CN109498017A - A kind of constant CPD method of quickly shifting suitable for more being tested the analysis of fMRI data - Google Patents

A kind of constant CPD method of quickly shifting suitable for more being tested the analysis of fMRI data Download PDF

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CN109498017A
CN109498017A CN201811510882.0A CN201811510882A CN109498017A CN 109498017 A CN109498017 A CN 109498017A CN 201811510882 A CN201811510882 A CN 201811510882A CN 109498017 A CN109498017 A CN 109498017A
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邝利丹
林秋华
龚晓峰
丛丰裕
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Abstract

A kind of constant CPD method of quickly shifting suitable for more being tested the analysis of fMRI data, belongs to medical signals process field.On the basis of moving constant CPD algorithm, using alternating least-squares to the shared SM ingredient of subject, shared TC ingredient and each subject intensity more new estimation；In the case where not influencing time delay estimation performance, by the high shared SM ingredient of dimension and original more subject fMRI data data low with dimension is converted by matrix multiple, to accelerate algorithm arithmetic speed and reduce operation memory.Memory needed for the present invention is substantially reduced, and the task Related Component that fMRI data quickly and efficiently can more be tested to task state is estimated.

Description

A kind of constant CPD method of quickly shifting suitable for more being tested the analysis of fMRI data
Technical field
The present invention relates to medical signals process fields, are tested functional mri fMRI more particularly to one kind more The analysis method of (functional magnetic resonance imaging) data.
Background technique
It is scanned using brain of the magnetic resonance scanner to multiple subjects, the brain function data of acquisition are known as more subjects FMRI data.Advantages, become current brain science research one are important greatly by its not damaged and spatial resolution is high etc. by fMRI Technology.More subject fMRI data are generally regarded as to be tieed up as a three-dimensional tensor, including space dimension, time dimension and subject, can be used Tensor resolution algorithm is handled.CPD (canonical polyadic decomposition) is a kind of typical tensor resolution Algorithm.More subject fMRI data are decomposed between each subject and share by CPD explicit physical meaning in mostly subject fMRI data analysis Brain spatial activation ingredient (spatial map, SM) and shared time course ingredient (time course, TC), and be respectively tested Strength difference information.These information can provide important evidence for brain function research and cerebral disease diagnosis.
Otherness when more subject fMRI data are inevitably present empty between subject.Wherein time difference opposite sex problem is main Be due to each subject response time and Hemodynamics time delay in terms of have differences caused by.For this problem,Et al. Article in 2008 "M.,Hansen,L.K.,Arnfred,S.M.,Lim,L.H.,Madsen,K.H.,Shift- invariant multilinear decomposition of neuroimaging data.NeuroImage 42,2018, A kind of constant CPD algorithm of shifting is proposed in 1439-1450. ", be joined subject TC time delay estimation in without constraint CPD model, is held Perhaps it is tested TC delay variation, separating property is better than without constraint CPD algorithm.
In recent years, the research of much more large-scale subject fMRI data (subject number from tens to up to ten thousand) was increasingly by people Concern, and the space dimensionality of fMRI data is usually very high, such as a intracerebral voxel more than 50,000, therefore calculates when moving constant CPD When method is applied to more subject fMRI data, it there is a problem that the speed of service is slow and memory requirements is high, especially in subject time delay Update estimation procedure in, the data volume for needing to store is bigger.
Summary of the invention
The constant CPD method of quickly shifting that the present invention provides a kind of suitable for being tested fMRI data more, by matrix multiple and Transformation allows subject time delay estimating speed to become faster, running memory reduction, and performance will not decline.
On the basis of moving constant CPD algorithm, using alternating least-squares to the shared SM ingredient of subject, shared TC ingredient With each subject intensity more new estimation；In the case where not influencing time delay estimation performance, by the high shared SM ingredient of dimension and original More subject fMRI data data low with dimension is converted by matrix multiple, to accelerate algorithm arithmetic speed and reduce fortune Calculate memory.
Steps are as follows for technical solution of the present invention:
Step 1: input is tested fMRI dataWherein I indicates that intracerebral voxel number is (empty Between tie up), J indicate scanning times (time dimension), K indicate subject number.
Step 2: initialization.Being set as point number is D (D is positive integer and 0 < D≤J).Random initializtion shares SM ingredientShared TC ingredient With subject intensityInitialization subject time delay For zero moment Battle array.Enable the number of iterations iter=0, relative error Δ εiter=1, calculate iteration error εiter:
Wherein, bd(j-τk,d) indicate to bj,dTime shift τk,d(for integer) a point, τk,dFor kth d-th of ingredient of subject Time delay.If τk,d> 0, kth is tested d-th of TC ingredientRelatively shared TC ingredient bdRing shift left τk,dIt is a, if τk,d< 0, then ring shift right | τk,d| a point.Formula (1) is also to move constant CPD algorithm model.
Step 3: updating shared TC ingredient B.Using article "M.,Hansen,L.K.,Arnfred,S.M., Lim,L.H.,Madsen,K.H.Shift-invariant multilinear decomposition of neuroimaging The update method (alternating least-squares) of TC ingredient B is shared in data.NeuroImage 42,2018,1439-1450. " to B It is updated.
Step 4: to shared SM ingredient A andXCarry out dimensionality reduction.Following operation is carried out to A:
WhereinSince D (generally less than 100) is generally much smaller than I (general 5 × 105), therefore use dimension LowThe high A (D × I) of dimension is substituted, to accelerate the estimation for being tested time delay, and reduces calculating memory.Into One step enables
WhereinForX1 mould expanded form, willTensor turns to Its dimension also much smaller thanX。
Step 5: updating subject time delayIt willIt is unfolded by 3 moulds, obtains matrixUsing article "M.,Hansen,L.K.,Arnfred,S.M.,Lim,L.H.,Madsen,K.H.Shift-invariant Quilt in multilinear decomposition of neuroimaging data.NeuroImage 42,1439-1450. " Delay time estimation method is tried, and in the 4th stepWithReplace the A and X in article(3)(ForX3 mould exhibitions Open form formula), realize subject time delayQuick estimation.
Step 6: updating shared SM ingredient A.Using article "M.,Hansen,L.K.,Arnfred,S.M., Lim,L.H.,Madsen,K.H.Shift-invariant multilinear decomposition of neuroimaging The method that A is updated in data.NeuroImage 42,2018,1439-1450. " updates A.
Step 7: updating subject intensity C.Using article "M.,Hansen,L.K.,Arnfred,S.M.,Lim, L.H.,Madsen,K.H.Shift-invariant multilinear decomposition of neuroimaging The method that C is updated in data.NeuroImage 42,2018,1439-1450. " updates C.
Step 8: calculating error.Enable iter=iter+1；According to formula (1), current iteration error ε is calculatediter, Yi Jixiang To error delta epsiloniter:
Δεiter=| (εiter-1-εiter)/εiter-1|。 (4)
Step 9: if εiterLess than default error threshold εiter_min, the 12nd step is jumped to, the tenth step is otherwise executed.
Step 10: if Δ εiterLess than default relative error threshold value Δ εiter_min, the 12nd step is jumped to, otherwise executes 11 steps.
Step 11: if iter is greater than default maximum number of iterations itermax, the 12nd step is jumped to, third is otherwise executed Step.
Step 12: exporting shared SM ingredient A, shared TC ingredient B, subject time delayWith subject intensity C.
Present invention effect achieved and benefit are can be quickly and efficiently tested fMRI data to task state to appoint more Business Related Component is estimated.In the fMRI data analysis for tapping finger task to 10 subjects, the feelings of identical initial value are set Under condition, the required convergence number of the present invention is identical with moving constant CPD algorithm, but the speed of service needed for iteration fastly about 9.33 every time Times, and be tested time delay and estimate that required memory is approximately move constant CPD algorithm 2/25.The present invention and the constant CPD algorithm estimation of shifting Shared task Related Component and priori reference signal the ratio between related coefficient mean value about 1, separating property is similar.Therefore, originally Invention can quickly and efficiently extract the shared brain function information of more subjects, and future can be with independent component analysis and rarefaction representation The methods of combine, improve separating property, extensive fMRI data research from now on and in terms of also have it is good Development prospect.
Detailed description of the invention
Fig. 1 is the work flow diagram of the more subject fMRI data of present invention analysis.
Specific embodiment
Below with reference to technical solution and attached drawing, a specific embodiment of the invention is described in detail.
Existing 10 subject executes the fMRI data for tapping and acquiring under finger task, i.e. K=10.Each subject has carried out J =165 scanning, 53 × 63 × 46 full brain data of each scanning collection remove the outer data voxel of brain, retain intracerebral data Voxel I=59610.Assuming that the ingredient number D=30 of shared SM and TC ingredient, carries out more subject fMRI data point using the present invention The step of analysis, is as shown in the picture.
Step 1: input is tested fMRI data
Step 2: initialization.Random initializtion shares TC ingredientShared SM ingredient It is tested intensityInitialization subject time delayFor null matrix, the number of iterations iter=0, relative error Δ εiter=1, iteration error ε is calculated according to formula (1)iter。
Step 3: updating shared TC ingredient B.Using article "M.,Hansen,L.K.,Arnfred,S.M., Lim,L.H.,Madsen,K.H.Shift-invariant multilinear decomposition of neuroimaging The update method (alternating least-squares) of TC ingredient B is shared in data.NeuroImage 42,2018,1439-1450. " to B It updates, wherein B is enabled to be transformed into the frequency point number F=J of frequency domain form.
Step 4: to shared SM ingredient A andXCarry out dimensionality reduction.According to formula (2) and formula (3), by A andXDimensionality reduction atWithTo accelerate the subject time delay estimation of the 5th step, and reduce calculating memory.
Step 5: updating subject time delayUsing article "M.,Hansen,L.K.,Arnfred,S.M., Lim,L.H.,Madsen,K.H.Shift-invariant multilinear decomposition of neuroimaging Delay time estimation method is tested in data.NeuroImage 42,1439-1450. ", and will be in the 4th stepWithReplace A andX, realize subject time delayQuick estimation.
Step 6: updating shared SM ingredient A.Using article "M.,Hansen,L.K.,Arnfred,S.M., Lim,L.H.,Madsen,K.H.Shift-invariant multilinear decomposition of neuroimaging The method that A is updated in data.NeuroImage 42,2018,1439-1450. " updates A.
Step 7: updating subject intensity C.Using article "M.,Hansen,L.K.,Arnfred,S.M.,Lim, L.H.,Madsen,K.H.Shift-invariant multilinear decomposition of neuroimaging The method that C is updated in data.NeuroImage 42,2018,1439-1450. " updates C.
Step 8: calculating error.Iter=iter+1 is enabled, according to formula (1) and formula (4), calculates separately current iteration error εiterWith relative error Δ εiter。
Step 9: default error threshold εiter_min=10-4.If εiter<εiter_min, the 12nd step is jumped to, is otherwise executed Tenth step.
Step 10: default relative error threshold value Δ εiter_min=10-6.If Δ εiter<Δεiter_min, jump to the 12nd Otherwise step executes the 11st step.
Step 11: default maximum number of iterations itermax=500.If iter > itermax, the 12nd step is jumped to, it is no Then execute third step.
Step 12: exporting shared SM ingredient A, shared TC ingredient B, subject time delayWith subject intensity C.

