Tensor tomography

Vector tomography has been shown to be useful in areas of applied physics and medical imaging. However, as of yet, there is little work on tomographic reconstruction of tensor fields, which has potential for applications in several areas of medical imaging. These include MRI diffusion imaging, various applications of imaging deformation, and imaging applications involving solutions of electromagnetic inverse problems such as ECG and MCG. A symmetric tensor can be decomposed into a solenoidal and an irrotational component. In this paper, Fourier projection theorems are developed for the reconstruction of these components. Results of a computer simulation are presented that demonstrate the validity of the mathematical results