Relying on a rank-2 tensor model for diffusion within a voxel, conventional streamline tractography utilizes principal component analysis (PCA) to detect the orientation of a single fiber within a voxel. When more than one fibers or tracts intersect within a voxel, the PCA estimated orientation lies somewhere in-between the multiple fiber directions and is obviously an incomplete and incorrect representation of the underlying fibers in the voxel. This paper investigates the applicability of independent component analysis (ICA) to estimate individual tensors when multiple tensors corresponding to multiple intersecting fibers are present within a voxel. After establishing non-Gaussianity of the diffusion tensor imaging (DTI) signals, which is a pre-requisite for ICA, a Monte Carlo simulation study is conducted to show the accuracy of recovering the orientations of two or three tensors (fibers) mixed within a voxel. It is concluded that the principal eigen vectors but not the eigen values of multiple fibers are recoverable by conventional fast ICA.