In recent years, diffusion tensor imaging (DTI) has become a popular in vivo diagnostic imaging technique in Radiological sciences. In order for this imaging technique to be more effective, proper image analysis techniques suited for analyzing these high dimensional data need to be developed. In this paper, we present a novel definition of tensor "distance" grounded in concepts from information theory and incorporate it in the segmentation of DTI. In a DTI, the symmetric positive definite (SPD) diffusion tensor at each voxel can be interpreted as the covariance matrix of a local Gaussian distribution. Thus, a natural measure of dissimilarity between SPD tensors would be the Kullback-Leibler (KL) divergence or its relative. We propose the square root of the J-divergence (symmetrized KL) between two Gaussian distributions corresponding to the diffusion tensors being compared and this leads to a novel closed form expression for the "distance" as well as the mean value of a DTI. Unlike the traditional Frobenius norm-based tensor distance, our "distance" is affine invariant, a desirable property in segmentation and many other applications. We then incorporate this new tensor "distance" in a region based active contour model for DTI segmentation. Synthetic and real data experiments are shown to depict the performance of the proposed model.

In this paper, we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from complex valued diffusion-weighted images (DWI). The constrained variational principle involves the minimization of a regularization term of L(P) norms, subject to a nonlinear inequality constraint on the data. The data term we employ is the original Stejskal-Tanner equation instead of the linearized version usually employed in literature. The complex valued nonlinear form leads to a more accurate (when compared to the linearized version) estimate of the tensor field. The inequality constraint requires that the nonlinear least squares data term be bounded from above by a known tolerance factor. Finally, in order to accommodate the positive definite constraint on the diffusion tensor, it is expressed in terms of Cholesky factors and estimated. The constrained variational principle is solved using the augmented Lagrangian technique in conjunction with the limited memory quasi-Newton method. Experiments with complex-valued synthetic and real data are shown to depict the performance of our tensor field estimation and smoothing algorithm.

Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new imaging modality in the field of medical imaging. This modality of imaging allows one to capture the structural connectivity if any between functionally meaningful regions for example, in the brain. The data however can be noisy and requires restoration. In this paper, we present a unified model for simultaneous smoothing and estimation of diffusion tensor field from DT-MRI. The diffusion tensor field is estimated directly from the raw data with L/sup P/ smoothness and positive definiteness constraints. The data term we employ is from the original Stejskal-Tanner equation instead of the linearized version as usually done in literature. In addition, we use Cholesky decomposition to ensure positive definiteness of the diffusion tensor. The unified model is discretized and solved numerically using limited memory quasi-Newton method. Both synthetic and real data experiments are shown to depict the algorithm performance.