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首页> 外文期刊>NeuroImage >Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI
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Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI

机译：非负球形反卷积（NNSD）用于估计单壳/多壳扩散MRI中的纤维取向分布函数

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Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S-2. However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S-2. Maximum Entropy SD(MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions. (C) 2014 Elsevier Inc. All rights reserved.
机译：球形反卷积（SD）通常用于根据扩散加权信号估计光纤定向分布函数（fODF）。现有的SD方法可以分为两类：1）基于连续表示的SD（CR-SD），其中通常使用球谐（SH）表示方便的分析解决方案，以及2）基于离散表示的SD（DR-SD），其中信号分布图由均匀分布在单位球面上的一组离散基函数表示。可行的fODF应该是非负的，并且应该在整个单位球体S-2中整合为一体。但是，据我们所知，大多数现有的基于SH的SD方法仅对离散点而不是S-2的整个连续体强制执行非负性。最大熵SD（MESD）和笛卡尔张量纤维取向分布（CT-FOD）是确保整个单位球面均非负性的唯一SD方法。但是它们需要大量的计算，并且容易受到球面数值积分引起的误差的影响。还已知现有的SD方法会高估光纤方向的数量，尤其是在各向异性低的区域。由于单位球的角度离散化，DR-SD在峰值检测中引入了其他误差。本文提出了一种SD框架，称为非负SD（NNSD），以克服上述所有限制。 NNSD明显不容易受到假阳性峰的影响，使用SH表示法进行有效的球形反卷积分析，并可以在整个单位球体内进行准确的峰检测。我们进一步表明，通过引入三维纤维响应函数，NNSD和大多数现有的SD方法可以扩展为处理多壳数据。我们将NNSD与约束SD（CSD），CSD，MESD的二次编程变体以及L1范数正则化非负最小二乘DR-SD进行了比较。对合成和真实的单壳/多壳数据进行的实验表明，NNSD在角度的平均差，峰值检测一致性以及各向同性和各向异性区域之间的各向异性对比方面提高了估计性能。 （C）2014 Elsevier Inc.保留所有权利。

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