DTI Interpolation And Registration Methods Based On Quaternion

Diffusion tensor imaging which can reflect the random motion of water molecules in living tissue is a new kind of magnetic resonance imaging technique. With the rapid development of this technology, the interpolation and registration processes in tensor field also have been widespread concern. But due to some characteristics of tensors such as high dimension and high amount of information, the processing results of tensor images are unsatisfactory until now. In this paper, the classical interpolation and registration algorithms of tensor images are mainly studied, and two new algorithms about interpolation and registration are proposed on the basis of quaternion theory.Aimed at the shortcomings of some important parameters are not linear and the optimization of weights are not reasonable and so on, the newly proposed anisotropic measure DA is simultaneously used to revise the weights of tensor shape and direction during the process of interpolation. To make the corresponding parameters of result tensors more linear, we revise the weights of eigenvalues according to the concrete direction of Fractional Anisotropy deviates from the ideal curve. We also use DA instead of HA(Hilbert anisotropy) to optimize the weights of direction, because of the definition of DA has fully considered the influence of eigenvalues on anisotropy, the interpolation error is smaller. Meanwhile, modelled on the processing of tensor data by the spectral-quaternion algorithm, this paper proposes a new kind of registration method whose computing efficiency between the methods in tensor field and scalar field. Again, it performs the spectral decomposition of tensors firstly, then deal with tensor shape and direction with demons algorithm respectively, and synthesize the new tensor image by registration results finally. Our new method represents the tensor orientation by unit quaternions, which significantly enhances the efficiency of interpolation, in addition, the average of overlap of eigenvalue-eigenvector is also higher.The improved method, spectral-quaternion method and Log-Euclidean method are applied to the synthetic and real canine heart diffusion tensor data for comparison, the results show that compared with spectral-quaternion method, the linearity of FA, Mode, RA, Det produced by our method are increased by 9.50%, 8.16%, 8.49% and 8.16% in turn, and it is also more in line with the diffusion regularity of water molecules in biological tissues. We as well verify the new proposed registration algorithm with real canine heart data, the results show that it can make the tensor directions more consistent with surrounding structure, and the registration accuracy is also higher obviously.