阅读说明：本技术 一种基于贝叶斯的儿童脑活动异常病灶区成像系统 (Bayes-based imaging system for focal zone with abnormal brain activity of children ) 是由 蔡畅 陈靓影 杨宗凯 徐如意 于 2020-12-24 设计创作，主要内容包括：本发明公开了一种基于贝叶斯的儿童脑活动异常病灶区成像系统。该系统包括：信号处理模块,用于获取脑电磁采样数据,对电磁采样数据进行预处理；脑活动异常识别模块,用于从预处理后的脑电磁采样数据中识别出异常波和非异常波；噪声估计模块,用于从非异常波中估计背景干扰噪声；脑源活动重构模块,用于结合异常波与估计的背景干扰噪声,采用贝叶斯估计方法获取脑异常活动病灶区位置及其病灶区脑源活动时间序列；成像模块,用于根据脑源活动进行成像。本发明可以极大地提高病灶区定位和重构的精准性,特别适用于自闭症儿童的儿童脑电活动异常病灶区成像。(The invention discloses a Bayes-based imaging system for a focal zone with abnormal brain activity of children. The system comprises: the signal processing module is used for acquiring electroencephalogram magnetic sampling data and preprocessing the electromagnetic sampling data; the brain activity abnormity identification module is used for identifying abnormal waves and non-abnormal waves from the preprocessed electroencephalogram and magnetic sampling data; a noise estimation module for estimating background interference noise from the non-abnormal waves; the brain source activity reconstruction module is used for combining the abnormal wave and the estimated background interference noise and acquiring the focal region position of the brain abnormal activity and the brain source activity time sequence of the focal region by adopting a Bayesian estimation method; and the imaging module is used for imaging according to the brain source activity. The method can greatly improve the accuracy of localization and reconstruction of the focal zone, and is particularly suitable for imaging the focal zone with abnormal brain electrical activity of children with autism.)

1. A Bayesian-based imaging system for a focal zone of abnormal brain activity in a child, comprising:

the signal processing module is used for acquiring electroencephalogram sampling data and preprocessing the electroencephalogram sampling data;

the brain activity abnormity identification module is used for identifying abnormal waves and non-abnormal waves from the preprocessed electroencephalogram and magnetic sampling data;

the noise estimation module is used for constructing a first sampling data generation model of the non-abnormal wave, solving the first sampling data generation model by adopting a variational Bayesian method and acquiring the distribution information of background interference noise of data acquisition;

the brain electrical source activity reconstruction module is used for constructing a second sampling data generation model of the abnormal wave, the distribution information of the background interference noise is a parameter in the second sampling data generation model, and the second sampling data generation model is solved by adopting an empirical Bayesian method to obtain a brain electrical source activity time sequence;

and the imaging module is used for imaging according to the brain electrical source activity time sequence.

2. The bayesian-based imaging system of a focal zone of brain activity abnormality of a child according to claim 1, wherein said signal processing module comprises:

the sampling offset removing module is used for removing sampling offset in the electroencephalogram magnetic sampling data;

the interference removing module is used for removing noise of the signal from which the sampling offset is removed by adopting an independent component analysis method and a space projection method;

and the filtering module is used for filtering the signal subjected to denoising processing.

3. The bayesian-based imaging system for a focal zone of brain activity abnormality in a child according to claim 1, wherein said first sampled data generating model is:

Y_conFU + E, wherein Y_conNon-abnormal waves, F is an unknown M x K weighting matrix, and U is an unknown K x t_KFactor parameter of, t_KIs the number of samples in the non-anomalous wave, U ═ U₁,u₂,...,u_K]^TE is a residual signal after the decomposition of the non-abnormal wave, M is the number of channels of the acquisition point, and K is less than M.

