Using Mathematics to Improve Effectiveness of Tomography

Novel mathematical theories could advance imaging techniques in optical tomography — a technique for creating three-dimensional images of the internal structures of a solid object by analyzing the travel of waves of energy, such as x-rays, electromagnetic or acoustic waves, through the object.

Gaik Ambartsoumian, UTA associate professor of mathematics and principal investigator of the project, with his team. Courtesy of UTA.

Researchers at the University of Texas at Arlington (UTA) are developing new mathematical theories that can help solve outstanding problems. The project could have a sizable impact on imaging technologies.

Gaik Ambartsoumian, UTA associate professor of mathematics, said their techniques include single-scattering optical tomography and gamma ray emission tomography, which are used in medicine for diagnostics and treatment monitoring of various diseases. The project also focuses on Compton camera imaging, which is used for detection of radiation sources in homeland security and in radio astronomy.

"We are working on the development of a new mathematical theory necessary for the advancement of imaging techniques in optical tomography and cameras using Compton scattering effect," Ambartsoumian said. "More specifically, we are studying the properties and deriving inversion formulas and algorithms for the broken-ray and conical Radon transforms, which are at the forefront of scientific endeavors in modern integral geometry and inverse problems."

Jianzhong Su, professor and chair of the Department of Mathematics, said the project has the potential to improve the technology used to diagnose and treat cancer and other diseases.

"Dr. Ambartsoumian's project can help to make key improvements in the effectiveness of various methods of tomography," said Su. "Improving these transforms can lead to greater accuracy of the images obtained from imaging modalities such as computed tomography, which is also known as CT, and ultrasound scanning, and could lead to improved airport security and advances in space exploration."

The UTA project, titled "Conical Radon transforms and their applications in tomography," is funded by a three-year grant from the National Science Foundation's Division of Mathematical Sciences.

Imaging technologies that could benefit from this research include: modern health care equipment, national security, space exploration and industrial applications.