CN106097359A - A kind of adaptive local feature extracting method based on nuclear magnetic resonance - Google Patents

Abstract

A kind of adaptive local feature extracting method based on nuclear magnetic resonance, comprises the steps: 1) set up the sphere of data-driven and deconvolute model；2) process of each area-of-interest being obtained new complete dictionary, process is as follows: the regularization of 2.1 local fODFs；The dimensionality reduction imaging of 2.2 data-driven local shape factor；Limit the cost function that sphere deconvolutes under 2.3 total variations, realize adaptive local feature extraction by solving above-mentioned optimization problem (10).The present invention deconvolute based on sphere under reconstruct fiber orientation distribution (fODF) sparse dictionary method in realize optimal denoising.

Description

A kind of adaptive local feature extracting method based on nuclear magnetic resonance

Technical field

The present invention relates to the medical imaging under computer graphics, neuroanatomy field, especially one based on magnetic altogether Shake the adaptive local feature extracting method of imaging.

Background technology

Diffusion-Weighted MR Imaging and tracking technique can obtain macroscopic internal tectonic information；Fine angular resolution imaging (HARDI) a widely sampled data is provided, it has been demonstrated that it contrasts with diffusion tensor imaging, it is possible to well table Levy the voxel of object structure of complexity；By data-driven method on the basis of HARDI, as sphere deconvolution method (SD) has become For studying the emphasis in brain field.

Summary of the invention

In order to solve cannot in the sparse dictionary method of the reconstruct fiber orientation distribution (fODF) under deconvoluting based on sphere The problem accomplishing optimal denoising, method proposes a kind of adaptive local based on nuclear magnetic resonance spy reaching optimal denoising Levy extracting method.

As follows in order to solve above-mentioned technical problem the technical solution used in the present invention:

A kind of adaptive local feature extracting method based on nuclear magnetic resonance, comprises the steps:

1) setting up the sphere of data-driven to deconvolute model, process is as follows:

The deconvolute method expression-form of s (g | u) of sphere is as follows:

$s\left(g\right|u)={\∫}_{S^2}r(g,v)f\left(v\right|u)d\mathrm{\μ}\left(v\right)+\mathrm{\ξ}---\left(1\right)$

Wherein ξ is noise, and this is the principal element affecting image quality；U is unit hemisphere uniform sampling vector；V is to adopt Sample prescription to；By kernel r (g, v) and the convolution of fODFf (v | u) describes Fiber morphology structure；Propose data-driven sphere and remove volume Long-pending new model f^c, it is reduced to:

f^c=f (c, Ω_c,ξ) (2)

Wherein Ω_cIt is the neighbor information of fODF, f^cBeing the c voxel, it can find according to the fiber of current voxel accordingly Direction, f (c, Ω_c, ξ) and it is to comprise c, Ω_c, a function of ξ；

2) process of each area-of-interest being obtained new complete dictionary, process is as follows:

The regularization of 2.1 local fODFs

Consider the voxel (3 × 3 × 3) around a voxel T, allowRepresent a matrix, it Each rowCorresponding to the fODF in a high spectrum image spatial neighborhood voxel；This matrix is represented as Relative to a most constant new joint sparse matrix F=[f₁,f₁,...,f_T], f_i, i=1,2 ..., T；Row coefficient square Battle array F reclaims by solving the matrix in following near-end computing:

$\underset{F}{\min }\frac{1}{2}{||\tilde{F}-F||}_F^2+{\mathrm{\λ}}_1{||F||}_{1,2}+{\mathrm{\λ}}_2\underset{i}{\Σ}{||F_j||}_1---\left(3\right)$

Wherein F_jIt it is matrix F jth column vector；N and T is coefficient；λ₁And λ₂It it is the parameter manually arranged；

The dimensionality reduction imaging of 2.2 data-driven local shape factor

At a single voxel, sparse dictionary can be along the machine direction of current voxel, and this procedural representation is:

Represent the dictionary base obtained from current voxel machine direction,Represent i-th fODF in the c voxel, Represent the fibre orientation obtained from the fODF of current voxel, n_iIt it is the number of dictionary base；For represent the dictionary of fibre orientation from The local orientation distribution characteristics that the fODF of adjacent voxels extracts obtains；Last dictionary table is shown as:

Joint sparse model contributes to regulating fODF structure, improves the fibre structure rebuild sparse；Local feature is by searching Rope easily obtains from the fODFs peak of the data of neighbouring diffusion voxel；FODF in the middle of so is by sparse new distribution of orientations base table Show；AllowIt is mapped to a new dictionary,Represent the dictionary base of all voxel machine directions, then use these dictionaries Reconstruct the fODF that a linear weighted combination represents unknown:

WhereinBeing position parameter, i, j are coefficients；

The cost function that sphere deconvolutes is limited under 2.3 total variations

The regular data that fODF extracts from measure with local feature can build a relative sparse dictionary, it is considered to becomes This function (7), by taking neighborhood information and about the noise in reconstruction result, it is thus achieved that the estimation of interior voxel fibre structure:

$\begin{array}{c}\min {||s-Hw||}_2^2+\mathrm{\λ}(\mathrm{\α}{||WZ-w||}_2+\\ \begin{array}{cc}(1-\mathrm{\α}){||w||}_{TV})& s.t.w\≥0\end{array}\end{array}---\left(7\right)$

Behalf measurement data, w represents voxel, and calculation matrix H is kernel and the convolution results of sparse dictionary in step 2.2, It is described as:

H=r (g, v) * f (c, Ω_c,ξ) (8)

Parameter lambda and α are commonly used for angle of equilibrium resolution and robustness, matrix W=[w₁,w₂,...,w_T] by initializing adjacent body The fODF coefficient of element obtains, matrix Z=[β₁,β₂,...,β_T]^TRepresent the similarity combination of center voxel and neighboring voxel；Pass through Calculating the similarity measurement partial structurtes between each voxel and adjacent element thereof, the similarity between two voxels is by remaining The measurement signal that chordal distance calculating obtains:

${\mathrm{\β}}_i=1-\frac{\left|s_{f^{\′}}\·s_i\right|}{||s_{f^{\′}}||||s_i||}---\left(9\right)$

The L1 norm of integral image gradient, is referred to as total variance canonical, and optimization problem (7) is rewritten into another kind of form such as Under:

$min{||(2H^{T}H+{\mathrm{\λ\αI}}^{T}I)w-(2H^{T}s+\mathrm{\λ}\mathrm{\α}WZ)||}_2^2+\mathrm{\λ}(1-\mathrm{\α}){||w||}_{TV}---\left(10\right)$

I is unit matrix；

Adaptive local feature extraction is realized by solving above-mentioned optimization problem (10).

Further, described step 2.3) in, optimization problem (10) is a total variation constrained least-squares problem, passes through " DeconvTV " workbox solves.

The technology of the present invention is contemplated that: by replacing ball humorous on the basis of SD dictionary, and include fibre orientation based on SD in Distribution function (fODF) is as local shape factor, and this method can form adaptive sparse dictionary base.

The method comprises the steps:

(1) set up the sphere under data-driven to deconvolute model

On the basis of sphere deconvolution method, owing to sphere deconvolution method is affected by noise greatly, thus propose The sphere of data-driven deconvolutes this new model；

(2) fODF adaptive local feature extraction is estimated

On the basis of above-mentioned model, first individually calculate initial fODF at area-of-interest, and initialize fODF, then Calculate the local regularization of its center voxel at each area-of-interest, and all fODFs calculated are created as one newly Dictionary, finally calculate cost function, obtain complete dictionary.

The invention have the benefit that the sparse dictionary of reconstruct fiber orientation distribution (fODF) under deconvoluting based on sphere Method, it is achieved optimal denoising.

Specific implementation process

Hereinafter the present invention will be described in further details.

