Multi-compartment model estimation and analysis in high angular resolution diffusion imaging

Abstract

Diffusion weighted magnetic resonance images offer unique insights into the neural networks of in vivo human brain. In this study, we investigate estimation and statistical analysis of multi-compartment models in high angular resolution diffusion imaging (HARDI) involving the Rician noise model. In particular, we address four important issues in multi-compartment diffusion model estimation, namely, the modelling of Rician noise in diffusion weighted (DW) images, the automatic determination of the number of compartments in the diffusion signal, the application of spatial prior on multi-compartment models, and the evaluation of parameter indeterminacy in diffusion models. We propose an expectation maximization (EM) algorithm to estimate the parameters of a multi-compartment model by maximizing the Rician likelihood of the diffusion signal. We introduce a novel scheme for automatically selecting the number of compartments, via a sparsity-inducing prior on the compartment weights. A non-local weighted maximum likelihood estimator is proposed to improve estimation accuracy utilizing repetitive patterns in the image. Experimental results show that the proposed algorithm improves estimation accuracy in low signal-to-noise-ratio scenarios, and it provides better model selection than several alternative strategies. In addition, we derive the Cram´er-Rao Lower Bound (CRLB) of the maximum Rician likelihood estimator for the balland-stick model and general differentiable diffusion models. The CRLB provides a general theoretical tool for comparing diffusion models and examining parameter indeterminacy in the maximum likelihood estimation problem.