CN104459809A - Full-wave nuclear magnetic resonance signal denoising method based on independent component analysis - Google Patents
Full-wave nuclear magnetic resonance signal denoising method based on independent component analysis Download PDFInfo
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- CN104459809A CN104459809A CN201410611932.XA CN201410611932A CN104459809A CN 104459809 A CN104459809 A CN 104459809A CN 201410611932 A CN201410611932 A CN 201410611932A CN 104459809 A CN104459809 A CN 104459809A
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Abstract
The invention discloses a full-wave nuclear magnetic resonance signal denoising method based on independent component analysis. The full-wave nuclear magnetic resonance signal denoising method is mainly used for power frequency harmonic interference or certain single-frequency interference in full-wave nuclear magnetic resonance signals. The method comprises the steps that firstly, utilizing a nuclear magnetic resonance sounding water detecting instrument for collecting MRS signals, obtaining the frequency of power frequency harmonic interference or certain single-frequency interference contained in the collected signals through spectral analysis, and adopting a digital orthogonal method for constructing input channel signals to solve the underdetermined blind source separation problem; then, using the constructed input channel signals and the collected MRS signals as input signals for conducting independent component analysis to obtain separated MRS signals; finally, adopting the spectrum correcting method for solving the problem that the separated MRS signals have uncertain amplitude, and then extracting denoised MRS signals. According to the full-wave nuclear magnetic resonance signal denoising method, the problem of the underdetermined blind source and the problem of the uncertain amplitude usually existing in independent component analysis are solved, the power frequency harmonic interference or the certain single-frequency interference in the noised MRS signals is effectively filtered out, and compared with a traditional MRS signal denoising method, the full-wave nuclear magnetic resonance signal denoising method has the advantages of being high in arithmetic speed, high in signal to noise ratio, high in practicability and the like.
Description
Technical field
The present invention relates to a kind of nuclear magnetic resonance depth measurement (Magnetic Resonance Sounding, MRS) signal noise filtering method, specifically utilize the filtering method of the all-wave NMR signal noise based on independent component analysis principle.
Background technology
Nuclear magnetic resonance depth measurement (Magnetic Resonance Sounding, MRS) underground water direct detection method that is a kind of high-new, harmless, high resolution that technology is that developed recently gets up, it is a kind of Weak Signal Detection, and its ultimate principle is that the NMR signal produced by Hydrogen Proton resonant transition in Underground water realizes underground water detection.The general expression of all-wave NMR signal is:
(10)
Four key parameter: E of MRS signal are comprised in formula (10)
0(q),
ω
0,
represent the angular Larmor frequency from the signal initial amplitude that stratum water cut is correlated with, the relaxation time (the relaxation time scope of free water be 30ms-1000ms) relevant with water-bearing zone factor of porosity, zones of different with different numerical value, the initial phase relevant with water-bearing zone electric conductivity respectively.
Although MRS method has all advantages in underground water detection, detect nuclear magnetic signal at present and belong to and receive volt level signal, extremely faint, be very easily subject to the impact of neighbourhood noise.Especially when the Hz noise in neighbourhood noise or a certain mono-tone interference frequency are near Larmor frequency, the complete None-identified of MRS signal will be caused, thus be difficult to accurately extract the key parameter such as initial amplitude, relaxation time, have a strong impact on follow-up inversion interpretation work.
