Estimation Of Orientation Probability Density Function In High Angular Resolution Diffusion Imaging

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.