Regularization Of Diffusion Tensor Images Of Partial Differential Equations And Their Applications, The Dt-mri

DT-MRI(or DTI) is a relatively new medical image modality. It's quality degradation caused by noise in the imaging process may result in bad influence on its post-processing steps. The voxel values of DTI are diffusion tensors, so in this paper we consider the regularization of diffusion tensor image.In this paper, we take up the idea proposed in [1]:operating spectral decomposition to diffusion tensors in the tensor image, and then separately processing the vector field that consists of the eigenvalues and the rotation matrix field that consists of the eigenvectors. For the vector field, we use a trace-form model for its processing after analyzing how to choose certain parameters in the model; for the rotation matrix field, we give the necessary and sufficient condition for a PDE flow to preserve its orthogonal constraint, illuminate how to transform any vector field processing flow to a orthogonal constraint preserving flow through geometric projection, and naturally deduce a numerical scheme of the transformed model that also preserves the orthogonal constraint.Moreover, to overcome the "fake discontinuity" problem of the rotation matrix field caused by the nonuniqueness of eigenvectors in spectral decomposition, we propose a pre-processing step before regularization of the rotation matrix field, which efficiently controls the appearances of such problem.Finally, we implement our PDE model to both synthetic tensor field and real DTI dataset, and find out that the model removes the noise and preserves the image boundary well at the same time. Also, the fiber tract result of DTI could be improved after such regularization. We then compare the performance of spectral method with several other tensor field regularization methods. Result shows that the spectral method proposed in this paper does a better job on preserving the boundaries of different regions and some important quantitative indices of DTI.