At present, for the Theories and methods of NMR signal noise filtering, domestic and international experts and scholars have carried out a large amount of research work.On hardware implementing, generally adopt Trushkin D V, Shushakov O A, the data investigation method that Legchenko A V proposes in " The potential of a noise-reducing antenna for surface NMRgroundwater surveys in the earth's magnetic field " (" Geophysical Prospecting " the 42nd volume 8 phase in 1994: 855-862 page) and Konstantinos Chalikakis, Mette Ryom Nielsen, Anatoly Legchenko is at " MRS applicability for a study of glacialsedimentary aquifers in Central Jutland, Denmark " (" Journal of AppliedGeophysics " the 66th volume 3 phase in 2008: 176 – 187 pages) middle " 8 " font coil raising signal to noise ratio (S/N ratio) proposed, but can cause the reduction of instrument investigation depth and work efficiency low, the hyperchannel GeoMRI instrument of in recent years representative VistaClara company of U.S. development and French IRIS company release last word NUMISPOLY instrument and all propose to adopt reference channel mode, improve signal to noise ratio (S/N ratio) based on adaptive noise cancellation method.The de-noising thought of above-mentioned algorithm is all realize SNR estimation and compensation based on the correlativity of noise in reference channel noise and main channel signals and associated noises, but due to the irregularities of some noise and the uncertainty of instability and mixed mechanism, limit the application of algorithm.
Due in most cases, source signal, noise and mixed mechanism are all unknown, and therefore, a kind of independent component analysis (Independent Component Analysis, ICA) method of rising in recent years solves problems.ICA is the effective separation means of one developed on the basic model of blind source separating problem, and its basic model is X=AS (X is observation signal, and A is unknown linear combination matrix, and S is source signal) and solving model is Y=W
t(Y is separation signal to X, A
-1=W
tfor separation matrix).ICA is transformed into solving model by certain optimized algorithm and objective function from basic model, and then obtains separation signal.
Patent CN101908138A discloses " a kind of identification method of image target of synthetic aperture radar based on noise independent component analysis, belongs to the technical field of diameter radar image target identification "; Patent CN102697493A discloses " a kind of method that in EEG signals fast, eye electricity artefact automatically identifies and removes ", belongs to medical signals field; Patent CN102867189A discloses one " the ADAPTIVE MIXED separation of images method based on independent component analysis ", belongs to image processing field; Patent CN103854660A discloses " a kind of four Mike's sound enhancement methods based on independent component analysis ", belongs to field of voice signal.Visible independent component analysis has been successfully applied the every field of signal transacting, but there is not yet it and be applied in the noise filtering of MRS signal.
At present, when applying traditional independent component analysis and carrying out Signal separator, main Problems existing is: owe to determine blind source separating problem, separation signal amplitude is indefinite.So-called owing determines blind source separating problem, refers in the noise source that MRS signal comprises, and noise is complicated, and cause independent source number unknown, and consider the restriction of instrument and equipment, the number of the observation signal collected is less than the situation of the number of source signal.Problems is undoubtedly by the application of restriction ICA in the filtering of nuclear magnetic resonance depth measurement signal noise.In addition, if noisy MRS signal is after ICA, the amplitude being separated MRS signal can not get accurate estimation, then stratum water cut estimated error rate in follow-up inversion interpretation can be caused to increase, affect engineering progress.
Summary of the invention
Technical matters to be solved by this invention is the filtering method providing a kind of all-wave NMR signal noise based on independent component analysis principle.
The present invention is achieved in that a kind of all-wave NMR signal noise filtering method based on independent component analysis, comprises the following steps:
Step (1): utilize nuclear magnetic resonance depth measurement to visit water instrument and collect one group of observation MRS signal X
1(t);
Step (2): to the observation MRS signal X gathered
1t () carries out Fourier transform, obtain its frequency spectrum, determines the frequency f of industrial frequency harmonic or a certain mono-tone interference N (t) contained in signal
0, f
1f
n;
What industrial frequency harmonic interference represented is the integral multiple of 50Hz, and such as can represent industrial frequency harmonic a: X=a*cos (2*pi*f*t) as follows, a is wherein amplitude, can get arbitrary constant, and f is 2350Hz (being 47 times of 50); A certain mono-tone interference refers to the interference that frequency is not the integral multiple of 50Hz.
