CN106097359A

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

Info

Publication number: CN106097359A
Application number: CN201610437517.6A
Authority: CN
Inventors: 冯远静; 何建忠; 吴烨; 张军; 徐田田; 周思琪; 毛祖杰; 张大宏
Original assignee: Zhejiang University of Technology ZJUT; Zhejiang Provincial Peoples Hospital
Current assignee: Zhejiang University of Technology ZJUT; Zhejiang Provincial Peoples Hospital
Priority date: 2016-06-16
Filing date: 2016-06-16
Publication date: 2016-11-09

Abstract

一种基于磁共振成像的自适应局部特征提取方法，包括如下步骤：1)建立数据驱动的球面去卷积模型；2)对每个感兴趣区域处理得到新的完备的字典，过程如下：2.1局部fODFs的正则化；2.2数据驱动局部特征提取的降维成像；2.3全变差下限制球面去卷积的成本函数，通过解决上述优化问题(10)实现自适应局部特征提取。本发明基于球面去卷积下的重构纤维取向分布(fODF)的稀疏字典方法中实现最佳去噪。An adaptive local feature extraction method based on magnetic resonance imaging, comprising the following steps: 1) establishing a data-driven spherical deconvolution model; 2) processing each region of interest to obtain a new complete dictionary, the process is as follows: 2.1 Regularization of local fODFs; 2.2 Data-driven dimensionality reduction imaging for local feature extraction; 2.3 Cost function for constrained spherical deconvolution under total variation, enabling adaptive local feature extraction by solving the above optimization problem (10). The present invention achieves optimal denoising in the sparse dictionary method based on reconstructed fiber orientation distribution (fODF) under spherical deconvolution.

Description

An Adaptive Local Feature Extraction Method Based on Magnetic Resonance Imaging

技术领域technical field

本发明涉及计算机图形学下的医学成像、神经解剖学领域，尤其是一种基于磁共振成像的自适应局部特征提取方法。The invention relates to the fields of medical imaging and neuroanatomy under computer graphics, in particular to an adaptive local feature extraction method based on magnetic resonance imaging.

背景技术Background technique

扩散加权成像和跟踪技术可以得到肉眼可见的体内构造信息；高角分辨率成像(HARDI)提供了一个更广泛的采样数据，已经证明了其与扩散张量成像对比，能够很好的表征复杂的内部体素结构；在HARDI基础上通过数据驱动方法，如球面去卷积方法(SD)现已成为研究脑领域的重点。Diffusion-weighted imaging and tracking techniques can obtain macroscopic in vivo structure information; high angular resolution imaging (HARDI) provides a wider sampling data, which has been proved to be good at characterizing complex interiors compared with diffusion tensor imaging Voxel structure; on the basis of HARDI through data-driven methods, such as spherical deconvolution method (SD) has become the focus of the research brain field.

发明内容Contents of the invention

为了解决基于球面去卷积下的重构纤维取向分布(fODF)的稀疏字典方法中无法做到最佳去噪的问题，本方法提出了一种达到最佳去噪的基于磁共振成像的自适应局部特征提取方法。In order to solve the problem that the sparse dictionary method based on reconstructed fiber orientation distribution (fODF) under spherical deconvolution cannot achieve optimal denoising, this method proposes an MRI-based automatic Adaptive local feature extraction method.

为了解决上述技术问题本发明采用的技术方案如下：In order to solve the problems of the technologies described above, the technical scheme adopted by the present invention is as follows:

一种基于磁共振成像的自适应局部特征提取方法，包括如下步骤：A method for extracting adaptive local features based on magnetic resonance imaging, comprising the steps of:

1)建立数据驱动的球面去卷积模型，过程如下：1) Establish a data-driven spherical deconvolution model, the process is as follows:

球面去卷积s(g|u)的方法表达形式如下：The method of spherical deconvolution s(g|u) is expressed as follows:

$s the s ((g g | | u u)) = = {&Integral; &Integral;}_{{S S}^{22}} r r ((g g,, v v)) f f ((v v | | u u)) d d μ μ ((v v)) + + ξ ξ - - - - - - ((11))$

