1. An Analytical Algorithm for Tensor Tomography From Projections Acquired About Three Axes
- Author
-
Weijie Tao, Damien Rohmer, Grant T. Gullberg, Youngho Seo, and Qiu Huang
- Subjects
directional X-ray projections ,Ellipsoids ,Image Processing ,Bioengineering ,Tensors ,Phantoms ,Imaging ,Imaging, Three-Dimensional ,Computer-Assisted ,Engineering ,Information and Computing Sciences ,Image Processing, Computer-Assisted ,Filtered back-projection algorithm ,Humans ,Electrical and Electronic Engineering ,Biomedical measurement ,Tomography ,Radiological and Ultrasound Technology ,Phantoms, Imaging ,solenoidal and irrotational components ,X-ray imaging ,X-Ray Computed ,Computer Science Applications ,Nuclear Medicine & Medical Imaging ,Three-Dimensional ,Image reconstruction ,Biomedical Imaging ,Three-dimensional displays ,tensor tomography ,Tomography, X-Ray Computed ,Filtering algorithms ,Algorithms ,Software - Abstract
Tensor fields are useful for modeling the structure of biological tissues. The challenge to measure tensor fields involves acquiring sufficient data of scalar measurements that are physically achievable and reconstructing tensors from as few projections as possible for efficient applications in medical imaging. In this paper, we present a filtered back-projection algorithm for the reconstruction of a symmetric second-rank tensor field from directional X-ray projections about three axes. The tensor field is decomposed into a solenoidal and irrotational component, each of three unknowns. Using the Fourier projection theorem, a filtered back-projection algorithm is derived to reconstruct the solenoidal and irrotational components from projections acquired around three axes. A simple illustrative phantom consisting of two spherical shells and a 3D digital cardiac diffusion image obtained from diffusion tensor MRI of an excised human heart are used to simulate directional X-ray projections. The simulations validate the mathematical derivations and demonstrate reasonable noise properties of the algorithm. The decomposition of the tensor field into solenoidal and irrotational components provides insight into the development of algorithms for reconstructing tensor fields with sufficient samples in terms of the type of directional projections and the necessary orbits for the acquisition of the projections of the tensor field.
- Published
- 2022