A kind of adaptive local feature extracting method based on nuclear magnetic resonance, comprises the steps:

1) setting up the sphere of data-driven to deconvolute model, process is as follows:

The deconvolute method expression-form of s (g | u) of sphere is as follows:

$s\left(g\right|u)={\∫}_{S^2}r(g,v)f\left(v\right|u)d\mathrm{\μ}\left(v\right)+\mathrm{\ξ}---\left(1\right)$

Wherein ξ is noise, and this is the principal element affecting image quality；U is unit hemisphere uniform sampling vector；V is to adopt Sample prescription to；Sphere deconvolution method as the technology of most popular data-driven, it directly by kernel r (g, v) and The convolution of fODFf (v | u) describes Fiber morphology structure；But spherical convolution has only to consider structure and the noise of current voxel, Have ignored the impact on fiber imaging of the fODF adjacent domain information；Therefore, proposed here that data-driven sphere deconvolutes is new Model f^c, can be reduced to:

f^c=f (c, Ω_c,ξ) (2)

Wherein Ω_cIt is the neighbor information of fODF, f^cBeing the c voxel, it can find according to the fiber of current voxel accordingly Direction, f (c, Ω_c, ξ) and it is to comprise c, Ω_c, a function of ξ.

2) process of each area-of-interest being obtained new complete dictionary, process is as follows:

The regularization of 2.1 local fODFs

In voxel of object fODF field, in a small neighbourhood, voxel is generally made up of similar signal, therefore derives from body The fODFs of prime information should have dependency at space structure；The reconstruct that processing method is fibre structure that voxel is relevant is usual Cannot ensure its spatial coherence, because it simply estimates the fODF of current voxel；On the other hand voxel dependency can be by one Individual joint sparse model is assuming that the bottom sparse vector being associated with these voxels is shared a common degree of rarefication and supported also Enter, so make use of this method herein, to fODF process；Consider the voxel (3 × 3 × 3) around a voxel T, allowRepresent a matrix, its each rowCorresponding at a high spectrum image sky FODF in voxel near between；This matrix can be represented as relative to a most constant new joint sparse matrix F= [f₁,f₁,...,f_T], f_i, i=1,2 ..., T；Row coefficient matrix F can be by solving the matrix in following near-end computing back and forth Receive:

$\underset{F}{\min }\frac{1}{2}{||\tilde{F}-F||}_F^2+{\mathrm{\λ}}_1{||F||}_{1,2}+{\mathrm{\λ}}_2\underset{i}{\Σ}{||F_j||}_1---\left(3\right)$

Wherein F_jIt it is matrix F jth column vector；N and T is coefficient；λ₁And λ₂It it is the parameter manually arranged.

The dimensionality reduction imaging of 2.2 data-driven local shape factor

General, fODF can represent by crossing complete dictionary, but dictionary is redundancy all the time, and actually it may Owing to the spatial continuity between neighbouring voxel is represented by a suitable sparse dictionary；Fibre orientation is directly represented due to fODF Distribution estimating in each pixel, it more fully summarises information trace technology；At a single voxel, sparse dictionary Can be along the machine direction of current voxel, this process is represented by:

Represent the dictionary base obtained from current voxel machine direction,Represent i-th fODF in the c voxel, Represent the fibre orientation obtained from the fODF of current voxel, n_iIt it is the number of dictionary base；For representing that the dictionary of fibre orientation can Obtain with the local orientation distribution characteristics extracted from the fODF of adjacent voxels；Last dictionary can be expressed as:

This peacekeeping greatly reducing dictionary base improves computational efficiency；Joint sparse model contributes to regulating fODF knot Structure, improves the fibre structure rebuild sparse；Local feature can be light from the fODFs peak of the data of neighbouring diffusion voxel by search Pine obtains；FODF in the middle of so can be by sparse new distribution of orientations basis representation；AllowIt is mapped to a new dictionary, Representing the dictionary base of all voxel machine directions, then we can use these dictionaries one linear weighted combination of reconstruct to carry out table Show the unknown fODF:

WhereinBeing position parameter, i, j are coefficients.

