CN1775172A - Noise Elimination of Functional Magnetic Resonance Data Based on Independent Component Spatial Correlation - Google Patents
Noise Elimination of Functional Magnetic Resonance Data Based on Independent Component Spatial Correlation Download PDFInfo
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Abstract
本发明公开了一种基于独立成份空间相关性消除功能磁共振数据噪声的方法，先对图像的灰质区域和脑脊液区域进行图像分割，分别对其进行主成份分析、频谱分析，确定并消除主成分分量中的随机噪声成分，重建消除随机噪声后的灰质数据和脑脊液数据，对重建后数据进行独立成份分解，利用独立成份分别构造矩阵，再进行典型相关分后，排序，将这些成分置零后得到一组新的独立成份，重建消除各种噪声成份后的数据，重复以上步骤直至消除各层灰质数据与脑脊液数据中相关最大的各种噪声成分。本发明能够有效地消除多层功能磁共振数据中生理噪声，能够消除与脑脊液区域数据中相关最大的其它低频噪声成份，较好地实现了多层功能磁共振数据中噪声的消除。
The invention discloses a method for eliminating the noise of functional magnetic resonance data based on the spatial correlation of independent components. First, image segmentation is performed on the gray matter area and the cerebrospinal fluid area of the image, and principal component analysis and spectrum analysis are performed on them respectively to determine and eliminate the principal components. The random noise component in the component, reconstruct the gray matter data and cerebrospinal fluid data after eliminating the random noise, decompose the independent components of the reconstructed data, use the independent components to construct the matrix separately, and then perform the canonical correlation score, sort, and set these components to zero. Obtain a new set of independent components, reconstruct the data after eliminating various noise components, and repeat the above steps until the various noise components with the greatest correlation between the gray matter data of each layer and the cerebrospinal fluid data are eliminated. The invention can effectively eliminate physiological noise in multi-layer functional magnetic resonance data, can eliminate other low-frequency noise components most correlated with cerebrospinal fluid area data, and better realize the elimination of noise in multi-layer functional magnetic resonance data.
Description
Technical field
The present invention relates to data processing field in the functional mri technology, relate in particular to a kind of method of eliminating functional magnetic resonance data noise based on independent component space relativity.
Background technology
Rely on (Blood Oxygenation Level Dependent based on blood oxygen level, BOLD) contrast mechanisms, (functional MRI fMRI) can detect the regional flow's kinetics that is associated with the cerebral cortex neural activity and change functional mri in real time.But, change very for a short time based on the magnetic resonance signal of BOLD effect, have only 0.5～2% in magnetic field intensity during for 1.5T.In addition, the cycle breathing all can cause the relevant MRI signal change of many physiology with cerebral tissue pulsation and the motion of some other complex physical that heart movement causes in the sequence image gatherer process.The MRI signal change that these physiology are relevant has constituted the physiological noise of functional MRI data.Except the physiological noise relevant with breathing with heart, also comprise the random noise and other low-frequency noise that come from radio-frequency coil and person under inspection in the functional MRI data, these low-frequency noises mainly be since after the instability of scanning device, motion correction factors such as residual motion association effect, secular physiology drift cause.These noise components and neural activity are irrelevant in the functional MRI data, have not only reduced the significance to the functional MRI data statistical analysis, and have directly influenced the sensitivity and the sterically defined reliability of functional MRI.
Noise in the functional MRI data mainly is because the physiological effect of the non-neuropathic relevant with breathing with heart causes.Except the physiological noise relevant with breathing with heart, also comprise the random noise and other low-frequency noise that come from radio-frequency coil and person under inspection in the functional MRI data, these low-frequency noises mainly be since after the instability of scanning device, motion correction factors such as residual motion association effect, secular physiology drift cause.Therefore, the functional MRI data model can be expressed as:
y
i(t)＝s
i(t)+p
i(t)+r
i(t) (1)
Wherein, y
i(t) represent the time course of each pixel, s
i(t) function signal that expression is real relevant with neural activity changes, p
i(t) the physiological effect physiological noise and the various low-frequency noise that cause of expression non-neuropathic, r
i(t) random noise of expression system.
