWherein Y (t)={ y (t1),y(t2),…,y
(tN)={ y1,y2,…,yN}。
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