其中ξ是噪声，这是影响成像质量的主要因素；u是单位半球均匀采样向量；v是采样方向；通过内核r(g,v)和fODFf(v|u)的卷积描述纤维解剖结构；提出数据驱动球面去卷积的新模型f^c，简化为：where ξ is noise, which is the main factor affecting the imaging quality; u is the uniform sampling vector of the unit hemisphere; v is the sampling direction; the fiber anatomy is described by the convolution of the kernel r(g,v) and fODFf(v|u); A new model fc for data-driven spherical ^{deconvolution} is proposed, which simplifies to:

f^c＝f(c,Ω_c,ξ) (2)f ^c ＝f(c,Ω _c ,ξ) (2)

其中Ω_c是fODF的邻近信息，f^c是第c个体素，它可以根据当前体素的纤维找到相应的方向，f(c,Ω_c,ξ)是包含c，Ω_c，ξ的一个函数；Where Ω _c is the adjacent information of fODF, f ^c is the cth voxel, it can find the corresponding direction according to the fiber of the current voxel, f(c, Ω _c , ξ) is a function including c, Ω _c , ξ ;

2)对每个感兴趣区域处理得到新的完备的字典，过程如下：2) Process each region of interest to obtain a new complete dictionary, the process is as follows:

2.1局部fODFs的正则化2.1 Regularization of local fODFs

考虑一个体素T周围的体素(3×3×3)，让代表一个矩阵，它的每个列对应于在一个高光谱图像空间附近体素内的fODF；该矩阵被表示为相对于线性不变的一个新的联合稀疏矩阵F＝[f₁,f₁,...,f_T]，f_i,i＝1,2,...,T；行系数矩阵F通过求解下面近端运算上的矩阵来回收：Consider the voxels (3×3×3) around a voxel T, let Represents a matrix, each column of which Corresponds to the fODF within a voxel in the vicinity of a hyperspectral image space; this matrix is expressed as a new joint sparse matrix F=[f ₁ ,f ₁ ,...,f _T ] that is linearly invariant with respect to f _i , i=1,2,...,T; the row coefficient matrix F is recovered by solving the matrix on the following proximal operation:

$\underset{F f}{min min} \frac{11}{22} {|| || \overset{~ ~}{F f} - - F f || ||}_{F f}^{22} + + {λ λ}_{11} {|| || F f || ||}_{11,, 22} + + {λ λ}_{22} \underset{i i}{Σ Σ} {|| || {F f}_{j j} || ||}_{11} - - - - - - ((33))$

其中F_j是矩阵F第j个列向量；n和T是系数；λ₁和λ₂是手动设置的参数；Where F _j is the jth column vector of matrix F; n and T are coefficients; λ ₁ and λ ₂ are parameters set manually;

2.2数据驱动局部特征提取的降维成像2.2 Data-driven dimensionality reduction imaging for local feature extraction

在一个单一的体素，稀疏的字典会沿着当前体素的纤维方向，该过程表示为：In a single voxel, the sparse dictionary will be along the fiber direction of the current voxel, and the process is expressed as:

代表从当前体素纤维方向获取的字典基，代表第c个体素中的第i个fODF，表示从当前体素的fODF得到的纤维取向，n_i是字典基的数目；用于表示纤维取向的词典从相邻体素的fODF提取的局部取向分布特征来获取；最后的字典表示为： Represents the dictionary basis obtained from the current voxel fiber direction, represents the i-th fODF in the c-th voxel, Represents the fiber orientation obtained from the fODF of the current voxel, n _i is the number of dictionary bases; the dictionary used to represent the fiber orientation is obtained from the local orientation distribution features extracted from the fODF of adjacent voxels; the final dictionary is expressed as:

联合稀疏模型有助于调节fODF结构，提高重建的纤维结构稀疏；局部特征通过搜索从附近扩散体素的数据的fODFs峰轻松获取；这样中间的fODF由稀疏新的取向分布基表示；让映射到一个新的字典，代表所有体素纤维方向的字典基，然后使用这些字典重构一个线性加权组合来表示未知的fODF：The joint sparse model helps to adjust the fODF structure and improve the sparseness of the reconstructed fiber structure; local features are easily obtained by searching fODFs peaks from nearby diffuse voxel data; such that the intermediate fODF is represented by a sparse new orientation distribution basis; let maps to a new dictionary, A dictionary basis representing the orientations of all voxel fibers is then used to reconstruct a linearly weighted combination to represent the unknown fODF:

其中是位置系数，i,j都是系数；in Is the position coefficient, i, j are coefficients;

2.3全变差下限制球面去卷积的成本函数2.3 Cost function of restricted spherical deconvolution under total variation

fODF和局部特征从测量中提取的正规化数据能够构建一个相对稀疏字典，考虑成本函数(7)，通过取邻域信息和关于重构结果中的噪声，获得内体素纤维结构的估计：The fODF and local features normalized data extracted from the measurements enable the construction of a relatively sparse dictionary, taking into account the cost function (7), to obtain an estimate of the fiber structure within the voxel by taking neighborhood information and noise in the reconstruction result:

$\begin{matrix} min min {|| || s the s - - H h w w || ||}_{22}^{22} + + λ λ ((α α {|| || W W Z Z - - w w || ||}_{22} + + \\ \begin{matrix} ((11 - - α α)) {|| || w w || ||}_{T T V V})) & s the s . . t t . . w w &GreaterEqual; &Greater Equal; 00 \end{matrix} \end{matrix} - - - - - - ((77))$

s代表测量数据，w代表体素，测量矩阵H是步骤2.2中内核和稀疏字典的卷积结果，描述成：s represents the measurement data, w represents the voxel, and the measurement matrix H is the convolution result of the kernel and the sparse dictionary in step 2.2, described as:

H＝r(g,v)*f(c,Ω_c,ξ) (8)H=r(g,v)*f(c,Ω _c ,ξ) (8)

参数λ和α常用作平衡角分辨率和鲁棒性，矩阵W＝[w₁,w₂,...,w_T]由初始化相邻体素的fODF系数获取，矩阵Z＝[β₁,β₂,...,β_T]^T代表中心体素与邻近体素的相似性组合；通过计算每个体素及其相邻元素之间的相似性测量局部结构，两个体素之间的相似性是通过余弦距离计算获得的测量信号：The parameters λ and α are often used to balance angular resolution and robustness. The matrix W=[w ₁ ,w ₂ ,...,w _T ] is obtained by initializing the fODF coefficients of adjacent voxels. The matrix Z=[β ₁ , β ₂ ,...,β _T ] ^T represents the similarity combination of the central voxel and neighboring voxels; the local structure is measured by calculating the similarity between each voxel and its neighboring elements, and the similarity between two voxels is the measured signal obtained by cosine distance calculation:

${β β}_{i i} = = 11 - - \frac{| | {s the s}_{{f f}^{' '}} \cdot \cdot {s the s}_{i i} | |}{|| || {s the s}_{{f f}^{' '}} || || || || {s the s}_{i i} || ||} - - - - - - ((99))$

整合图像梯度的L1范数，被称为总变差正则，优化问题(7)被改写成另一种形式如下：Integrating the L1 norm of the image gradient, known as total variation regularization, the optimization problem (7) is rewritten in another form as follows:

$m m i i n no {|| || ((22 {H h}^{T T} H h + + {λαI λαI}^{T T} I I)) w w - - ((22 {H h}^{T T} s the s + + λ λ α α W W Z Z)) || ||}_{22}^{22} + + λ λ ((11 - - α α)) {|| || w w || ||}_{T T V V} - - - - - - ((1010))$

I是单位矩阵；I is the identity matrix;

通过解决上述优化问题(10)实现自适应局部特征提取。Adaptive local feature extraction is achieved by solving the above optimization problem (10).