Because the functional magnetic resonance signal that physiological movement causes changes, to have proposed many effective methods in order reducing, to have reached based on spatial estimation of k-and alignment technique etc. as adopting ecg-gating scanning, navigator echo, digital filtering, the property recalled correction.These methods or requirement are gathered or monitoring physiological movement information in real time, perhaps require specific scanning sequence, are cost to increase data acquisition burden or Data Post complexity all.In addition, in order to catch the physiological movement cycle, these methods require the frequency acquisition of functional MRI data to be higher than the physiological movement frequency.Some scholars propose to adopt component analyzing method that functional MRI data is carried out composition to decompose recently, determine and eliminate corresponding physiological noise composition by separated component being carried out spectrum estimation then.Though this method does not need additionally to gather physiological movement information, Data Post is comparatively simple.But, in order to estimate and definite physiological noise composition that this method still requires the frequency acquisition of performance data to be higher than the physiological movement frequency.
In order to cover between enough Naokongs, functional MRI often adopts Multi Slice Mode mode image data.Because the sample rate of time series image is lower than the physiological movement frequency, causes the high frequency physiological noise to be aliased into low-frequency component, physiological noise no longer keeps original waveform, can't determine the physiological noise composition of multilamellar functional MRI data based on frequency spectrum analysis method.
Summary of the invention
The invention provides a kind of method of eliminating functional magnetic resonance data noise based on independent component space relativity, can eliminate physiological noise in the multilamellar functional MRI data effectively, solving the corresponding physiological noise composition of existing elimination must be the problem that cost or the frequency acquisition that necessarily requires performance data are higher than harsh conditions such as physiological movement frequency to increase the Data Post complexity.
The technical solution used in the present invention is:
A kind of method based on independent component space relativity elimination functional magnetic resonance data noise, adopt the following step:
1) time sampling of establishing functional MRI volume data sequence is counted and is N, and each volume data comprises the S tomographic image, and grey matter zone and the cerebrospinal fluid zone with the i tomographic image is template respectively, constructs the grey matter data matrix Y of this layer time-series image correspondence
gWith cerebrospinal fluid data matrix Y
c, matrix Y
gAnd Y
cRow expressed the time course of pixel;
2) to grey matter data matrix Y
gCarry out principal component analysis, obtain N characteristic root and corresponding characteristic vector thereof, choose grey matter data matrix Y greater than 90% according to the accumulation variance contribution ratio of preceding p eigenvalue characteristic of correspondence vector by descending
gMain composition component;
3) to cerebrospinal fluid data matrix Y
cCarry out principal component analysis, obtain N characteristic root and corresponding characteristic vector thereof, choose cerebrospinal fluid data matrix Y greater than 90% according to the accumulation variance contribution ratio of preceding q eigenvalue characteristic of correspondence vector by descending
cMain composition component;
4) adopt the fourier spectrum analytical method respectively to grey matter data matrix Y
gWith cerebrospinal fluid data matrix Y
cThe main constituent component carry out spectrum analysis, determine and eliminate grey matter data matrix Y according to the random noise decision criteria
gWith cerebrospinal fluid data matrix Y
cRandom noise composition in the main constituent component;
5) the main constituent component that utilizes step 4) to keep is respectively rebuild the grey matter data of eliminating after the random noise
With the cerebrospinal fluid data
6) to the grey matter data
Carry out independent component and decompose, obtain separation matrix W
gAnd m statistics goes up separate composition c
i g(t), i=1,2, Λ m;
7) to the cerebrospinal fluid data
Carry out independent component and decompose, obtain separation matrix W
cAnd n statistics goes up separate composition c
j c(t), j=1,2, Λ n;
8) utilize m independent component c of grey matter data
i g(t) structural matrix X
M * N, utilize n independent component c of cerebrospinal fluid data
j c(t) structural matrix Y
N * N
9) to matrix X
M * NAnd Y
N * NCarry out canonical correlation analysis, obtain c
i g(t) weighting coefficient matrix A
M * r, c
j c(t) weighting coefficient matrix B
N * rAnd the row that comprises r element is vectorial
R is a number less among m and the n,
K element be matrix X
M * NAnd Y
N * NEach the row respectively with matrix A
M * rAnd B
N * rThe k column element be the canonical variable that obtains after the weight coefficient weighting canonical correlation coefficient square, k=1,2, Λ r;
10) calculate the row vector
Each element to matrix A
M * rThe weighted sum of each row element obtains expressing each independent component c in the grey matter data
i g(t) with the cerebrospinal fluid data in each independent component c
j c(t) column vector of correlated measure
11) to column vector
Each element sort from big to small, so, the column vector after the ordering
The independent element c of grey matter data of preceding r element correspondence
i g(t) be with the cerebrospinal fluid data in each independent component c
j c(t) relevant maximum noise contribution will obtain one group of new independent component after these composition zero setting
12) use separation matrix W
gInverse matrix multiply by by independent component
The composition matrix that constitutes is rebuild each independent component c in elimination and the cerebrospinal fluid data
j c(t) the grey matter data behind the various noise components of relevant maximum;
14) repeating step 1) to 12), in eliminating each layer of functional MRI time series data grey matter data with the cerebrospinal fluid data in the various noise contributions of relevant maximum.