4. The bayesian-based imaging system for a focal zone of abnormal brain activity in a child according to claim 3, wherein said solving the first sampled data generating model using the variational bayesian method comprises the steps of:

let the prior distribution of the factor parameter U be a standard gaussian distribution:

the distribution of the background interference noise E for data acquisition is:

wherein Λ ═ diag (λ)₁,λ₂,...,λ_M) Is a diagonal matrix, Λ is the prior variance of E,

the weighting matrix F is set to gaussian:

wherein, F_m,kAs a value in the weighting matrix F, alpha_kThe prior variance of the weighting matrix F is more than or equal to 1 and less than or equal to K, the first sampling data generation model is evolved based on variational Bayesian estimation, and the updating mode of the weighting matrix F and the factor parameter U is as follows:

Ψ＝R_uu+α

wherein R is_yyFor the covariance matrix of the sampled data, R_uuTo estimate the factor covariance matrix, R_uyFor multiplying the estimation factor by the sample data, α ═ diag (α)₁,α₂...,α_k)；

Performing iterative cycle according to the updating mode of the weighting matrix F and the factor parameter U until the values of the weighting matrix F and the factor parameter U are not changed any more, and acquiring a reduced-dimension and background interference noise covariance matrix sigma according to the values of the weighting matrix F and the factor parameter U at the moment_EComprises the following steps:

5. the bayesian-based imaging system for a focal zone of brain activity abnormality in a child according to claim 1, wherein said second sampled data generating model is:

Y_act＝LS+ε，

wherein, Y_actIs an abnormal wave, Y_act＝[y(t₁),y(t₂),...,y(t_K)]，t_KIs the number of sampling points of the abnormal wave,obtaining the extracerebral sampling intensity generated by known unit source activity, wherein N is the number of sources to be solved, S is the time sequence of the electroencephalogram source activity, epsilon is background interference noise, and the extracerebral sampling intensity generated by the unit source activity at the position N is L_n＝[l₁,l₂,...,l_M]N is less than N, M is the channel number of the acquisition point, M is less than N, and S is [ S ═ S [₁,S₂,...,S_N]^T。

6. The bayesian-based imaging system for a focal zone of abnormal brain activity in a child according to claim 5, wherein said solving the second sampled data generating model using an empirical bayesian approach comprises the steps of:

setting the brain electrical source activity time sequence S to be mutually independent in space and time and obey Gaussian distribution, and converting the second sampling data generation model into a second sampling data probability generation model by adopting an empirical Bayes method;

and constructing a cost function based on the convex function plane boundary, and solving the second sampling data probability generation model by optimizing the cost function.

7. The Bayesian-based imaging system for brain activity abnormality focal zone of children as recited in claim 6, wherein said second sampled data probabilistic generative model is:

the brain electrical activity time series S are spatially and temporally independent of each other and obey a gaussian distribution:

being the variance of the prior gaussian distribution for position n, the conditional probability distribution p (Y | S) is,

Σ_Ethe covariance matrix of the background interference noise acquired by the noise estimation module is obtained based on an empirical Bayesian model:

posterior probability distribution p (S | Y)_act) Comprises the following steps:

Γ^-1in order to be a hyper-parameter, and Γ^-1The posterior probability mean and variance of the source activity are sampled at time t, respectively.

8. A Bayesian-based imaging system of focal zones of abnormal brain activity in children as recited in claim 7,

hyper-parameter gamma^-1By maximizing the edge distribution p (Y)_act| γ), edge distribution logarithmic model logp (Y)_actγ) is:

is an abnormal wave covariance matrix model,is the n-th source activity pointConstruction based on gamma^-1Log | Σ of_yThe | boundary function is such that,

tr (×) is the trace of the computation matrix;

the cost function based on the convex function plane boundary is:

Λ_nand Λ₀Is an auxiliary variable;

the posterior distribution p (S | Y) can be obtained from the probability generation model of the second sampling data_act) The mean and variance of (a) are as follows:

for cost functionSolving for the over parameter gamma_nAnd auxiliary parameter Λ_nThe reciprocal, one can obtain:

make itIs zero, over-parameter gamma_nAnd auxiliary parameter Λ_nThe formula of (1) is as follows:

by iteration of loopsΓ^-1And gamma_nUntil the edge distribution logarithm model converges, at which timeI.e. to solve the brain power activity time series.

