PENALIZED-LIKELIHOOD ESTIMATION OF DIFFUSION TENSORS FROM K-SPACE MR DATA

In diffusion MRI, an acquisition of Fourier-domain (K-space) samples of the imaged object is performed with each of a set of diffusion-encoding gradients. Diffusion tensor imaging (DTI) uses this diffusion-weighted (DW) data to estimate a tensor map that represents the dominant direction of water diffusion at each voxel in the imaged volume. Typical in vivo DW data suffers from low SNR, object-dependent artifacts due to field inhomogeneities, and direction-dependent artifacts due to eddy currents. If they are not accounted for, these factors result in degradation of the estimated tensor maps and the scalar diffusion measures (such as fractional anisotropy and mean diffusivity) obtained from the tensors. Here we propose a penalized-likelihood approach to the estimation of diffusion tensor maps directly from the raw K-space measurements. Our method inverts a detailed forward model of the diffusion tensors that can take into account field inhomogeneities, eddy-current effects, and imaging noise. It can also regularize the mean diffusivity and/or fractional anisotropy maps to counter the effects of noise and facilitate convergence. The penalized-likelihood estimator that we propose provides a unified framework for K-space reconstruction, field in homogeneity and eddy-current compensation, and denoising of tensor maps. Preliminary results from simulated data show our method to be effective and computationally tractable.