CN106097314B - A kind of spherical surface deconvolution regularization method based on dictionary - Google Patents
A kind of spherical surface deconvolution regularization method based on dictionary Download PDFInfo
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Abstract
A kind of spherical surface deconvolution regularization method based on dictionary, comprising the following steps: step 1. pretreatment, spherical surface deconvolution method can directly describe Fiber morphology structure, obtain combining closest to desired fODF by solving a non-negative least square problem；The training of step 2. sparse dictionary, the spatial regularization of step 3. sparse dictionary, by calculating the similarity measurement partial structurtes between each voxel and its adjacent element, the optimal combination for obtaining reconstruct fODF and promoting fODF sparse.The present invention provides that a kind of reduction redundancy, voxel spatial continuity be good, the higher spherical surface deconvolution regularization method based on dictionary of accuracy.
Description
Technical field
The present invention relates to the medical imagings under computer graphics, Nervous System Anatomy field, especially a kind of to be based on dictionary
Spherical surface deconvolution regularization method.
Background technique
Spherical surface Deconvolution Technique based on dictionary has been successfully used to the estimation of fiber orientation distribution (fODF).So
And these methods have been found dictionary has the problem of high redundancy and voxel lack spatial continuity.
Summary of the invention
In order to solve the spherical surface deconvolution techniques based on dictionary for estimating height present in fiber orientation distribution (fODF)
Spend redundant dictionary and lack the lower deficiency of spatial continuity problem, accuracy of voxel, the present invention provide a kind of reduction redundancy,
Voxel spatial continuity is good, the higher spherical surface deconvolution regularization method based on dictionary of accuracy.
The technical solution that the present invention uses:
A kind of spherical surface deconvolution regularization method based on dictionary, comprising the following steps:
Step 1. pretreatment
Spherical surface deconvolution method can directly describe Fiber morphology structure, i.e. the convolution r of fiber orientation distribution f kernel；
Wherein diffusion gradient g ∈ S2Measured signal s (g | u) it is by without diffusion-weighted s0(u) what is measured standardizes
It arrives；By being based on discrete direction collectionWith locality collectionExcessively complete distribution of orientations { d (v, ui) | i=
1,...muIntroduce for indicating voxel fibre structure uiRepresent i-th of locality, muAnd mvRespectively indicate the quantity of u and v；
Basic function is evenly distributed on unitary space, thus generate one it is fODF scheduled, the base D=of linear weighted combination d (v,
ui) | i=1 ... muIt is used to indicate fODF:
Due to most of coefficient wiIt is 0, so needing to eliminate these neutral elements, is reduced to Indicate the quantity of u after zero-suppressing；It obtains combining closest to desired fODF by solving a non-negative least square problem；
The training of step 2. sparse dictionary
Enable F=[f1,f2,...fT] matrix is represented, its each column fj, j=1,2 ..., T respectively corresponds inner bulk
The proximity space of plain fODF, j are coefficients；Finally, fODF is indicated by sparse excessively complete dictionary, new dictionary is by all
The initialization estimation of neighbouring fODF；After removing almost conllinear fODF by Principal Component Analysis, neighbouring fODF is by as one
The new basic function of group is the fibre structure estimation that central body is usually voxel of object, allowsBe mapped to one it is new
Dictionary base f '；Then, the linear weighted combination reconstructed with these dictionaries
Wherein, f represents dictionary base summation, vjRepresent j-th of discrete direction, behalf diffusion signal,Represent vjA power
Weight coefficient,Represent vjA kernel function,Represent the new dictionary base；
The spatial regularization of step 3. sparse dictionary
By calculating the similarity measurement partial structurtes between each voxel and its adjacent element；It is attached in a small range
Closely, the influence in addition to noise to reconstruction result may influence the integrality of fibre bundle closest to associated voxel, be summarized as following
Problem:
Wherein, ε represents noise, observation matrixH{wf′, H { ff′, H { sf′Respectively
Represent the penalty term of difference between adjacent dictionary coefficient, coefficient wf′It represents and is spread under given base by the part of implicit association, wf′Layer
Spatial smoothness and reconstruct fiber space smoothing be closely related；Weighting coefficient δiIt is considered as voxel of object fiber architecture about
Beam force is the Similarity measures based on diffusion signal；Similitude between two connection mappings is measured by COS distanceI is coefficient, sf′Represent the diffusion signal of voxel itself, siRepresent the diffusion signal of voxel surrounding voxels；At
This function is defined as extracting the fibre structure estimation of voxel of object:
Wherein λ1, λ2, λ3It is regularization parameter, observed matrix Af′Signal is recycled for being fitted,
It is orientated the difference between adjacent coefficient for regularization bottom fiber, this optimization is a separable spatial domain, by using increasing
Wide Lagrangian method solves:
New coefficient is represented, wherein I indicates unit matrix, λ1, λ2, λ3It is setting parameter；
The optimal combination for obtaining reconstruct fODF and promoting fODF sparse.