Compared with prior art, the present invention has following advantage:
The method that the present invention proposes to eliminate functional magnetic resonance data noise based on independent component space relativity based on physiological noise composition time course in the cerebral gray matter zone and the spatial coherence in cerebrospinal fluid zone, by the independent component decomposition is carried out in cerebrospinal fluid zone and grey matter area data, utilize the spatial coherence of canonical correlation analysis methods analyst cerebrospinal fluid zone and grey matter zone independent component time course, can identify in the grey matter area data with the cerebrospinal fluid area data in relevant maximum noise component, the method that the present invention proposes not only can be eliminated physiological noise in the multilamellar functional MRI data effectively, and can eliminate with the cerebrospinal fluid area data in relevant other maximum low-frequency noise composition, realized the elimination of noise in the multilamellar functional MRI data preferably.
Because the method date processing that the present invention proposes is simple, do not need to gather in real time or monitoring physiological movement information, can carry out processed offline to the functional MRI data of early stage collection, therefore be a kind of functional MRI data processing method that comparatively is suitable for, be very suitable for clinical hospital and research unit and utilize functional MRI to carry out brain science research.
Description of drawings
Fig. 1 stimulates sequential chart for the auditory function experiment
The 30th tomographic image to experimental data when Fig. 2-1 is correlation coefficient threshold T=0.60 directly carries out the detected possible activation pixel of correlation analysis
When Fig. 2-2 is correlation coefficient threshold T=0.25 the 30th tomographic image is directly carried out the detected possible activation pixel of correlation analysis
After the method that Fig. 2-3 proposes for employing the present invention is eliminated the various noises that physiology is relevant in the grey matter data, detected activation pixel during correlation coefficient threshold T=0.60
Fig. 2-4 is for being mapped to the testing result of Fig. 2-3 result on experimental data the 30th tomographic image
Fig. 3-1 is 10 independent components in the grey matter data
Fig. 3-2 is 5 independent components in the cerebrospinal fluid data
Fig. 4-1 is that a certain activation pixel is eliminated noise time course before
Fig. 4-2 is that a certain activation pixel is eliminated noise time course afterwards
Fig. 5-1 compares for the correlation coefficient of eliminating noise front and back activation picture point time process and functional stimulus reference function
Fig. 5-2 for eliminate activate the picture point time process before and after the noise variance ratio
After the noise cancellation method that Fig. 6-1 proposes for employing the present invention to Fig. 6-6 was handled experimental data, the auditory function of the from the 28th to the 33rd layer of continuous 6 tomographic image that the employing correlational analysis method obtains activated mapping graph.