9. The bayesian-based imaging system of a focal zone of abnormal brain activity in a child according to claim 1, wherein said identifying of said abnormal waves and said non-abnormal waves comprises the steps of:

identifying a first candidate abnormal wave according to the amplitude of the preprocessed electromagnetic sampling signal;

and reading the standard abnormal wave stored in advance, matching the local part of the first candidate abnormal wave with the standard abnormal wave, and identifying the abnormal wave according to the matching result.

10. The bayesian-based imaging system of a focal zone of abnormal brain activity in a child according to claim 1, wherein said imaging based on a time series of brain electrical source activity comprises the steps of:

and obtaining pre-stored model parameters, and imaging according to the model parameters and the electroencephalogram source activity time sequence.

Technical Field

The invention belongs to the technical field of reconstruction of brain focal areas of autistic children, and particularly relates to a Bayes-based imaging system for brain activity abnormal focal areas of children.

Background

The brain is the most important part of the central nervous system and controls higher thinking of people, such as cognition, learning, social interaction and the like, and the cognitive learning process and brain function disorder brain operation mechanism of autistic children need to be clarified firstly in the education and brain function disorder intervention treatment of autistic children. Electroencephalogram source imaging is an important means for exploring brain activity mechanism, understanding various thinking and sensing dynamic change process of brain activity, and has important significance for disclosing the brain operation mechanism of autistic children.

The brain electrical source imaging inverse problem is a process of inverting neuron activity information in the brain by sampling brain electromagnetic data, and is the core of brain electrical source imaging. In recent years, the technology can be used for cognitive learning of autistic children and study of dysfunction electroencephalogram source imaging technology at home and abroad, but the existing brain source imaging technology is mostly based on a minimum norm method, the degree of freedom is limited, and the characteristics of high complexity and high resolution requirement of human brain source activities lead to low cognitive learning and dysfunction electroencephalogram source imaging accuracy of autistic children. How to realize the automatic identification of the electroencephalogram and magnetic anomaly sampling data, and how to quickly and accurately reconstruct the brain focus area activities and the positions of the brain focus area activities of the autistic children are still a challenge subject.

Disclosure of Invention

Aiming at least one defect or improvement requirement in the prior art, the invention provides a Bayes-based imaging system for the brain activity abnormal focal zone of the child, which can greatly improve the accuracy of localization and reconstruction of the focal zone and is particularly suitable for imaging the brain activity abnormal focal zone of the child with the autism.

In order to achieve the above object, the present invention provides a bayesian-based imaging system for a focal zone of abnormal brain activity of a child, comprising:

the signal processing module is used for acquiring electroencephalogram sampling data and preprocessing the electroencephalogram sampling data;

the brain activity abnormity identification module is used for identifying abnormal waves and non-abnormal waves from the preprocessed electroencephalogram and magnetic sampling data;

the noise estimation module is used for constructing a first sampling data generation model of the non-abnormal wave, solving the first sampling data generation model by adopting a variational Bayesian method and acquiring the distribution information of background interference noise of data acquisition;

the brain electrical source activity reconstruction module is used for constructing a second sampling data generation model of the abnormal wave, the distribution information of the background interference noise is a parameter in the second sampling data generation model, and the second sampling data generation model is solved by adopting an empirical Bayesian method to obtain a brain electrical source activity time sequence;

and the imaging module is used for imaging according to the brain electrical source activity time sequence.

Preferably, the signal processing module includes:

the sampling offset removing module is used for removing sampling offset in the electroencephalogram magnetic sampling data;

the interference removing module is used for removing noise of the signal from which the sampling offset is removed by adopting an independent component analysis method and a space projection method;

and the filtering module is used for filtering the signal subjected to denoising processing.

Preferably, the first sampling data generation model is:

Y_conFU + E, wherein Y_conNon-abnormal waves, F is an unknown M x K weighting matrix, and U is an unknown K x t_KFactor parameter of, t_KIs the number of samples in the non-anomalous wave, U ═ U₁,u₂,...,u_K]^TE is a residual signal after the decomposition of the non-abnormal wave, M is the number of channels of the acquisition point, and K is less than M.

