title: Fast estimation of diffusion tensors under Rician noise by the EM algorithm.
abstract: Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation.
authors.affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box (MaD), FI40014, Finland. Electronic address: jia.liu@jyu.fi.
authors.forename: Jia
authors.initials: J
authors.lastname: Liu
authors.affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI00014, Finland.
authors.forename: Dario
authors.initials: D
authors.lastname: Gasbarra
authors.affiliation: Helsinki University Hospital, Finland.
authors.forename: Juha
authors.initials: J
authors.lastname: Railavo
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology; D003198:Computer Simulation; D066264:Datasets as Topic; D004058:Diffusion; D056324:Diffusion Tensor Imaging / Q000379:methods*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016013:Likelihood Functions; D008279:Magnetic Resonance Imaging / Q000379:methods; D008959:Models, Neurological; D017711:Nonlinear Dynamics; D013995:Time; D066127:White Matter / Q000033:anatomy & histology
keywords: Data augmentation; Fisher scoring; Maximum a posteriori estimator; Maximum likelihood estimator; Reduced computation; Rician Likelihood