The specific embodiment
A kind of method based on independent component space relativity elimination functional magnetic resonance data noise, adopt the following step:
1) time sampling of establishing functional MRI volume data sequence is counted and is N, and each volume data comprises the S tomographic image, and grey matter zone and the cerebrospinal fluid zone with the i tomographic image is template respectively, constructs the grey matter data matrix Y of this layer time-series image correspondence
gWith cerebrospinal fluid data matrix Y
c, matrix Y
gAnd Y
cRow expressed the time course of pixel;
2) to grey matter data matrix Y
gCarry out principal component analysis, obtain N characteristic root and corresponding characteristic vector thereof, choose grey matter data matrix Y greater than 90% according to the accumulation variance contribution ratio of preceding p eigenvalue characteristic of correspondence vector by descending
gMain composition component;
3) to cerebrospinal fluid data matrix Y
cCarry out principal component analysis, obtain N characteristic root and corresponding characteristic vector thereof, choose cerebrospinal fluid data matrix Y greater than 90% according to the accumulation variance contribution ratio of preceding q eigenvalue characteristic of correspondence vector by descending
cMain composition component;
4) adopt the fourier spectrum analytical method respectively to grey matter data matrix Y
gWith cerebrospinal fluid data matrix Y
cThe main constituent component carry out spectrum analysis, determine and eliminate grey matter data matrix Y according to the random noise decision criteria
gWith cerebrospinal fluid data matrix Y
cRandom noise composition in the main constituent component;
5) the main constituent component that utilizes step 4) to keep is respectively rebuild the grey matter data of eliminating after the random noise
With the cerebrospinal fluid data
6) to the grey matter data
Carry out independent component and decompose, obtain separation matrix W
gAnd m statistics goes up separate composition c
i g(t), i=1,2, Λ m;
7) to the cerebrospinal fluid data
Carry out independent component and decompose, obtain separation matrix W
cAnd n statistics goes up separate composition c
j c(t), j=1,2, Λ n;
8) utilize m independent component c of grey matter data
i g(t) structural matrix X
M * N, utilize n independent component c of cerebrospinal fluid data
j c(t) structural matrix Y
N * N
9) to matrix X
M * NAnd Y
N * NCarry out canonical correlation analysis, obtain c
i g(t) weighting coefficient matrix A
M * r, c
j c(t) weighting coefficient matrix B
N * rAnd the row that comprises r element is vectorial
R is a number less among m and the n,
K element be matrix X
M * NAnd Y
N * NEach the row respectively with matrix A
M * rAnd B
N * rThe k column element be the canonical variable that obtains after the weight coefficient weighting canonical correlation coefficient square, k=1,2, Λ r;
10) calculate the row vector
Each element to matrix A
M * rThe weighted sum of each row element obtains expressing each independent component c in the grey matter data
i g(t) with the cerebrospinal fluid data in each independent component c
j c(t) column vector of correlated measure
11) to column vector
Each element sort from big to small, so, the column vector after the ordering
The independent element c of grey matter data of preceding r element correspondence
i g(t) be with the cerebrospinal fluid data in each independent component c
j c(t) relevant maximum noise contribution will obtain one group of new independent component after these composition zero setting
12) use separation matrix W
gInverse matrix multiply by by independent component
The composition matrix that constitutes is rebuild each independent component c in elimination and the cerebrospinal fluid data
c j(t) the grey matter data behind the various noise components of relevant maximum;
15) repeating step 1) to 12), in eliminating each layer of functional MRI time series data grey matter data with the cerebrospinal fluid data in the various noise contributions of relevant maximum.
Present embodiment can also pass through computing function experimental design sequential and above-mentioned steps 1) described grey matter data matrix Y
gIn the correlation coefficient of time course of the expressed pixel of every row, re-construct the matrix of grey matter data greater than the pixel of threshold value T with correlation coefficient.Above-mentioned random noise decision criteria is: if the mean power of a certain composition fourier spectrum, thinks then that this composition is the random noise composition more than or equal to the standard deviation of spectrum power.
We handle and analyze the method for verifying proposition by the auditory function MR data to reality.Experimental data is provided by the Wellcom of London University neuroimaging laboratory.Auditory experiment comprises tranquillization and excites two states, and quiescent stage does not apply any stimulation, and stimulating phase applies auditory stimulus with the speed of 60 double-tone joints of per minute English word.Such experiment repeats 8 times altogether, in each experiment, quiescent stage and stimulating phase is carried out 6 samplings respectively, each sampling obtains 64 successive transverse axis position cross-sectional images, scan matrix is 64 * 64 * 64, single sweep operation sampling repetition time TR=7s, whole Therapy lasted 6 minutes.The specific embodiment is as follows:
1) after the present comparatively general functional MRI statistical analysis software SPM of utilization carries out pretreatment such as motion correction, space criteriaization to experimental data, obtain comprising the data set of 96 79 * 95 * 68 volume datas, and concentrate first volume data to carry out image to data to cut apart, obtain grey matter (GM), white matter (WM) and cerebrospinal fluid (CSF), and with the grey matter cut apart and cerebrospinal fluid image as template, construct grey matter data set and cerebrospinal fluid data set respectively.
In experiment, we at first with the stimulation sequential of auditory function experiment as reference function ref (t), as shown in Figure 1, utilize (7) to calculate ref (t) and each picture point time process y of grey matter data centralization
i g(t) correlation coefficient.