进一步，所述步骤2.3)中，优化问题(10)是一个全变差约束最小二乘问题，通过“DeconvTV”工具箱解决。Further, in the step 2.3), the optimization problem (10) is a total variation constrained least squares problem, which is solved by the "DeconvTV" toolbox.

本发明的技术构思为：通过在SD字典基础上代替球谐，并纳入基于SD的纤维取向分布函数(fODF)作为局部特征提取，这种方法能够形成自适应稀疏字典基。The technical idea of the present invention is: by replacing spherical harmonics on the basis of SD dictionary and incorporating SD-based fiber orientation distribution function (fODF) as local feature extraction, this method can form an adaptive sparse dictionary basis.

该方法包括如下步骤：The method comprises the steps of:

(1)建立数据驱动下的球面去卷积模型(1) Establish a data-driven spherical deconvolution model

在球面去卷积方法的基础上，由于球面去卷积方法受噪声的影响大，从而提出了数据驱动的球面去卷积这个新的模型；Based on the spherical deconvolution method, because the spherical deconvolution method is greatly affected by noise, a new model of data-driven spherical deconvolution is proposed;

(2)估计fODF用自适应局部特征提取(2) Estimating fODF with adaptive local feature extraction

上述的模型基础上，首先在感兴趣区域单独计算最初的fODF，并初始化fODF，然后在每个感兴趣区域计算其中心体素的局部正则化，并将所有计算出的fODFs建立成一个新的字典，最后计算成本函数，得到完备的字典。Based on the above model, first calculate the initial fODF separately in the region of interest, and initialize the fODF, then calculate the local regularization of its central voxel in each region of interest, and build all the calculated fODFs into a new Dictionary, and finally calculate the cost function to get a complete dictionary.

本发明的有益效果为：基于球面去卷积下的重构纤维取向分布(fODF)的稀疏字典方法，实现最佳去噪。The beneficial effects of the present invention are: based on the sparse dictionary method of the reconstructed fiber orientation distribution (fODF) under spherical deconvolution, optimal denoising is realized.

具体实施过程Specific implementation process

以下将对本发明做进一步详细说明。The present invention will be further described in detail below.

其中ξ是噪声，这是影响成像质量的主要因素；u是单位半球均匀采样向量；v是采样方向；球面去卷积方法作为使用最广泛的数据驱动的技术，它直接通过内核r(g,v)和fODFf(v|u)的卷积描述纤维解剖结构；然而球面卷积只需要考虑当前体素的结构和噪声，忽略了fODF邻近区域信息对纤维成像的影响；因此，这里提出了数据驱动球面去卷积的新模型f^c，可以简化为：where ξ is noise, which is the main factor affecting the imaging quality; u is the unit hemisphere uniform sampling vector; v is the sampling direction; the spherical deconvolution method is the most widely used data-driven technique, which directly passes the kernel r(g, The convolution of v) and fODFf(v|u) describes the fiber anatomy; however, the spherical convolution only needs to consider the structure and noise of the current voxel, and ignores the influence of fODF adjacent area information on fiber imaging; therefore, the data presented here The new model f ^c driving spherical deconvolution can be simplified as:

f^c＝f(c,Ω_c,ξ) (2)f ^c ＝f(c,Ω _c ,ξ) (2)

其中Ω_c是fODF的邻近信息，f^c是第c个体素，它可以根据当前体素的纤维找到相应的方向，f(c,Ω_c,ξ)是包含c，Ω_c，ξ的一个函数。Where Ω _c is the adjacent information of fODF, f ^c is the cth voxel, it can find the corresponding direction according to the fiber of the current voxel, f(c, Ω _c , ξ) is a function including c, Ω _c , ξ .