Step (3): according to the industrial frequency harmonic determined in step (2) or a certain mono-tone interference N (t) frequency f
0, f
1f
n, adopt digital quadrature method structure input channel signal X
2(t), X
3(t) ... X
2n(t), X
2n+1(t);
Step (4): by the input channel signal X of structure in step (3)
2(t), X
3(t) ... X
2n(t), X
2n+1(t) and observation MRS signal X
1t () is in the lump as input signal X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)] carry out independent component analysis, obtain separation signal
Step (5): separation signal is carried out spectrum analysis respectively, according to desirable MRS signal S (t) feature determination target MRS signal
Step (6): adopt spectrum correction method to the separation signal after independent component analysis
carry out spectrum recovery, obtain MRS signal Y (t) after denoising.
Further, the concrete steps of the digital quadrature method in described step (3) are:
First, observation signal X is supposed
1t () is made up of, represented by (1): X desirable MRS signal S (t) and industrial frequency harmonic or a certain mono-tone interference N (t)
1(t)=AS (t)+BN (t)=AS (t)+Bsin (2 π f
0t+ θ
0), wherein A, B are respectively two arbitrary constants, f
0for the industrial frequency harmonic that obtains through Frequency Estimation method or a certain mono-tone interference frequency, θ
0for the phase place of industrial frequency harmonic interference;
Secondly, due to phase theta
0be difficult to estimate, therefore formula (1) done further decomposition:
X
1(t)＝A·S(t)+B·sin(2πf
0t+θ
0)＝
(2)
A·S(t)+B·sin(2πf
0t)·cos(θ
0)+B·cos(2πf
0t)·sin(θ
0)
Cos (θ in formula (2)
0), sin (θ
0) be time-independent constant, if:
B
1＝B·cos(θ
0),B
2＝B·sin(θ
0)
(3)
Then:
X
1(t)＝A·S(t)+B
1·sin(2πf
0t)+B
2·cos(2πf
0t) (4)
Finally, by observation signal X
1t () represents the form of an accepted way of doing sth (4), therefore construct input channel signal:
X
2(t)=B
1sin (2 π f
0t), X
3(t)=B
2cos (2 π f
0t) (5) are as observation signal X
1t () be two-way input channel signal in addition, if when having the interference of multiple industrial frequency harmonic or a certain mono-tone interference, can carry out according to the method described above constructing multiple input channel signal equally, that is: X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)];
Further, the independent component analysis in described step (4), adopts the fast fixed point FastICA algorithm based on negentropy to carry out noisy MRS signal X
1the separation of (t), concrete steps are:
1), digital quadrature method is adopted to obtain input signal X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)], carried out pre-service, comprise decentralization and albefaction, object makes the average of observation signal be zero and correlativity is less, obtains pretreated signal Z (t)=[Z
1(t); Z
2(t); Z
3(t); ... Z
2n(t); Z
2n+1(t)];
2), judge the Gaussian of desirable MRS signal S (t) and industrial frequency harmonic or a certain mono-tone interference N (t), be convenient to select suitable nonlinear function to carry out independent component separation, the measure formulas according to kurtosis:
Kurt=E{x
4}/E
2{ x
2}
-3(6) kurtosis value that can be calculated two kinds of signals is all less than zero, known S (t) and N (t) all belong to sub-Gaussian signals, therefore, selecting type (7) substitutes into iterative formula (8) as the nonlinear function of FastICA algorithm:
g(Y)＝Y
3
Wherein, g () the single order derived function that is G (); Y=(w
i t(p) X (t));
3), the condition of convergence is set, and initialization weight vector;
4), according to negentropy maximization condition, the iterative formula (8) adopting Newton iteration method to obtain and normalization formula (9) solve separation matrix W, thus obtain separation signal
w
i(p+1)＝E{Xg(w
i T(p)X(t))}-E{G″(w
i T(p)X(t))}w
i(p) (8)
w
i(p+1)＝w
i(p+1)/||w
i(p+1)|| (9)
P (p=1,2,3...n) in formula (9) is iterative steps, w
ip () is one of them row vector corresponding to W; Formula (9) realizes w
i(p+1) normalization.