Technical concept of the invention are as follows: in order to realize the visualization of better brain feature structure, the present invention combines diffusion
Tensor imaging technology proposes a kind of extracting method that is apparent, more effective, can more embodying brain feature structure.Propose one
The method of a spatial regularization, the sparse dictionary fODF estimation under diffusion signal, and sparse dictionary is from neighbouring voxel and sky
Between the fiber orientation training of structure regularization obtain.Above-mentioned this method can be improved the accuracy of fODF reconstruct.Sparse word
Allusion quotation is the fiber orientation obtained from the neighboring area regularization derived from a voxel and space structure, is completed by training；This
The accuracy of reconstruct fODF can be improved in kind combination.Process is as follows:
Step 1, it pre-processes
Data are handled first, with the dataset representation voxel fibre structure of discrete direction and locality；
Step 2, fODF structural sparse dictionaries
Assume have " gravitation " in the fiber orientation in the particular voxel around a voxel herein, so from sparse dictionary base
It can be trained from the fiber orientation of adjacent voxels on plinth；
Step 3, with spatial regularization technology, the consistency of adjacent voxels structure is further ensured that, to solve fiber
There are problems that high redundancy in distribution of orientations.
The invention has the benefit that reducing, redundancy, voxel spatial continuity are good, accuracy is higher.
Specific implementation process
The present invention will be described in further details below.
A kind of spherical surface deconvolution regularization method based on dictionary, comprising the following steps:
Step 1. pretreatment
Spherical surface deconvolution method can directly describe Fiber morphology structure, i.e. the convolution r of fiber orientation distribution f kernel.
Wherein diffusion gradient g ∈ S2Measured signal s (g | u) it is by without diffusion-weighted s0(u) what is measured standardizes
It arrives；The work of early period is by based on discrete direction collectionWith locality collectionExcessively complete distribution of orientations { d
(v,ui) | i=1 ... muIntroduce for indicating voxel fibre structure uiRepresent i-th of locality, muAnd mvRespectively indicate u and
The quantity of v；Basic function is evenly distributed on unitary space, to generate fODF scheduled, a base D for linear weighted combination
={ d (v, ui) | i=1 ... muIt is used to indicate fODF:
Due to most of coefficient wiBe 0, so need to eliminate these neutral elements, can simplify for Indicate the quantity of u after zero-suppressing；We are obtained by solving a non-negative least square problem
It is combined closest to desired fODF；
The training of step 2. sparse dictionary
Because in the small field of voxel of object, such as the neighboring voxel of (T=3 × 3 × 3) sample T, usually by analogous element structure
At enabling F=[f1,f2,...fT] matrix is represented, its each column fj, j=1,2 ..., T respectively corresponds voxel of object
The proximity space of fODF, j are coefficients；Finally, fODF can be indicated by sparse excessively complete dictionary；In order to avoid inefficient and
Dictionary redundancy caused by optimization is unstable, new dictionary are the initialization estimations by all neighbouring fODF；Pass through principal component
After analytic approach removes almost conllinear fODF, neighbouring fODF be central body is usually inner bulk by the basic function new as one group
The fibre structure estimation of element, allowsIt is mapped to a new dictionary base f '；Then, we can use these dictionary weights
The linear weighted combination of structure
Wherein, f represents dictionary base summation, vjRepresent j-th of discrete direction, behalf diffusion signal,Represent vjA power
Weight coefficient,Represent vjA kernel function,Represent the new dictionary base；Unlike other methods based on model, originally
The complexity that method calculates pertains only to the neighbouring value of ontology cellulose fiber beam, that is to say, that the complexity of calculating may be due to several
Fine angular resolution bring of the non-colinear dictionary search to fODF group；In addition, in order to develop the freedom degree of diffusion parameter, Wo Menxu
Prior information is wanted to prevent from constructing unreasonable fiber model；It is new we have proposed one so in order to solve this problem
Spatial regularization method.
The spatial regularization of step 3. sparse dictionary
In order to allow machine direction to strive accomplishing smooth and accurate, we are by calculating between each voxel and its adjacent element
Similarity measurement partial structurtes；Near a small range, influence in addition to noise to reconstruction result, closest to associated body
Element may influence the integrality of fibre bundle, be summarized as following problems:
Wherein, ε represents noise, observation matrixH{wf′, H { ff′, H { sf′Respectively
Represent the penalty term of difference between adjacent dictionary coefficient, coefficient wf′It represents and is spread under given base by the part of implicit association, wf′Layer
Spatial smoothness and reconstruct fiber space smoothing be closely related；Weighting coefficient δiIt is considered as voxel of object fiber architecture about
Beam force is the Similarity measures based on diffusion signal；Similitude between two connection mappings is measured by COS distanceI is coefficient, sf′Represent the diffusion signal of voxel itself, siRepresent the diffusion signal of voxel surrounding voxels；At
This function is defined as extracting the fibre structure estimation of voxel of object:
Wherein λ1, λ2, λ3It is regularization parameter, observed matrix Af′Signal is recycled for being fitted,
It is orientated the difference between adjacent coefficient for regularization bottom fiber, this optimization is a separable spatial domain, by using increasing
Wide Lagrangian method solves:
New coefficient is represented, wherein I indicates unit matrix, λ1, λ2, λ3It is parameter, it can be with self-setting；This method solution
The optimal combination determined nonnegative least problem, while reconstruct fODF can be obtained and promote fODF sparse.