Preferably, the solving of the first sampling data generation model by using the variational bayes method includes the steps of:

let the prior distribution of the factor parameter U be a standard gaussian distribution:

the distribution of the background interference noise E for data acquisition is:

wherein Λ ═ diag (λ)₁,λ₂,...,λ_M) Is a diagonal matrix, Λ is the prior variance of E,

the weighting matrix F is set to gaussian:

wherein, F_m,kAs a value in the weighting matrix F, alpha_kThe prior variance of the weighting matrix F is more than or equal to 1 and less than or equal to K, the first sampling data generation model is evolved based on variational Bayesian estimation, and the updating mode of the weighting matrix F and the factor parameter U is as follows:

Ψ＝R_uu+α

wherein R is_yyFor the covariance matrix of the sampled data, R_uuTo estimate the factor covariance matrix, R_uyFor multiplying the estimation factor by the sample data, α ═ diag (α)₁,α₂...,α_k)；

Performing iterative cycle according to the updating mode of the weighting matrix F and the factor parameter U until the values of the weighting matrix F and the factor parameter U are not changed any more, and acquiring the co-operation of the reduced dimension and the background interference noise according to the values of the weighting matrix F and the factor parameter U at the momentVariance matrix Σ_EComprises the following steps:

preferably, the second sampling data generation model is:

Y_act＝LS+ε，

wherein, Y_actIs an abnormal wave, Y_act＝[y(t₁),y(t₂),...,y(t_K)]，t_KIs the number of sampling points of the abnormal wave,obtaining the extracerebral sampling intensity generated by known unit source activity, wherein N is the number of sources to be solved, S is the time sequence of the electroencephalogram source activity, epsilon is background interference noise, and the extracerebral sampling intensity generated by the unit source activity at the position N is L_n＝[l₁,l₂,...,l_M]N is less than N, M is the channel number of the acquisition point, M is less than N, and S is [ S ═ S [₁,S₂,...,S_N]^T。

Preferably, the solving of the second sampling data generation model by using the empirical bayesian method includes the steps of:

setting the brain electrical source activity time sequence S to be mutually independent in space and time and obey Gaussian distribution, and converting the second sampling data generation model into a second sampling data probability generation model by adopting an empirical Bayes method;

and constructing a cost function based on the convex function plane boundary, and solving the second sampling data probability generation model by optimizing the cost function.

Preferably, the probability generation model of the second sampled data is:

the brain electrical activity time series S are spatially and temporally independent of each other and obey a gaussian distribution:

being the variance of the prior gaussian distribution for position n, the conditional probability distribution p (Y | S) is,

Σ_Ethe covariance matrix of the background interference noise acquired by the noise estimation module is obtained based on an empirical Bayesian model:

posterior probability distribution p (S | Y)_act) Comprises the following steps:

Γ^-1in order to be a hyper-parameter,and Γ^-1The posterior probability mean and variance of the source activity are sampled at time t, respectively.

Preferably, the hyperparameter Γ^-1By maximizing the edge distribution p (Y)_act| γ), edge distribution logarithmic model logp (Y)_actγ) is:

is an abnormal wave covariance matrix model,is the n-th source activity pointConstruction based on gamma^-1Log | Σ of_yThe | boundary function is such that,

tr (×) is the trace of the computation matrix;

the cost function based on the convex function plane boundary is:

Λ_nand Λ₀Is an auxiliary variable;

the posterior distribution p (S | Y) can be obtained from the probability generation model of the second sampling data_act) The mean and variance of (a) are as follows:

for cost functionSolving for the over parameter gamma_nAnd auxiliary parameter Λ_nThe reciprocal, one can obtain:

make itIs zero, over-parameter gamma_nAnd auxiliary parameter Λ_nThe formula of (1) is as follows:

by iteration of loopsΓ^-1And gamma_nUntil the edge distribution logarithm model converges, at which timeI.e. to solve the brain power activity time series.