The cost function that sphere deconvolutes is limited under 2.3 total variations

The regular data that fODF extracts from measure with local feature can build a relative sparse dictionary, and success Reduce basis dimension and computation complexity.Near a little scope, it is contemplated that following cost function, it is by taking Neighborhood information and about the noise in reconstruction result, it is thus achieved that the estimation of interior voxel fibre structure:

$\begin{array}{c}\min {||s-Hw||}_2^2+\mathrm{\λ}(\mathrm{\α}{||WZ-w||}_2+\\ \begin{array}{cc}(1-\mathrm{\α}){||w||}_{TV})& s.t.w\≥0\end{array}\end{array}---\left(7\right)$

Behalf measurement data, w represents voxel, and calculation matrix H is kernel and the convolution results of sparse dictionary in 2.2, permissible It is described as:

H=r (g, v) * f (c, Ω_c,ξ) (8)

The fibre orientation that regularization can ensure that concordance to a certain extent, parameter lambda and α are commonly used for the angle of equilibrium and differentiate Rate and robustness.Matrix W=[w₁,w₂,...,w_T] obtained by the fODF coefficient initializing adjacent voxels, matrix Z=[β₁, β₂,...,β_T]^TRepresent the similarity combination of center voxel and neighboring voxel.We are by calculating each voxel and adjacent element thereof Between similarity measurement partial structurtes.Similarity between two voxels is to be calculated the measurement obtained to believe by COS distance Number:

${\mathrm{\β}}_i=1-\frac{\left|s_{f^{\′}}\·s_i\right|}{||s_{f^{\′}}||||s_i||}---\left(9\right)$

In order to reduce to greatest extent because noise causes the purpose of undesired effect, set forth herein integral image gradient L1 norm, is referred to as total variance canonical (TV), TV technology, and it is primarily used to image is carried out denoising.Above-mentioned optimization problem can It is rewritten into another kind of form as follows:

$min{||(2H^{T}H+{\mathrm{\λ\αI}}^{T}I)w-(2H^{T}s+\mathrm{\λ}\mathrm{\α}WZ)||}_2^2+\mathrm{\λ}(1-\mathrm{\α}){||w||}_{TV}---\left(10\right)$

I is unit matrix, and this is a total variation constrained least-squares problem, and this problem can pass through " DeconvTV " Workbox solves.

Claims (2)

1. an adaptive local feature extracting method based on nuclear magnetic resonance, it is characterised in that: comprise the steps:

1) setting up the sphere of data-driven to deconvolute model, process is as follows:

The deconvolute method expression-form of s (g | u) of sphere is as follows:

$s\left(g\right|u)={\∫}_{S^2}r(g,v)f\left(v\right|u)d\mathrm{\μ}\left(v\right)+\mathrm{\ξ}---\left(1\right)$

Wherein ξ is noise, and this is the principal element affecting image quality；U is unit hemisphere uniform sampling vector；V is sampling side To；By kernel r (g, v) and the convolution of fODFf (v | u) describes Fiber morphology structure；Propose what data-driven sphere deconvoluted New model f^c, it is reduced to:

f^c=f (c, Ω_c,ξ) (2)

Wherein Ω_cIt is the neighbor information of fODF, f^cBeing the c voxel, it can find corresponding side according to the fiber of current voxel To, f (c, Ω_c, ξ) and it is to comprise c, Ω_c, a function of ξ；

2) process of each area-of-interest being obtained new complete dictionary, process is as follows:

The regularization of 2.1 local fODFs

Consider the voxel (3 × 3 × 3) around a voxel T, allowRepresent a matrix, it every Individual rowCorresponding to the fODF in a high spectrum image spatial neighborhood voxel；This matrix is represented as relatively In a most constant new joint sparse matrix F=[f₁,f₁,...,f_T], f_i, i=1,2 ..., T；Row coefficient matrix F Reclaim by solving the matrix in following near-end computing:

$\underset{F}{\min }\frac{1}{2}\left|\right|\tilde{F}-F|{|}_F^2+{\mathrm{\λ}}_1|\left|F\right|{|}_{1,2}+{\mathrm{\λ}}_2\underset{i}{\Σ}\left|\right|F_j|{|}_1---\left(3\right)$

Wherein F_jIt it is matrix F jth column vector；N and T is coefficient；λ₁And λ₂It it is the parameter manually arranged；

The dimensionality reduction imaging of 2.2 data-driven local shape factor

At a single voxel, sparse dictionary can be along the machine direction of current voxel, and this procedural representation is:

Represent the dictionary base obtained from current voxel machine direction, f_i ^cRepresent i-th fODF in the c voxel,Represent The fibre orientation obtained from the fODF of current voxel, n_iIt it is the number of dictionary base；For representing that the dictionary of fibre orientation is from adjacent The local orientation distribution characteristics that the fODF of voxel extracts obtains；Last dictionary table is shown as:

Joint sparse model contributes to regulating fODF structure, improves the fibre structure rebuild sparse；Local feature by search from The fODFs peak of the data of neighbouring diffusion voxel easily obtains；FODF in the middle of so is by sparse new distribution of orientations basis representation；AllowIt is mapped to a new dictionary,Represent the dictionary base of all voxel machine directions, then use these dictionaries reconstruct one Individual linear weighted combination represents unknown fODF:

WhereinBeing position parameter, i, j are coefficients；

The cost function that sphere deconvolutes is limited under 2.3 total variations

The regular data that fODF extracts from measure with local feature can build a relative sparse dictionary, it is considered to cost letter Number (7), by taking neighborhood information and about the noise in reconstruction result, it is thus achieved that the estimation of interior voxel fibre structure:

$\begin{array}{c}\min \left|\right|s-Hw|{|}_2^2+\mathrm{\λ}(\mathrm{\α}\left|\right|WZ-w|{|}_2+\\ \begin{array}{ccc}\left(1-\mathrm{\α}\right)\left|\right|w\left|{|}_{TV}\right)& s.t.& w\≥0\end{array}\end{array}---\left(7\right)$

Behalf measurement data, w represents voxel, and calculation matrix H is kernel and the convolution results of sparse dictionary in step 2.2, describes Become:

H=r (g, v) * f (c, Ω_c,ξ) (8)

Parameter lambda and α are commonly used for angle of equilibrium resolution and robustness, matrix W=[w₁,w₂,...,w_T] by initializing adjacent voxels FODF coefficient obtains, matrix Z=[β₁,β₂,...,β_T]^TRepresent the similarity combination of center voxel and neighboring voxel；By calculating Similarity measurement partial structurtes between each voxel and adjacent element thereof, the similarity between two voxels be by cosine away from From calculating the measurement signal obtained:

${\mathrm{\β}}_i=1-\frac{|s_{f^{\′}}\·s_i|}{\left|\right|s_{f^{\′}}\left|\right|\left|\right|s_i\left|\right|}---\left(9\right)$

The L1 norm of integral image gradient, is referred to as total variance canonical, and it is as follows that optimization problem (7) is rewritten into another kind of form:

$min\left|\right|(2H^{T}H+{\mathrm{\λ\αI}}^{T}I)w-(2H^{T}s+\mathrm{\λ}\mathrm{\α}WZ)|{|}_2^2+\mathrm{\λ}(1-\mathrm{\α})|\left|w\right|{|}_{TV}---\left(10\right)$

I is unit matrix；

Adaptive local feature extraction is realized by solving above-mentioned optimization problem (10).

A kind of adaptive local feature extracting method based on nuclear magnetic resonance, it is characterised in that: Described step 2.3) in, optimization problem (10) is a total variation constrained least-squares problem, by " DeconvTV " workbox Solve.