Multi-fiber Reconstruction from Diffusion MRI Using Mixture of Wisharts and Sparse Deconvolution

Abstract. In this paper, we present a novel continuous mixture of diffusion tensors model for the diffusion-weighted MR signal attenuation. The relationship between the mixing distribution and the MR signal attenuation is shown to be given by the Laplace transform defined on the space of positive definite diffusion tensors. The mixing distribution when parameterized by a mixture of Wishart distributions (MOW) is shown to possess a closed form expression for its Laplace transform, called the Rigaut-type function, which provides an alternative to the Stejskal-Tanner model for the MR signal decay. Our model naturally leads to a deconvolution formulation for multi-fiber reconstruction. This deconvolution formulation requires the solution to an ill-conditioned linear system. We present several deconvolution methods and show that the nonnegative least squares method outperforms all others in achieving accurate and sparse solutions in the presence of noise. The performance of our multi-fiber ...

• Type: Conference
• Year: 2007
• Where: IPMI
• Authors: Bing Jian, Baba C. Vemuri
• Keywords: Deconvolution Formulation, Diffusion Tensors Model, IPMI 2007, Medical Imaging, MR Signal Attenuation