A wherein
i, b represents i picture point time process y in the grey matter data respectively
i gThe meansigma methods of the time course of meansigma methods (t) and reference function ref (t).
If correlation coefficient, thinks then that this pixel is possible activation pixel greater than preset threshold T.Re-construct the grey matter data set by these possible activation pixels then.Through such primary dcreening operation, the data of handling reduce in a large number, the corresponding raising of data-handling efficiency on the one hand, not only guaranteed to comprise in the main constituent of grey matter data set the real function signal composition relevant on the other hand, and the accuracy of grey matter data set independent element estimation has also been improved with neural activity.
Correlation coefficient threshold T can determine according to the significance level of statistical test.Here, we choose T=0.60, and the corresponding Z quantile is greater than 6, and the significance level α of statistical test is less than 0.01.27 possible activation pixels in experimental data the 30th tomographic image when highlight regions has shown threshold value T=0.60 as shown in Fig. 2-1.Because effect of noise directly utilizes correlation analysis method only to detect the possible activation pixel of minority.In order to increase the sample of possible activation pixel, we reduce threshold value T.262 possible activation pixels in experimental data the 30th tomographic image when highlight regions has shown threshold value T=0.25 among Fig. 2-2.Comparison diagram 2-1 and Fig. 2-2, because correlation coefficient threshold reduces, detected possible activation pixel showed increased also obviously increases but puppet activates pixel.Various noise components cause this result just because of comprising in the functional MRI data.The sterically defined reliability of functional MRI reduces.So in order to eliminate the various noise components that comprise in the functional MRI data, we re-construct the grey matter data set with 262 possible activation pixels among Fig. 2-2.
2) adopt unusual decomposition algorithm (SVD) to carry out principal component analysis respectively to grey matter data set and the cerebrospinal fluid data set that re-constructs, and choose main composition component greater than 90% according to the accumulation variance contribution ratio of the eigenvalue characteristic of correspondence vector that keeps, main composition to grey matter data and cerebrospinal fluid data utilizes Fourier transform to carry out spectrum analysis, if the mean power of a certain composition entire spectrum is more than or equal to the standard deviation of entire spectrum power, think that then this composition is system's random noise composition, and, eliminate the random noise composition with this composition zero setting.Through such processing, the grey matter data centralization keeps 10 main constituents, and the cerebrospinal fluid data centralization keeps 5 main constituents.
3) utilizing step 2 respectively) the main constituent component that obtains rebuilds the grey matter data
With the cerebrospinal fluid data
The correlation coefficient of the time course by the visual grey matter of computing function experimental design sequential and each zone pixel re-constructs the matrix of grey matter data greater than the pixel of threshold value T with correlation coefficient.
4) the quick fixed point independent composition analysis algorithm (fastICA) to the grey matter The data Hyvarinen after the elimination random noise carries out the independent element decomposition, and the result is shown in Fig. 3-1.
5) the cerebrospinal fluid data of eliminating after the random noise being adopted respectively and 4) same algorithm carries out independent element and decomposes, and the result is shown in Fig. 3-2.
6) in order to determine the relevant noise contribution of physiology in the grey matter data, matrix X and one 5 * 96 matrix Y that we utilize the independent component shown in Fig. 3-1, Fig. 3-2 to construct one 10 * 96 respectively.
7) matrix X and Y are carried out canonical correlation analysis, can obtain independent component c in the grey matter data
i g(t) weighting coefficient matrix A
5 * 5, independent component c in the cerebrospinal fluid data
j c(t) weighting coefficient matrix B
10 * 5And the row that comprises 5 elements is vectorial
The row vector
K element each row that is matrix X and Y respectively with matrix A
M * rAnd B
N * rThe weighting of k column element after canonical correlation coefficient square.