Further, the spectrum correcting method in described step (6), concrete steps are:
1), independent component analysis is separated the target MRS signal obtained
carry out Fourier transform with desirable MRS signal S (t), obtain both frequency spectrums;
2), contrast both the difference degree of spectral magnitude at Larmor frequency place, the former frequency spectrum multiple is returned to the amplitude of the latter's frequency spectrum;
3), by the frequency spectrum of separation signal after correcting through Fourier inversion to time domain, obtain MRS signal Y (t) after denoising.
The present invention compared with prior art, beneficial effect is: the present invention proposes the all-wave NMR signal noise filtering method based on independent component analysis, not only achieve the industrial frequency harmonic interference near MRS signal Larmor frequency or effective filtering of mono-tone interference, and the method utilizes the input channel signal of digital quadrature method structure except observation signal passage, without the need to the requirement of traditionally ICA, extra instrument and equipment is used to gather input multiplexer signal, break the harsh conditions of ICA application, save a large amount of manpower and materials.Meanwhile, the separation signal amplitude indeterminate problem utilizing spectrum correction method to solve traditional IC A to be used to have, for the initial amplitude extracting MRS signal has accurately and efficiently carried out sufficient preparation.Compared with traditional MRS signal antinoise method, the inventive method can reduce MRS signal message and lose, and fast operation, signal to noise ratio (S/N ratio) is high.In addition, the inventive method also opens the new world of independent component analysis in NMR signal de-noising field, is the applications expanding thinking of follow-up independent component analysis.
Accompanying drawing explanation
Fig. 1 is based on the FB(flow block) of the all-wave NMR signal noise filtering method of independent component analysis;
Fig. 2 Fixed point algorithm FB(flow block);
Fig. 3 Spectrum Correction process schematic;
The desirable MRS signal of Fig. 4 (a);
The desirable MRS signal spectrum of Fig. 4 (b);
The noisy MRS signal of Fig. 5 (a);
The noisy MRS signal spectrum of Fig. 5 (b);
Fig. 6 (a) is separated MRS signal;
Fig. 6 (b) is separated MRS signal spectrum;
MRS signal after Fig. 7 (a) Spectrum Correction;
MRS signal spectrum after Fig. 7 (b) Spectrum Correction;
Fig. 8 (a) observes MRS signal;
Fig. 8 (b) observes MRS signal spectrum;
Fig. 9 (a) observes MRS separation signal;
Fig. 9 (b) observes MRS separation signal frequency spectrum;
Actual measurement MRS signal before and after Figure 10 (a) ICA process;
Actual measurement MRS signal spectrum before and after Figure 10 (b) ICA process.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.
As shown in Figure 1, a kind of all-wave NMR signal noise filtering method based on independent component analysis, comprises the following steps:
Step (1): utilize nuclear magnetic resonance depth measurement to visit water instrument and collect one group of observation MRS signal X
1(t);
Step (2): to the observation MRS signal X gathered
1t () carries out Fourier transform, obtain its frequency spectrum, determines the frequency f of industrial frequency harmonic or a certain mono-tone interference N (t) contained in signal
0, f
1f
n;
Step (3): according to the industrial frequency harmonic determined in step (2) or a certain mono-tone interference N (t) frequency f
0, f
1f
n, adopt digital quadrature method structure input channel signal X
2(t), X
3(t) ... X
2n(t), X
2n+1(t);
Step (4): by the input channel signal X of structure in step (3)
2(t), X
3(t) ... X
2n(t), X
2n+1(t) and observation MRS signal X
1t () is in the lump as input signal X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)] carry out independent component analysis, obtain separation signal
Step (5): separation signal is carried out spectrum analysis respectively, according to desirable MRS signal S (t) feature determination target MRS signal
Step (6): adopt spectrum correction method to the separation signal after independent component analysis
carry out spectrum recovery, obtain MRS signal Y (t) after denoising.
