A Novel Geometrical Approach for a Rapid Estimation of the HARDI Signal in Diffusion MRI

In this paper, we address the problem of the diffusion signal reconstruction from a limited number of samples. The HARDI (High Angular Resolution Diffusion Imaging) technique was proposed as an alternative to resolve the problems of crossing fibers in the case of Diffusion Tensor Imaging (DTI). However, it requires a long scanning time for the acquisition of the Diffusion Weighted (DW) images. This fact makes hard the clinical applications. We propose here a novel geometrical approach to accurately estimate the HARDI signal from a few number of DW images. The missing diffusion data are obtained according to their neighborhood from a reduced set of diffusion directions on the sphere of the q-space. The experimentations are performed on both synthetic data and many digital phantoms simulating crossing fibers on the brain tissues. The obtained results show the accuracy of the reconstruction of the Fiber Orientation Distribution (FOD) function from the estimated diffusion signal.