Determination of Fiber Direction in High Angular Resolution Diffusion Images using Spherical Harmonics Functions and Wiener Filter

Diffusion tensor imaging (DTI) MRI is a noninvasive imaging method of the cerebral tissues whose fibers directions are not evaluated correctly in the regions of the crossing fibers. For the same reason the high angular resolution diffusion images (HARDI) are used for estimation of the fiber direction in each voxel. One of the main methods to specify the direction of fibers is usage of the spherical deconvolution. The spherical deconvolution is a method which is very sensitive to noise and creates negative values in the orientation distribution function (ODF) of the fiber. To solve this problem, methods such as Laplace-Beltrami regularized spherical deconvolution (LB-SD), the gradient based spherical deconvolution(GB-SD) and the constrained spherical deconvolution (CSD) are used. In this paper the method for SD based on Wiener filter (WB-SD) is presented. Regarding the results, the direction of the crossing fibers is specified correctly. The proposed algorithm has specified the direction of the fibers as zero degree with 4.9 standard deviation and 89.9 degree with 3.6 standard deviation against two crossing fibers with 90 degree angle.