A kind of concrete steps of digital quadrature method of the all-wave NMR signal noise filtering method based on independent component analysis are:
First, observation signal X is supposed
1t () is made up of, represented by (1): X desirable MRS signal S (t) and industrial frequency harmonic or a certain mono-tone interference N (t)
1(t)=AS (t)+BN (t)=AS (t)+Bsin (2 π f
0t+ θ
0), wherein A, B are respectively two arbitrary constants, f
0for the industrial frequency harmonic that obtains through Frequency Estimation method or a certain mono-tone interference frequency, θ
0for the phase place of industrial frequency harmonic interference,
Secondly, due to phase theta
0be difficult to estimate, therefore formula (1) done further decomposition:
X
1(t)＝A·S(t)+B·sin(2πf
0t+θ
0)＝
(2)
A·S(t)+B·sin(2πf
0t)·cos(θ
0)+B·cos(2πf
0t)·sin(θ
0)
Cos (θ in formula (2)
0), sin (θ
0) be time-independent constant, if:
B
1＝B·cos(θ
0),B
2＝B·sin(θ
0)
(3)
Then:
X
1(t)＝A·S(t)+B
1·sin(2πf
0t)+B
2·cos(2πf
0t) (4)
Finally, by observation signal X
1t () represents the form of an accepted way of doing sth (4), therefore construct input channel signal:
X
2(t)=B
1sin (2 π f
0t), X
3(t)=B
2cos (2 π f
0t) (5) are as observation signal X
1t () be two-way input channel signal in addition, if when having the interference of multiple industrial frequency harmonic or a certain mono-tone interference, can carry out according to the method described above constructing multiple input channel signal equally, that is: X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)];
As shown in Figure 2, independent composition analysis algorithm provided by the invention, the Fixed point algorithm based on negentropy (FastICA) adopting the people such as Hyvarinen to propose carries out noisy MRS signal X
1the separation of (t), concrete steps are:
1), digital quadrature method is adopted to obtain input signal X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)], carried out pre-service, comprise decentralization and albefaction, object makes the average of observation signal be zero and correlativity is less, obtains pretreated signal Z (t)=[Z
1(t); Z
2(t); Z
3(t); ... Z
2n(t); Z
2n+1(t)];
2), judge the Gaussian of desirable MRS signal S (t) and industrial frequency harmonic or a certain mono-tone interference N (t), be convenient to select suitable nonlinear function to carry out independent component separation, the measure formulas according to kurtosis:
Kurt=E{x
4}/E
2{ x
2}
-3(6) kurtosis value that can be calculated two kinds of signals is all less than zero, known S (t) and N (t) all belong to sub-Gaussian signals, therefore, selecting type (7) substitutes into iterative formula (8) as the nonlinear function of FastICA algorithm:
g(Y)＝Y
3
Wherein, g () the single order derived function that is G (); Y=(w
i t(p) X (t));
3), the condition of convergence is set, and initialization weight vector;
4), according to negentropy maximization condition, the iterative formula (8) adopting Newton iteration method to obtain and normalization formula (9) solve separation matrix W, thus obtain separation signal
w
i(p+1)＝E{Xg(w
i T(p)X(t))}-E{G″(w
i T(p)X(t))}w
i(p) (8)
W
i(p+1)=w
i(p+1)/|| w
i(p+1) || the p (p=1,2,3...n) in (9) formula (9) is iterative steps, w
ip () is one of them row vector corresponding to W;
Formula (9) realizes w
i(p+1) normalization, wherein needs in separation matrix W to judge | w
i(p)-w
i(p+1) | whether being less than the condition of convergence, in this way, then stopping iteration, if not being return iterative formula (8), re-starting orthogonal, normalization.