8) calculate the row vector
Each element to matrix A
M * rThe weighted sum of each row element obtains expressing each independent component c in the grey matter data
i g(t) with the cerebrospinal fluid data in each independent component c
j cThe column vector of correlated measure (t)
To column vector
Each element sort from big to small, the result as the table 1-1 shown in:
Independent component time course canonical correlation analysis result (the 30th layer) in table 1 grey matter and the cerebrospinal fluid
| M | 1.1833 | 0.9625 | 0.8489 | 0.8255 | 0.8167 | 0.7313 | 0.6081 | 0.5389 | 0.5238 | 0.2226 |
| | 1 | 7 | 10 | 5 | 6 | 4 | 8 | 9 | 3 | 2 |
From the ranking results of table 1 as seen, the correlated measure M that 10 independent components of the grey matter data centralization shown in Fig. 3-1 are relevant with 5 independent elements of the cerebrospinal fluid data centralization shown in Fig. 3-2 one is followed successively by the 1st, 7,10,5,6,4,8,9,3,2 from big to small.The 2nd the independent element correlated measure minimum relevant shown in Fig. 3-1 with 5 independent elements of the cerebrospinal fluid data centralization shown in Fig. 3-2, this independent element and auditory function experiment stimulation sequential basically identical shown in Figure 2 have reflected the time course of cerebral gray matter zone to the auditory function stimuli responsive.
9) according to the canonical correlation analysis method of introducing previously, we choose the noise contributions that preceding 5 independent elements of table 1 are correlated with as relevant maximum physiology with 5 independent components in the cerebrospinal fluid data.After these composition zero setting,
10) rebuild the grey matter data set according to (8)
Wherein, W
-1The inverse matrix of expression separation matrix W, C
0 gThe grey matter composition matrix of expression after with noise component zero setting.Solid line is represented same activation pixel respectively before eliminating noise and eliminate time course after the noise among Fig. 4-1, Fig. 4-2, and dotted line represents to reflect the time course of the reference function of auditory function experiment stimulation sequential.As seen, eliminate after the noise, the waveform that activates the picture point time process obviously improves, the tranquillization of auditory function experiment with excite the two states contrast also more obvious.
For the further quantitatively elimination effect of explanation noise, the time course that we distinguish calculating pixel before noise is eliminated and afterwards with the time course of the correlation coefficient of reference function and pixel before noise is eliminated and variance afterwards.The time course of 262 possible activation pixels of grey matter data centralization that dotted line has shown reconstruct among Fig. 6-1 before eliminating noise with the correlation coefficient of reference function, solid line has shown the correlation coefficient of eliminating after the noise with reference waveform, as seen, correlation coefficient obviously becomes big after eliminating noise, the correlation coefficient maximum is 0.6715 before, and meansigma methods is 0.4261; The correlation coefficient maximum is 0.7547 afterwards, and meansigma methods is 0.6097, and the correlation coefficient meansigma methods increases by 43.09%.The time course of 262 pixels of grey matter data centralization that dotted line and solid line have shown reconstruct respectively among the 6-2 is before eliminating noise and mean square deviation afterwards.As seen, mean square deviation obviously diminishes after the elimination noise, and mean square deviation is 5541.2 before, and mean square deviation is 3110.6 afterwards, and mean square deviation reduces 43.86%.
The highlight regions of Fig. 2-3 shown eliminate after the noise with the correlation coefficient of reference function greater than 0.60 activation pixel.Compare with Fig. 2-1, though choose same correlation coefficient threshold, under the situation that the significance to the functional MRI data statistical analysis remains unchanged, detected activation number of pixels is increased to 160, and the sensitivity of functional MRI improves.Compare with Fig. 2-2, the pseudo-number of pixels that activates also obviously reduces, and the sterically defined reliability of functional MRI improves.Fig. 2-4 activates mapping graph for the auditory function that Fig. 2-3 is mapped on experimental data collection the 30th tomographic image.
Table 2 is eliminated the noise front and back for functional MRI data and is changed relatively with reference function correlation coefficient and variance.Num_B, Num_A represent to eliminate before the noise respectively and the possible activation pixel of each data Layer afterwards.Eliminating noise correlation coefficient threshold before is T=0.25, and eliminating noise correlation coefficient threshold afterwards is T=0.60.Dmax_B, dmax_A represent to eliminate the maximum correlation coefficient of the forward and backward activation pixel of noise respectively, and dmean_B, dmean_A represent to eliminate the correlation coefficient meansigma methods of the forward and backward activation pixel of noise respectively.The correlation coefficient meansigma methods changed percentage ratio after Δ d% represented to eliminate noise.Cmean_B, Cmean_A represent to eliminate the mean square deviation of the forward and backward activation pixel of noise respectively, and Δ v% represents to eliminate the mean square deviation percentage ratio that activates pixel in the noise front and back and changes.