Preferably, the identifying of the abnormal wave and the non-abnormal wave comprises the steps of:

identifying a first candidate abnormal wave according to the amplitude of the preprocessed electromagnetic sampling signal;

and reading the standard abnormal wave stored in advance, matching the local part of the first candidate abnormal wave with the standard abnormal wave, and identifying the abnormal wave according to the matching result.

Preferably, the imaging according to the brain electrical source activity time sequence comprises the following steps:

and obtaining pre-stored model parameters, and imaging according to the model parameters and the electroencephalogram source activity time sequence.

In general, compared with the prior art, the invention has the following beneficial effects: the brain activity background interference noise extraction method based on variational Bayes is adopted in the imaging system of the lesion areas with abnormal brain activity of the children, and the lesion areas with abnormal brain activity of the children are reconstructed and positioned based on the empirical Bayes model by combining with the sampled abnormal brain electromagnetic data. Is particularly suitable for imaging focal zones of autistic children with abnormal brain activities.

Drawings

FIG. 1 is a schematic block diagram of an imaging system according to an embodiment of the invention;

fig. 2 is a functional diagram of an imaging system according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

As shown in fig. 1, the bayesian-based imaging system for a focal zone of abnormal brain activity of a child according to an embodiment of the present invention includes a signal acquisition and processing module, a brain activity abnormality recognition module, a noise estimation module, an electroencephalogram source activity reconstruction module, and an imaging module. The system can be applied to various scenes for identifying diseases through imaging of the focal region with the abnormal brain electromagnetic activity, and is particularly suitable for the infantile autism.

And the signal processing module is used for acquiring the electromagnetic sampling data and preprocessing the electromagnetic sampling data.

A preferred implementation of the signal processing module is described below.

Signal acquisition:

inputting brain electromagnetic sampling data, Y_raw＝[y_raw(1),y_raw(2),...,y_raw(T)]T is the number of original signal sampling points, y_raw(t)＝[y₁(t),y₂(t),…,y_M(t)]^TWhere M is the number of channels of acquisition points and T represents the transpose matrix. The input data needs to be preliminarily screened to ensure the validity of the sampled dataAnd integrity, such as data format conversion and parameter validation, including sampled data information.

Signal preprocessing:

the signal acquisition processing module comprises a sampling offset removing module, an interference removing module and a filtering module, and is used for preprocessing input data, including preprocessing such as sampling offset removing, drying removing and filtering.

The formula for removing the sampling offset is as follows:

the interference removal needs to be performed based on the sampled data characteristics.

Preferably, based on Independent Component Analysis (ICA) or spatial projection, such as interference elimination based on ICA (including electro-oculogram), the following formula is:

wherein A ═ a₁,a₂,...,a_N]To decompose the weighting matrix, X ═ X₁,x₂,...,x_N]^TIs an independent component, let x_mContaining significant interference or noise, the de-dried sampled data Y_newThe following were used:

preferably, the signal after the ICA-based interference removal processing is further processed by using a projection-based interference removal method. The interference elimination method based on projection needs to find out a projection matrix, which can be based on features such as brain structure space information, etc., assuming that the projection matrix is W, the interference elimination formula is:

Y_clean＝W^TY_new (4)

filtering, namely filtering the sampled data to remove the sampled data of the non-brain activity frequency band, mainly applying time-frequency filtering based on Fourier or wavelet transform and reserving the interested frequency band data. The accuracy of subsequent abnormal recognition is guaranteed through the preprocessed data.

And the brain activity abnormity identification module is used for identifying abnormal waves and non-abnormal waves from the preprocessed electroencephalogram and magnetic sampling data.

Preferably, brain activity abnormalities are identified based on the amplitude and local waveform of the sampled brain electrical data.

Primarily selecting according to the amplitude: carrying out statistical analysis on the amplitude of the sampled electroencephalogram data, and setting a threshold value to screen potential abnormal sampling waveforms; the threshold is set to be roughly selected, and preferably, a plurality of sampling data segments are satisfied as a first candidate abnormal wave to enter the identification of the next stage.