As shown in Figure 3, spectrum correcting method provided by the invention, the spectrum correcting method in described step (6), concrete steps are:
1), independent component analysis is separated the target MRS signal (signal as shown in Fig. 3 B1) obtained and desirable MRS signal S (t) (signal as shown in Fig. 3 A1) carries out Fourier transform, obtain both frequency spectrums, signal collection of illustrative plates as shown in Fig. 3 B2 is the frequency spectrum of target MRS signal, the frequency spectrum of desirable MRS signal as shown in figure 3 a 2;
2), contrast both the difference degree of spectral magnitude at Larmor frequency place, the former frequency spectrum multiple is returned to the amplitude of the latter's frequency spectrum;
3), by the frequency spectrum (frequency spectrum of separation signal as shown in Figure 3 C) of separation signal after correcting through Fourier inversion to time domain, obtain MRS signal Y (t) after denoising (the MRS signal after denoising as shown in Figure 3 D).
Embodiment 1
The present embodiment is the emulation experiment of the inventive method of carrying out under MATLAB 7.0 programmed environment.
Based on the simulation algorithm of the all-wave NMR signal noise filtering method of independent component analysis, with reference to Fig. 1, comprise the following steps:
Step (1): utilizing formula (10) to construct Larmor frequency is 2325Hz, amplitude e
0for 150nV, the relaxation time
for the desirable MRS signal of 0.15s, as shown in Fig. 4 (a), the frequency spectrum that Fig. 4 (b) is its correspondence.Near this signal Larmor frequency, add the Hz noise of 2350Hz and 2300Hz, form through certain linear combination the observation MRS signal X that signal to noise ratio (S/N ratio) is-6.7471dB
1t () (being row vector), as shown in Fig. 5 (a);
Step (2): to observation MRS signal X
1t () carries out Fourier transform, obtain its frequency spectrum, as shown in Fig. 5 (b).Determine that the work frequency in signals and associated noises is respectively f
0=2300Hz, f
1=2350Hz;
Step (3): according to the noise frequency determined in step (2), adopts digital quadrature method structure input channel signal X
2(t)=sin (2 π f
0t), X
3(t)=cos (2 π f
0t), X
4(t)=sin (2 π f
1t), X
5(t)=cos (2 π f
1t);
Step (4): by the input channel signal X of structure in step (3)
2(t), X
3(t), X
4(t), X
5(t) and observation MRS signal X
1t () is in the lump as input signal X (t)=[X
1(t); X
2(t); X
3(t); X
4(t); X
5(t)] carry out independent component analysis, obtain independent component and separation signal
Step (5): by separation signal
carry out spectrum analysis respectively, according to desirable MRS signal S (t) feature determination target MRS signal
as shown in Fig. 6 (a), the frequency spectrum that Fig. 6 (b) is its correspondence, its Time Domain Amplitude is about 2.5nV as seen, has a long way to go with pure MRS signal amplitude;
Step (6): adopt spectrum correction method to the separation signal after independent component analysis
carry out spectrum recovery, obtain MRS signal Y (t) after denoising, as shown in Fig. 7 (a), the frequency spectrum that Fig. 7 (b) is its correspondence;
In order to verify the practicality of the inventive method, MRS signal Y (t) after denoising being carried out signal to noise ratio (S/N ratio) (SNR) and having estimated.As calculated, its SNR=23.2521dB, the SNR before being comparatively separated improves 29.9992 dB; Then envelope extraction and data fitting have been carried out to Y (t), to obtain the key parameter initial amplitude E of separation signal
0(q) and relaxation time T
2 *, can be calculated, E
0(q)=152.3249nV, T
2 *=0.1453s, relative error is respectively 1.55% ,-3.11%, all controls within ± 5%, meets application requirement.