Claims (1)

1. a kind of constant CPD method of quickly shifting suitable for more being tested fMRI data, feature the following steps are included:
Step 1: input is tested fMRI dataWherein I indicates intracerebral voxel number, and J expression is swept Number is retouched, K indicates subject number；
Step 2: initialization: being set as point number is D, and D is positive integer and 0 < D≤J；Random initializtion shares SM ingredientShared TC ingredientIt is strong with subject DegreeInitialization subject time delayIt is zero Matrix；Enable the number of iterations iter=0, relative error Δ εiter=1, calculate iteration error εiter:
Wherein, bd(j-τk,d) indicate to bj,dTime shift τk,d(for integer) a point, τk,dThe time delay of d-th of ingredient is tested for kth. If τk,d> 0, kth is tested d-th of TC ingredientRelatively shared TC ingredient bdIt follows Ring moves to left τk,dIt is a, if τk,d< 0, then ring shift right | τk,d| a point；Formula (1) is also to move constant CPD method model；
Step 3: updating shared TC ingredient B；
Step 4: to shared SM ingredient A andXCarry out dimensionality reduction；Following operation is carried out to A:
WhereinIt is low with dimension since D is less than IThe high A (D × I) of dimension is substituted, to accelerate It is tested the estimation of time delay, and reduces calculating memory；Further enable
WhereinForX1 mould expanded form, willTensor turns toIts Dimension also much smaller thanX；
Step 5: updating subject time delayIt willIt is unfolded by 3 moulds, obtains matrixWith in the 4th step WithA and X in replacement subject time delay estimation(3), realize subject time delayQuick estimation, whereinForX 3 mould expanded forms；
Step 6: updating shared SM ingredient A；
Step 7: updating subject intensity C；
Step 8: calculating error: enabling iter=iter+1；According to formula (1), current iteration error ε is calculatediterAnd relative error Δεiter:
Δεiter=| (εiter-1-εiter)/εiter-1|； (4)
Step 9: if εiterLess than default error threshold εiter_min, the 12nd step is jumped to, the tenth step is otherwise executed；
Step 10: if Δ εiterLess than default relative error threshold value Δ εiter_min, the 12nd step is jumped to, otherwise executes the 11st Step；
Step 11: if iter is greater than default maximum number of iterations itermax, the 12nd step is jumped to, third step is otherwise executed；
Step 12: exporting shared SM ingredient A, shared TC ingredient B, subject time delayWith subject intensity C.
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