As seen from Table 2, after the method that adopts this paper to propose is eliminated the noise of noise functional MRI data, activate the time course of pixel and all consistent increase of maximum correlation coefficient, average correlation coefficient of reference function, activate all consistent the reducing of variance of picture point time process.Detected activation pixel quantity showed increased, the pseudo-pixel quantity that activates also obviously reduces.
Table 2 functional MRI data changes relatively with reference function correlation coefficient and variance before and after eliminating noise
| Num_B | dmax_B | dmax_A | dmean_B | dmean_A | Δd％ | Cmax_B | Cmax_A | Δv％ | Num_A | |
| Slice28 | 169 | 0.7046 | 0.7309 | 0.4090 | 0.5228 | 27.82％ | 4854.8 | 3179.5 | 52.69％ | 55 |
| Slice29 | 211 | 0.6907 | 0.7380 | 0.4342 | 0.5416 | 24.74％ | 6248.6 | 4206.3 | 48.55％ | 88 |
| Slice30 | 262 | 0.6715 | 0.7547 | 0.4261 | 0.6097 | 43.09％ | 5541.2 | 3110.6 | 43.8％ | 160 |
| Slice31 | 295 | 0.6867 | 0.7208 | 0.4168 | 0.5347 | 28.27％ | 4615.3 | 2184.6 | 111.3％ | 129 |
| Slice32 | 274 | 0.6475 | 0.7002 | 0.4007 | 0.5582 | 39.31％ | 3903.9 | 2420.7 | 73.40％ | 137 |
| Slice33 | 183 | 0.5705 | 0.6348 | 0.3628 | 0.4557 | 25.61％ | 2846.1 | 1583.1 | 79.78％ | 9 |
Fig. 6-1 adopts the auditory function of the from the 28th to the 33rd layer of continuous 6 tomographic image that correlational analysis method obtains to activate mapping graph after Fig. 6-6 has shown that respectively noise cancellation method that first employing proposes is handled experimental data then.From testing result as seen: the last temporal lobe of the brain left and right sides and ambitus cerebri's leaf show activation more significantly, and the active region testing result conforms to substantially with empirical auditory center functional anatomy zone; The language Gou Hui district of the brain left and right sides also shows a spot of activation signal, this is when adopting double-tone joint English word as auditory stimulus owing to this functional experiment, person under inspection's language understanding district function also has the cause of response, and this result further illustrates effectiveness and the reliability that this paper proposes to eliminate the noise method of functional MRI data.
Principle of the present invention:
The random noise decision criteria is: if the mean power of a certain composition fourier spectrum, thinks then that this composition is the random noise composition more than or equal to the standard deviation of spectrum power.
(Principal Component Analysis is a kind of signal decomposition technology based on second-order statistic PCA) to principal component analysis, its objective is with signal decomposition to be the composition of mutually orthogonal on some statistical significances (or uncorrelated).(Independent Component Analysis is a kind of based on a kind of signal decomposition technology of high-order statistic ICA) to independent component analysis, its objective is that with signal decomposition be composition separate on some statistical significances.Because principal component analysis can separate and eliminate random noise preferably, the independent component analysis can separate and eliminate physiological noise and various low-frequency noise preferably, therefore can carry out principal component analysis to functional MRI data earlier, utilize Fourier transform that each composition is carried out spectrum analysis, if the mean power of a certain composition fourier spectrum is more than or equal to the standard deviation of spectrum power, think that then this composition is the random noise composition, and with this composition zero setting, rebuild then and eliminate random noise composition functional MRI data, again the functional MRI data of eliminating random noise is carried out independent component analysis, to eliminate physiological noise and various low-frequency noise.
Suppose to adopt principal component analysis to eliminate after system's random noise, the function signal in the functional MRI data, physiological noise and various low-frequency noise are linear hybrid, and the functional MRI data model can further be expressed in matrix as:
Y＝AC (2)
Wherein, A represents unknown linear hybrid matrix, and C represents to comprise the matrix of function signal and various noise contributions.For function signal in the assessment function MR data and noise contribution, can seek a separation matrix W who satisfies (3):
C＝WY (3)
When separation matrix W is the inverse matrix of hybrid matrix A, function signal in the functional MRI data and noise contribution can be separated.Separation matrix W can adopt estimating based on information-theoretical quick fixed-point algorithm iteration of Hyv rinen proposition.