Embodiment 2
The MRS signal that the present embodiment gathers using enamelware pot town, Changchun (this ground Larmor frequency is for 2326Hz) is as the handling object of the inventive method.As shown in Figure 1, based on the all-wave NMR signal noise filtering method of independent component analysis, comprise the following steps:
Step (1): utilize nuclear magnetic resonance depth measurement (MRS) to visit water instrument and collect one group of observation MRS signal X
1(t) (being row vector), as shown in Fig. 8 (a), calculating its signal to noise ratio (S/N ratio) is SNR=-4.9186dB;
Step (2): to the observation MRS signal X gathered
1t () carries out Fourier transform, obtain its frequency spectrum, as shown in Fig. 8 (b), can see that this signal is at f
0=2300Hz, f
1=2350Hz, f
2all there is stronger industrial frequency harmonic interference at=2450Hz place, in addition, at f
3=2383.5Hz place receives strong mono-tone interference;
Step (3): according to the noise frequency determined in step (2), adopts digital quadrature method structure input channel signal X
2(t)=sin (2 π f
0t), X
3(t)=cos (2 π f
0t), X
4(t)=sin (2 π f
1t), X
5(t)=cos (2 π f
1t), X
6(t)=sin (2 π f
2t), X
7(t)=cos (2 π f
2t), X
8(t)=sin (2 π f
3t), X
9(t)=cos (2 π f
3t);
Step (4): by the input channel signal X of structure in step (3)
2(t), X
3(t), X
4(t), X
5(t), X
6(t), X
7(t), X
8(t), X
9(t) and observation MRS signal X
1t () is in the lump as input signal X (t)=[X
1(t); X
2(t); X
3(t); X
4(t); X
5(t); X
6(t); X
7(t); X
8(t); X
9(t)] carry out independent component analysis, obtain independent component and separation signal
Step (5): by separation signal
carry out spectrum analysis respectively, according to desirable MRS signal S (t) feature determination target MRS signal
as shown in Fig. 9 (a), be observation MRS separation signal, the frequency spectrum that Fig. 9 (b) is its correspondence;
Step (6): adopt spectrum correction method to the separation signal after independent component analysis
carry out spectrum recovery, obtain MRS signal Y (t) that the signal to noise ratio (S/N ratio) after denoising is 2.9698dB, light-colored part as larger in area in Figure 10 (a) is depicted as raw observation MRS signal, the frequency spectrum that the dark parts that area is less in Figure 10 (a) is the signal to noise ratio (S/N ratio) after denoising be MRS signal Y (t) of 2.9698dB, Figure 10 (b) is its correspondence;
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.
Claims (4)
1., based on an all-wave NMR signal noise filtering method for independent component analysis, it is characterized in that, comprise the following steps:
Step (1): utilize nuclear magnetic resonance depth measurement to visit water instrument and collect one group of observation MRS signal X
1(t);
Step (2): to the observation MRS signal X gathered
1t () carries out Fourier transform, obtain its frequency spectrum, determines the frequency f of industrial frequency harmonic or a certain mono-tone interference N (t) contained in signal
0, f
1f
n;
Step (3): according to the industrial frequency harmonic determined in step (2) or a certain mono-tone interference N (t) frequency f
0, f
1f
n, adopt digital quadrature method structure input channel signal X
2(t), X
3(t) ... X
2n(t), X
2n+1(t);
Step (4): by the input channel signal X of structure in step (3)
2(t), X
3(t) ... X
2n(t), X
2n+1(t) and observation MRS signal X
1t () is in the lump as input signal X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)] carry out independent component analysis, obtain separation signal
Step (5): separation signal is carried out spectrum analysis respectively, according to desirable MRS signal S (t) feature determination target MRS signal
Step (6): adopt spectrum correction method to the separation signal after independent component analysis
carry out spectrum recovery, obtain MRS signal Y (t) after denoising.