Claims (1)
1. a kind of spherical surface deconvolution regularization method based on dictionary, it is characterised in that: the following steps are included:
Step 1. pretreatment
Spherical surface deconvolution method can directly describe Fiber morphology structure, i.e. the convolution r of fiber orientation distribution f kernel；
Wherein diffusion gradient g ∈ S2Measured signal s (g | u) it is by without diffusion-weighted s0(u) standardization measured obtains
's；By being based on discrete direction collectionWith locality collectionExcessively complete distribution of orientations { d (v, ui) | i=
1,...muIntroduce for indicating voxel fibre structure uiRepresent i-th of locality, muAnd mvRespectively indicate the quantity of u and v；
Basic function is evenly distributed on unitary space, thus generate one it is fODF scheduled, the base D=of linear weighted combination d (v,
ui) | i=1 ... muIt is used to indicate fODF:
Due to most of coefficient wiIt is 0, so needing to eliminate these neutral elements, is reduced to Table
Show the quantity of u after zero-suppressing；It obtains combining closest to desired fODF by solving a non-negative least square problem；
The training of step 2. sparse dictionary
Enable F=[f1,f2,...fT] matrix is represented, its each column fj, j=1,2 ..., T respectively corresponds voxel of object
The proximity space of fODF, j are coefficients；Finally, fODF indicates that new dictionary is by all neighbours by sparse excessively complete dictionary
The initialization estimation of nearly fODF；After removing almost conllinear fODF by Principal Component Analysis, neighbouring fODF is by as one group
New basic function is the fibre structure estimation that central body is usually voxel of object, allowsIt is mapped to a new word
Allusion quotation base f '；Then, the linear weighted combination reconstructed with these dictionaries
Wherein, f represents dictionary base summation, vjRepresent j-th of discrete direction, behalf diffusion signal,Represent vjA weight system
Number,Represent vjA kernel function,Represent vjA new dictionary base；
The spatial regularization of step 3. sparse dictionary
By calculating the similarity measurement partial structurtes between each voxel and its adjacent element；Near a small range, remove
Influence of the noise to reconstruction result may influence the integrality of fibre bundle closest to associated voxel, be summarized as following problems:
Wherein, ε represents noise, observation matrixH{wf′, H { ff′, H { sf′Respectively represent
The penalty term of difference, coefficient w between adjacent dictionary coefficientf′It represents and is spread under given base by the part of implicit association, wf′The sky of layer
Between smoothness and reconstruct fiber space smoothing be closely related；Weighting coefficient δiIt is considered as voxel of object fiber architecture restraining force
It is the Similarity measures based on diffusion signal；Similitude between two connection mappings is measured by COS distanceI is coefficient, sf′Represent the diffusion signal of voxel itself, siRepresent the diffusion signal of voxel surrounding voxels；At
This function is defined as extracting the fibre structure estimation of voxel of object:
Wherein λ1, λ2, λ3It is regularization parameter, observed matrix Af′Signal is recycled for being fitted,It is positive
Then change the difference between bottom fiber orientation adjacent coefficient, this optimization is a separable spatial domain, is drawn by using augmentation
Ge Lang method solves:
New coefficient is represented, wherein I indicates unit matrix；
The optimal combination for obtaining reconstruct fODF and promoting fODF sparse.
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Citations (3)
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| CN103279633A (en) * | 2013-03-26 | 2013-09-04 | 浙江工业大学 | Brain fiber three-dimensional display method based on diffusion-weighted magnetic resonance data |
| CN104392019A (en) * | 2013-12-23 | 2015-03-04 | 浙江工业大学 | High-order diffusion tensor mixed sparse imaging method used for tracking cerebral white matter fibers |
| CN104881873A (en) * | 2015-06-03 | 2015-09-02 | 浙江工业大学 | Multistage adjustment mixed weighted sparse imaging method for precise reconstruction of complex fiber bundles |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103279633A (en) * | 2013-03-26 | 2013-09-04 | 浙江工业大学 | Brain fiber three-dimensional display method based on diffusion-weighted magnetic resonance data |
| CN104392019A (en) * | 2013-12-23 | 2015-03-04 | 浙江工业大学 | High-order diffusion tensor mixed sparse imaging method used for tracking cerebral white matter fibers |
| CN104881873A (en) * | 2015-06-03 | 2015-09-02 | 浙江工业大学 | Multistage adjustment mixed weighted sparse imaging method for precise reconstruction of complex fiber bundles |
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| "Parametric spherical deconvolution: Inferring anatomical connectivity using diffusion MR imaging";Enrico Kaden etc;《NeuroImage》;20070518;第474-488页 * |
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