2.1局部fODFs的正则化2.1 Regularization of local fODFs

在内部体素fODF场，在一个小邻域内体素通常由相似的信号组成，因此来源于体素信息的fODFs应该在空间结构具有相关性；体素相关的处理方法为纤维结构的重构通常不能确保其空间相关性，因为它只是估计当前体素的fODF；另一方面体素相关性可通过一个联合稀疏模型在假设与这些体素相关联的底层稀疏向量共享一个共同的稀疏度支撑并入，所以本文利用了这种方法，对fODF进行处理；考虑一个体素T周围的体素(3×3×3)，让代表一个矩阵，它的每个列对应于在一个高光谱图像空间附近体素内的fODF；该矩阵可以被表示为相对于线性不变的一个新的联合稀疏矩阵F＝[f₁,f₁,...,f_T]，f_i,i＝1,2,...,T；行系数矩阵F可以通过求解下面近端运算上的矩阵来回收：In the intra-voxel fODF field, voxels usually consist of similar signals in a small neighborhood, so fODFs derived from voxel information should have correlations in the spatial structure; the voxel-related processing method is usually the reconstruction of fiber structure Its spatial correlation cannot be guaranteed, because it only estimates the fODF of the current voxel; on the other hand, voxel correlation can be obtained through a joint sparse model under the assumption that the underlying sparse vectors associated with these voxels share a common sparsity support and input, so this paper uses this method to process fODF; consider the voxels (3×3×3) around a voxel T, let Represents a matrix, each column of which Corresponds to the fODF within a voxel in the vicinity of a hyperspectral image space; this matrix can be expressed as a new joint sparse matrix F=[f ₁ ,f ₁ ,...,f _T ] that is invariant to linearity, f _i , i=1,2,...,T; the row coefficient matrix F can be recovered by solving the matrix on the following proximal operation:

其中F_j是矩阵F第j个列向量；n和T是系数；λ₁和λ₂是手动设置的参数。Where F _j is the jth column vector of matrix F; n and T are coefficients; λ ₁ and λ ₂ are parameters set manually.

一般的，fODF可以通过过完备字典来表示，然而字典始终是冗余的，实际上它可能由于附近体素之间的空间连续性通过一个相当稀疏字典表示；由于fODF直接表示纤维取向每个像素内的分布估计，它更全面地概括了信息跟踪技术；在一个单一的体素，稀疏的字典会沿着当前体素的纤维方向，该过程可表示为：In general, fODF can be represented by an over-complete dictionary, however, the dictionary is always redundant, in fact it may be represented by a rather sparse dictionary due to the spatial continuity between nearby voxels; since fODF directly represents the fiber orientation of each pixel distribution estimation within , which more fully generalizes the information tracking technique; in a single voxel, the sparse dictionary will follow the fiber direction of the current voxel, and the process can be expressed as:

代表从当前体素纤维方向获取的字典基，代表第c个体素中的第i个fODF，表示从当前体素的fODF得到的纤维取向，n_i是字典基的数目；用于表示纤维取向的词典可以从相邻体素的fODF提取的局部取向分布特征来获取；最后的字典可以表示为： Represents the dictionary basis obtained from the current voxel fiber direction, represents the i-th fODF in the c-th voxel, Represents the fiber orientation obtained from the fODF of the current voxel, and n _i is the number of dictionary bases; the dictionary used to represent the fiber orientation can be obtained from the local orientation distribution features extracted from the fODF of adjacent voxels; the final dictionary can be expressed as :

这大大降低了字典基的维和提高了计算效率；联合稀疏模型有助于调节fODF结构，提高重建的纤维结构稀疏；局部特征可以通过搜索从附近扩散体素的数据的fODFs峰轻松获取；这样中间的fODF可以由稀疏新的取向分布基表示；让映射到一个新的字典，代表所有体素纤维方向的字典基，然后我们可以使用这些字典重构一个线性加权组合来表示未知的fODF：This greatly reduces the dimensionality of the dictionary base and improves computational efficiency; the joint sparse model helps to adjust the fODF structure and improve the sparseness of the reconstructed fiber structure; local features can be easily obtained by searching the fODFs peaks of data from nearby diffuse voxels; The fODF of can be represented by a sparse new orientation distribution basis; let maps to a new dictionary, A dictionary basis representing the orientations of all voxel fibers, we can then use these dictionaries to reconstruct a linearly weighted combination to represent the unknown fODF:

其中是位置系数，i,j都是系数。in Is the position coefficient, i, j are coefficients.

fODF和局部特征从测量中提取的正规化数据能够构建一个相对稀疏字典，并成功地降低了基础维度和计算复杂度。在一个小范围附近，我们考虑下面的成本函数，其通过取邻域信息和关于重构结果中的噪声，获得内体素纤维结构的估计：The regularized data extracted from measurements by fODF and local features are able to build a relatively sparse dictionary and successfully reduce the underlying dimensionality and computational complexity. Around a small scale, we consider the following cost function, which obtains an estimate of the fiber structure within a voxel by taking neighborhood information and about noise in the reconstruction result:

s代表测量数据，w代表体素，测量矩阵H是2.2中内核和稀疏字典的卷积结果，可以描述成：s represents the measurement data, w represents the voxel, and the measurement matrix H is the convolution result of the kernel and the sparse dictionary in 2.2, which can be described as:

H＝r(g,v)*f(c,Ω_c,ξ) (8)H=r(g,v)*f(c,Ω _c ,ξ) (8)

正则化可以保证的纤维取向在一定程度上的一致性，参数λ和α常用作平衡角分辨率和鲁棒性。矩阵W＝[w₁,w₂,...,w_T]由初始化相邻体素的fODF系数获取，矩阵Z＝[β₁,β₂,...,β_T]^T代表中心体素与邻近体素的相似性组合。我们通过计算每个体素及其相邻元素之间的相似性测量局部结构。两个体素之间的相似性是通过余弦距离计算获得的测量信号：Regularization can guarantee the consistency of the fiber orientation to a certain extent, and the parameters λ and α are often used to balance angular resolution and robustness. Matrix W=[w ₁ ,w ₂ ,...,w _T ] is obtained by initializing the fODF coefficients of adjacent voxels, and matrix Z=[β ₁ ,β ₂ ,...,β _T ] ^T represents the central voxel Similarity combination with neighboring voxels. We measure local structure by computing the similarity between each voxel and its neighbors. The similarity between two voxels is a measure signal obtained by cosine distance calculation:

为了最大限度地减少因噪声引起不希望的效果的目的，本文提出整合图像梯度的L1范数，被称为总变差正则(TV)，TV技术，它主要是用来对图像进行去噪。上述优化问题可被改写成另一种形式如下：In order to minimize the undesired effects caused by noise, this paper proposes to integrate the L1 norm of the image gradient, called Total Variation Regularization (TV), TV technology, which is mainly used to denoise the image. The above optimization problem can be rewritten in another form as follows:

I是单位矩阵，这是一个全变差约束最小二乘问题，这个问题可以通过“DeconvTV”工具箱解决。I is the identity matrix, which is a total variation constrained least squares problem, which can be solved by the "DeconvTV" toolbox.

Claims

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 (g | u) = {&Integral;}_{S^{2}} r (g, v) f (v | u) d μ (v) + ξ - - - (1)

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:

\min_{F} \frac{1}{2} | | \tilde{F} - F | |_{F}^{2} + λ_{1} | | F | |_{1, 2} + λ_{2} \underset{i}{Σ} | | F_{j} | |_{1} - - - (3)

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{matrix} \min | | s - H w | |_{2}^{2} + λ (α | | W Z - w | |_{2} + \\ \begin{matrix} (1 - α) | | w | |_{T V}) & s . t . & w &GreaterEqual; 0 \end{matrix} \end{matrix} - - - (7)

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:

β_{i} = 1 - \frac{| s_{f^{'}} \cdot s_{i} |}{| | s_{f^{'}} | | | | s_{i} | |} - - - (9)

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:

m i n | | (2 H^{T} H + {λαI}^{T} I) w - (2 H^{T} s + λ α W Z) | |_{2}^{2} + λ (1 - α) | | w | |_{T V} - - - (10)

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.