2., according to a kind of all-wave NMR signal noise filtering method based on independent component analysis according to claim 1, it is characterized in that, the concrete steps of the digital quadrature method in described step (3) are:
First, observation signal X is supposed
1t () is made up of, represented by (1): X desirable MRS signal S (t) and industrial frequency harmonic or a certain mono-tone interference N (t)
1(t)=AS (t)+BN (t)=AS (t)+Bsin (2 π f
0t+ θ
0), wherein A, B are respectively two arbitrary constants, f
0for the industrial frequency harmonic that obtains through Frequency Estimation method or a certain mono-tone interference frequency, θ
0for the phase place of industrial frequency harmonic interference;
Secondly, due to phase theta
0be difficult to estimate, therefore formula (1) done further decomposition:
X
1(t)＝A·S(t)+B·sin(2πf
0t+θ
0)＝ (2)
A·S(t)+B·sin(2πf
0t)·cos(θ
0)+B·cos(2πf
0t)·sin(θ
0)
Cos (θ in formula (2)
0), sin (θ
0) be time-independent constant, if:
B
1＝B·cos(θ
0),B
2＝B·sin(θ
0)
(3)
Then:
X
1(t)＝A·S(t)+B
1·sin(2πf
0t)+B
2·cos(2πf
0t) (4)
Finally, by observation signal X
1t () represents the form of an accepted way of doing sth (4), therefore construct input channel signal:
X
2(t)＝B
1·sin(2πf
0t),X
3(t)＝B
2·cos(2πf
0t) (5)
As observation signal X
1t () be two-way input channel signal in addition, if when having the interference of multiple industrial frequency harmonic or a certain mono-tone interference, can carry out according to the method described above constructing multiple input channel signal equally, that is: X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)].
3. according to a kind of all-wave NMR signal noise filtering method based on independent component analysis according to claim 1, it is characterized in that, independent component analysis in described step (4), adopts the fast fixed point FastICA algorithm based on negentropy to carry out noisy MRS signal X
1the separation of (t), concrete steps are:
1), digital quadrature method is adopted to obtain input signal X (t)=[X
1(t); X
2(t); X
3(t); ... X
2n(t); X
2n+1(t)], carried out pre-service, comprise decentralization and albefaction, object makes the average of observation signal be zero and correlativity is less, obtains pretreated signal Z (t)=[Z
1(t); Z
2(t); Z
3(t); ... Z
2n(t); Z
2n+1(t)];
2), judge the Gaussian of desirable MRS signal S (t) and industrial frequency harmonic or a certain mono-tone interference N (t), be convenient to select suitable nonlinear function to carry out independent component separation, the measure formulas according to kurtosis:
kurt＝E{x
4}/E
2{x
2}
-3(6)
The kurtosis value that can be calculated two kinds of signals is all less than zero, and known S (t) and N (t) all belong to sub-Gaussian signals, and therefore, selecting type (7) substitutes into iterative formula (8) as the nonlinear function of FastICA algorithm:
g(Y)＝Y
3
Wherein, g () the single order derived function that is G (); Y=(w
i t(p) X (t));
3), the condition of convergence is set, and initialization weight vector;
4), according to negentropy maximization condition, the iterative formula (8) adopting Newton iteration method to obtain and normalization formula (9) solve separation matrix W, thus obtain separation signal
w
i(p+1)＝E{Xg(w
i T(p)X(t))}-E{G″(w
i T(p)X(t))}w
i(p) (8)
w
i(p+1)＝w
i(p+1)/||w
i(p+1)|| (9)
P (p=1,2,3...n) in formula (9) is iterative steps, w
ip () is one of them row vector corresponding to W; Formula (9) realizes w
i(p+1) normalization.
4., according to a kind of all-wave NMR signal noise filtering method based on independent component analysis according to claim 1, it is characterized in that, the spectrum correcting method in described step (6), concrete steps are:
1), independent component analysis is separated the target MRS signal obtained
carry out Fourier transform with desirable MRS signal S (t), obtain both frequency spectrums;
2), contrast both the difference degree of spectral magnitude at Larmor frequency place, the former frequency spectrum multiple is returned to the amplitude of the latter's frequency spectrum;
3), by the frequency spectrum of separation signal after correcting through Fourier inversion to time domain, obtain MRS signal Y (t) after denoising.
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