And (3) waveform matching, namely further selecting the primarily selected segments, matching the primarily selected waveforms based on abnormal wave forms pre-stored in a waveform library, realizing window size switching by adjusting sampling frequency, and further selecting abnormal waves between 200ms and 100ms for identification. In one embodiment, the brain activity sample data with a matching degree greater than 80% is preferably used as the threshold of abnormal activity. The step is used for marking the sampling abnormal wave at the same time, and marking the non-abnormal wave with the same time scale before the abnormal wave appears secondarily as the input of the noise estimation module.

A noise estimation module: the method comprises the steps of constructing a first sampling data generation model of the non-abnormal wave, solving the first sampling data generation model by adopting a variational Bayes method, and acquiring background interference noise of data acquisition, namely estimating background interference noise statistical distribution information by adopting a variational Bayes-based method to analyze the non-abnormal electroencephalogram.

Non-anomalous waves are also called stationary waves. Probability distribution information is solved by carrying out variational Bayesian estimation on the stationary wave to be used as a covariance matrix of background interference noise. The specific process is as follows, assuming that the non-abnormal wave is Y_conVariational bayesian factor analysis assumes that the sample data is represented as:

Y_con＝FU+E (5)

where F is an unknown M K weighting matrix, and U is [ U ]₁,u₂,...,u_K]^TIs unknown Kxt_KFactor parameter of, t_KAnd setting K < M for the number of sampling points in the non-abnormal wave, namely K is a preset arbitrary positive integer less than M, and E is a residual signal after the decomposition of the non-abnormal wave. The prior distribution of the factor parameters is set as the standard gaussian distribution as follows:

while the distribution of sensor noise is as follows:

Λ＝diag(λ₁,λ₂,...,λ_M) Is a diagonal matrix, λ_mIs the variance of the mth channel E, and Λ is the prior variance of E. The weighting matrix also satisfies the following gaussian distribution:

α_kk is more than or equal to 1 and less than or equal to K and is the prior variance of the weighting matrix F.

The update rule of unknown parameters based on variational bayes estimation is as follows:

Ψ＝R_uu+α (11)

wherein the content of the first and second substances,is the average of all the elements of the M x K weighting matrix,is Kxt_KThe mean value of the posterior probability distribution, R, of all elements in the factor parameter matrix of (1)_yyFor the covariance matrix of the sampled data, R_uuTo estimate the factor covariance matrix, R_uyFor multiplying the estimation factor by the sample data, α ═ diag (α)₁,α₂...,α_k). Equations 9 through 13 are iteratively cycled throughAndis not changing, according to which timeAndthe value of (A) can obtain the covariance matrix information sigma of the interference and the background noise with reduced dimension_EThe description is as follows:

equation 14 is the background interference information estimated based on the non-abnormal brain activity sampling data, which is used for the focal zone input of the brain source activity reconstruction module brain abnormal activity.

The brain source activity reconstruction module is used for constructing a second sampling data generation model of the abnormal wave, background interference noise is a parameter in the second sampling data generation model, the second sampling data generation model is solved by adopting an empirical Bayesian method, and a brain source activity time sequence is obtained.

Preferably, the solving of the second sampling data generation model by using the empirical bayesian method comprises the steps of: setting the brain electrical source activity time sequence S to be mutually independent in space and time and obey Gaussian distribution, and converting the second sampling data generation model into a second sampling data probability generation model by adopting an empirical Bayes method; and constructing a cost function based on the convex function plane boundary, and solving the second sampling data probability generation model by optimizing the cost function.

The following describes in detail a preferred implementation of the brain power activity reconstruction module.

Modeling the second sampling data generation model of the abnormal wave:

is provided with Y_act＝[y(t₁),y(t₂),...,y(t_K)]For identified abnormal electroencephalogram sampling data, t_KThe number of sampling points of the abnormal wave is the same as that of the non-abnormal wave. y (t)_k)∈R^M*1Is t_kAnd (3) sampling data of the electroencephalogram at a moment, wherein M is the number of channels. The brain source activity space comprises N source activity points, and the unit source activity of the position i generates the extracerebral sampling intensity of L_n＝[l₁,l₂,...,l_M]，L_nThe steering matrix of the nth source activity is a known parameter, can be solved through a source reconstruction positive problem, and can also be generated through open source software fieldtrip, nutmeg, spm and the like. The second sampling data generation model of the abnormal wave is as follows:

Y_act＝LS+ε (15)

S＝[S₁,S₂,...,S_N]^Tbeing a time sequence of source activities, S_nThe source activity time series for position n, ε is the noise and interference data, whose statistical signature information is solved by the noise estimation module equation 14. Let the brain source activities be spatially and temporally independent and obey a gaussian distribution as follows:

variance γ ═ diag (γ) of a priori gaussian distribution for position n₁,…,γ_n) The conditional probability distribution p (Y | S) is,

Σ_Eis the covariance matrix of the noise and interference estimated in S4. Based on an empirical Bayesian model, the following results can be obtained:

sample data p (Y)_act) The method is difficult to calculate, only has a reduction effect in the empirical Bayesian estimation process, and does not influence the estimation result. Due to the prior distribution p (S | gamma) and the conditional distribution p (Y)_actS) are all Gaussian distributions, posterior probability distribution p (S | Y)_act) Is composed of

Wherein the content of the first and second substances,is the mean, Γ, of the posterior probability distribution of the source activity^-1The posterior distribution equal variance.

Equations 16, 17, 18 and 19 constitute a second sample data probability generating model of the second sample data generating model, and model parameters are solved below.

S5.2: cost function optimization based on convex function plane boundary

Hyper-parameter gamma^-1By maximizing the edge distribution p (Y)_act| γ), edgeLog distribution model logp (Y)_actγ) is:

for the abnormal wave sampling data covariance matrix model, equation 21 can be optimized by expectation maximization algorithm (EM algorithm), but log | ∑ is_yThe convergence rate of | is extremely slow due to log | ∑ s_yIs gamma^-1Constructing a gamma-based convex function of^-1Log | ∑ of_yThe function of the | boundary(s),

optimized solution-log | sigma_yThe maximum of i, i.e. the minimum of the boundary cost function, is solved, as shown below,

Λ_nand Λ₀For auxiliary variables, tr (×) is the trace of the computation matrix, based on the cost function of the convex function boundarySatisfy always:

logp(Y_actthe maximum value of the [ gamma ]) is optimized to be the cost functionThe minimum value of (2) is solved.

S5.3 Complex focal zone reconstruction

By passing throughThe above analysis can show that the solution of brain electrical source first assumes that the source activity obeys mutually independent gaussian distributions, and by using empirical bayesian estimation, the value of the source activity is solved by substituting equations 16, 17 and 19 into equation 18 to solve posterior distribution p (sy)_act) The mean and variance of (a) are as follows:

is a diagonal matrix. Mean value in equation 20Namely a source activity time sequence to be solved, and the solution of the source activity time sequence needs to be known by the hyper-parameter gamma. Solving the maximum value of edge distribution to obtain the hyper-parameter gamma, and constructing a cost function based on a convex function boundaryModel, conversion to cost function by hyper-parametric gamma solutionAnd (4) optimizing. To functionSolving for the over parameter gamma_nAnd auxiliary parameter Λ_nThe reciprocal, one can obtain:

let equation 25 be zero, over-parameter γ_nAnd auxiliary parameter Λ_nThe formula of (1) is as follows:

by iteratively iterating equations 24 and 26 in a loop until cost function equation 20 converges,i.e. to solve the activity time series of the brain power.

And the imaging module is used for outputting and imaging the electroencephalogram source activity according to the electroencephalogram source activity time sequence acquired by the electroencephalogram source activity reconstruction module.

Obtaining brain power activity time seriesAnd then, displaying the result, and further, displaying the result based on the existing model parameters, such as the source position after brain space segmentation and brain structure information, wherein the MRI template is adopted in the patent, the source activity and the operation result on the general brain model are rendered, and the operation result is shown in fig. 2.

It must be noted that in any of the above embodiments, the methods are not necessarily executed in order of sequence number, and as long as it cannot be assumed from the execution logic that they are necessarily executed in a certain order, it means that they can be executed in any other possible order.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.