The key of utilizing the independent component analysis to eliminate various physiology correlated noises in the functional MRI data is various noise components how to determine that physiology is relevant.Under normal conditions, the cardiac pulse frequency of human body is 0.75～1.5Hz, and respiratory frequency is 0.1～0.5Hz.According to the Nayquist sampling thheorem, when the sample rate of functional MRI time series image is higher than 2 * 1.5Hz,, can determines heart and breathe relevant physiological noise composition by isolated composition is carried out spectrum analysis.But in order to cover between enough Naokongs, functional MRI often adopts Multi Slice Mode mode image data, and the sweeping repetition time, (TR) was usually more than or equal to 2000ms.Like this, the sample rate of each layer time series image is less than or equal to 0.5Hz, be lower than the Human Physiology motion frequency, cause the high frequency physiological noise to be aliased into low-frequency component, physiological noise no longer keeps original waveform, can't determine physiological noise composition in the multilamellar functional MRI data based on frequency spectrum analysis method.
Noise in the functional MRI data mainly is to be caused with the physiological effect of breathing relevant non-neuropathic by heart.Though the physiological effect of the non-neuropathic that periodic cardiac pulse and breathing cause is to different brain regional effect differences, cerebral gray matter zone and cerebrospinal fluid zone are influenced by the heart in cycle and respiratory noise simultaneously.Owing to can not have the function signal that is associated with the cerebral cortex neural activity to change in the cerebrospinal fluid data, can think that the signal in the cerebrospinal fluid only comprises physiology relevant noise, various low-frequency noise and system's random noise.
Therefore, we can be based on physiological noise composition time course in the cerebral gray matter zone and the spatial coherence in cerebrospinal fluid zone, by physiological noise composition in physiological noise Composition Estimation in the cerebrospinal fluid data and the definite grey matter data, finally eliminate the physiological noise of multilamellar functional MRI data.
Therefore, adopt the principal component analysis method to eliminate random noise in grey matter data, the cerebrospinal fluid data respectively after, the time course y of each pixel of cerebrospinal fluid zone
c(t) can represent with (4):
y
c(t)＝p(t) (t＝1，2，Λ，N) (4)
The time course y of each pixel of grey matter zone
g(t) can represent with (5):
y
g(t)＝s(t)+p(t) (t＝1，2，Λ，N) (5)
The grey matter data Y that adopts the independent component analytical method respectively (4), (5) to be represented
g, the cerebrospinal fluid data Y
cCarrying out independent component decomposes.Suppose to comprise in the grey matter data m statistics and go up separate composition c
i g(t), comprise n statistics in the cerebrospinal fluid data and go up separate composition c
j c(t).In order to determine the relevant noise contribution of physiology in the grey matter data, we utilize m independent component c of grey matter data
i g(t) structural matrix X
M * N, utilize n independent component c of cerebrospinal fluid data
j c(t) structural matrix Y
M * NBy to matrix X
M * NAnd Y
M * NCarry out canonical correlation analysis, can obtain c
i g(t) weighting coefficient matrix A
M * rAnd c
j c(t) weighting coefficient matrix B
N * rAnd the row that comprises r element is vectorial
R=min (m, n).
K element be matrix X
M * NAnd Y
M * NEach the row respectively with matrix A
M * rAnd B
N * rThe k column element be the weight coefficient canonical correlation coefficient that is weighted back gained canonical variable square.Obviously, canonical correlation coefficient square big more, each composition c in the cerebrospinal fluid
i g(t) with grey matter in each composition c
j c(t) dependency is big more; Composition c in the grey matter
i g(t) weight coefficient is big more, composition c in this composition and the cerebrospinal fluid
j c(t) dependency is also big more.Therefore, can be by calculating the row vector
Each element to matrix A
M * rThe weighted sum of each row element obtains expressing each independent component c in the grey matter data
i g(t) with the cerebrospinal fluid data in each independent component c
j c(t) column vector of correlated measure
To column vector
Each element sort from big to small, so, the column vector after the ordering
The independent element c of preceding r element correspondence
i g(t) be with the cerebrospinal fluid data in each independent component c
j c(t) relevant maximum noise contribution with these composition zero setting, just can be eliminated relevant maximum various noise components with various noise components in the cerebrospinal fluid data in the grey matter data.Real functional MRI data result of the test has been proved that this method is effectively.
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