Mathematics of Tomography

Regents Of The University Of Idaho, Moscow ID

Investigators

Abstract

Photoacoustic tomography is an emerging hybrid method of imaging that combines the good contrast of optical imaging and high resolution of ultrasound imaging. Although significant progress has been made in this area, there are still many challenging problems whose solutions would not only contribute to understanding the mathematical foundation of tomography but also fundamentally innovate the state of the art in imaging technologies. The goals of this project are to analyze the possibilities and limitations of tomographic methods, as well as to design efficient algorithms for image reconstruction. Through collaborations with biomedical engineers, some of these results will be used in designs and/or algorithms for biomedical imaging methods. They may help better early detection of cancer and other diseases. This project has two parts, research problems in photoacoustic tomography (PAT) and integral geometry problems arising in tomography. The project in PAT will focus on the issues arising in imaging moving objects, PAT with integrating detectors, sampling theory, transcranial imaging, PAT with presence of air voids, and quantitative PAT. The problems in integral geometry problems include microlocal analysis of geometric integral transforms and theory of interior tomography. This interdisciplinary project will include close collaboration with biomedical engineers and the results have the may advance methods in biomedical imaging.