Tensor tomography

Tensors of diffusion, deformation (stress and strain), and conductivity are physical quantities of biological tissue, which can be used to characterize particular disease states. Tensor tomography may be a useful imaging technique for eliciting these tensor quantities when applied in conjunction with an imaging modality such as magnetic resonance imaging (MRI). This paper presents a method for reconstructing a 2×2 second-order tensor field from scalar projection measurements of the tensor field. The reconstruction of the four components of a 2×2 tensor may require as many as four distinct scalar measurements for each projection ray through the tensor field. Fourier projection theorems have been developed for the reconstruction of a tensor field which is decomposed into solenoidal and irrotational components. Results of a computer simulation that demonstrate the validity of the mathematical formulations are presented. A method is also proposed to obtain a diffusion tensor field tomographically from MRI projection measurements of the diffusion tensor field. The method is evaluated experimentally and results of an MRI phantom study are presented