【作者】 张娜；

【导师】 李冲； 蒋田仔；

【作者基本信息】 浙江大学 ， 计算数学， 2012， 博士

【摘要】 在生物组织中,水分子的运动受周围组织结构的影响。水分子运动的轨迹反应了周围组织的微观结构。扩散磁共振成像(dMRI, diffusion magnetic resonance imaging)是唯一的一种无创的,可以活体检测生物组织内水分子扩散信息的技术。通过测量水分子的扩散,dMRI可以提供生物组织的微观结构信息。扩散张量成像(DTI, diffusion tensor imaging)是最常用的一种探测大脑白质纤维结构的dMRI技术,但是DTI模型受Gaussian假设的限制,在每个体素内只能给出一根纤维方向的信息,不能解决多纤维交叉等问题。为给出复杂的大脑白质结构信息,如解决纤维交叉等问题,高角度分辨率扩散成像(HARDI, high angular resolution diffusion imaging)技术被提出来。本论文中高角度分辨率扩散成像简称为高角分辨率成像。HARDI的采样分布在一个球壳或多个球壳上,由此被分为两类：单球壳HARDI(sHARDI, single-shell HARDI)和多球壳HARDI(mHARDI,multi-shell HARDI)本论文着重考虑sHARDI技术,主要贡献有：1.给出一种sHARDI中不基于信号具体模型的估计方向概率密度函数(OPDF, orientation probabiltiy density function)的方法。Q-Ball成像(QBI, Q-Ball imaging)是一种基于Funk-Radon变换(FRT,Funk-Radon transform)的可估计方向分布函数(ODF,orientation distribution function)的被广泛应用的sHARDI技术。QBI不需要采样球壳外的HARDI信号的假设。然而QBI中估计的ODF不是一个真正的概率密度函数,OPDF确是真正的概率密度函数,具有正确的概率解释。论文中我们给出的这个sHARDI模型也是基于FRT的,但是可以解析估计OPDF。换句话说,这个模型可以看做一个可估计OPDF的QBI的一种变形。2.给出sHARDI中估计OPDF的iOPDT模型(改进的OPDT模型)。OPDT是由Tristan-Vega等给出的一种基于FRT的估计OPDF的模型,它存在由FRT引入的误差。Aganj等证明了OPDF的径向部分等于一个常数,它是与信号无关的。基于这种考虑,我们给出了一种改进的OPDT模型(iOPDT),且有闭形式解。它通过将OPDT中的径向部分替换为其在球面上的平均值来降低FRT误差。iOPDT是一种基于FRT的单球壳HARDI模型,与OPDT比较,它提高了角分辨率,且几乎保持了高的角度准确性,抗噪性和计算效率。在仿真数据和真实数据上的结果均证实了它的有效性。3.利用压缩传感的知识,在iOPDT模型中用球脊波(SR,spherical ridgelet)函数解析地估计OPDF。SR已经被证明可以稀疏表示HARDI信号,虽然在HARDI中一般用球调和(SH,spherical harmonic)函数,但是SH不具备稀疏表示HARDI信号的能力。SR已经被用在QBI模型中解析估计ODF,但是尚没有用SR估计OPDF的方法。我们利用本论文所给出的iOPDT模型,根据iOPDT模型的特性,用SR解析地估计OPDF。更多还原

【Abstract】 In biological tissue, the motion of water molecule is constrained by the surround-ing tissue structure. The path of the water molecule reflects the microscopic structure of the surrounding tissue. dMRI is an in-vivo technique which can recover information of the water diffusion in biological tissue non-invasively. dMRI can provide the information of microscopic structure about the biological tissue by measuring the diffusion of water molecules.DTI (diffusion tensor imaging) is the most common dMRI technique which can probe the structure of white matter fibers in the brain. However DTI is limited by its Gaussian assumption. It can only provide one fiber orientation in every voxel, and can not resolve multiple fibers. In order to recover the complex geometry of the white matter, HARDI(high angular resolution diffusion imaging) is proposed. The sampling of HARD I is distributed on one q-shell or multi q-shells. HARDI can be divided to sHARDI(single-shell HARDI) and mHARDI(multi-shell HARDI).This study mainly focused on sHARDI. The main contributions of this thesis are as follows:1. We proposed one OPDF (orientation probability density function) estimator in sHARDI without signal model. Q-Ball imaging (QBI) is a widely used sHARDI tech-nique based on Funk-Radon transform (FRT), which can compute orientation distribution function (ODF). This technique does not require any assumption about the diffusion sig-nal outside the sampling sphere. However the originally proposed ODF (the radial project of the probability density function (PDF)) is not a true ODF. In contrast the OPDF with solid angle consideration, represents a true ODF with a correct probabilistic interpretation. In this thesis a sHARDI estimator for analytical reconstruction of OPDF based on Funk-Radon transform (FRT) is proposed. In other words, we proposed a transformation of QBI for OPDF. 2. We proposed an iOPDT model (improved OPDT model) in sHARDI. OPDT is a s HARDI estimator for OPDF, which is proposed by Tristan-Vega et al.. OPDT is based on the FRT, so there is blurring introduced by FRT. Aganj et al. have proved that the radial part of the OPDF equals a constant, which is independent of the diffusion signal. With this consideration, we propose an improved form of OPDT with a closed form expression, which can reduce the FRT blurring in OPDT by replacing the radial part (a non-constant function) with its mean value over the sphere. Compared with OPDT, the proposed FRT-based single-shell HARDI estimator improves the angular resolution, and almost maintains the higher angular accuracy, robustness and computational efficiency。3. We gave a framework to estimate the OPDF with spherical ridgelets (SR) in iOPDT model analytically utilizing knowledge of compressed sensing. The SR has been demon-strated that it can represent the HARDI signals sparsely, while the spherical harmonic (SH) basis, which is commonly used in HARDI, does not provide sparse representation of HAR-DI signals. The SR has been used to estimate ODF in QBI, while it has not been used to estimate OPDF. We use SR to estimate OPDF in iOPDT, which is proposed in this thesis, according to the characteristics of iOPDT estimator.更多还原