An OMP-TV2 algorithm for detecting white matter fiber crossings in brain MRI

This paper introduces a novel algorithm for solving non-Gaussian mixture models of diffusion tensor imaging (DTI). In particular, these models are used for detecting the orientations of white matter fibers in brain. In our approach, any DT-MRI model (mathematically) is represented by an under-determined system of linear equations. The proposed algorithm uses an orthogonal matching pursuit (OMP) method coupled with Tikhonov regularization for solving such an under-determined system effectively, which results in better reconstruction of the fibers orientation. These linear systems depend on the number of the gradient directions used for generating the signals and for reconstruction process. OMP is a greedy iterative algorithm that picks the column of coefficient matrix that has the maximum correlation or projection on the residual at each stage. Using OMP with Tikhonov regularization shows tremendous reduction in the angular error when compared with an existing scheme where non-negative least square method (NNLS) is used. The proposed work is validated with both artificial simulations as well as real data experiments. The reduction in angular error is more pronounced when the angle of separation between the fibers is small.