Hybrid Imaging with Acoustic and Optics: Efficient Computation via Constructive Analysis

University Of Texas At Austin, Austin TX

Investigators

Abstract

This project is concerned with the development of mathematical theory and computational tools for some hybrid methods in medical imaging. By hybrid methods we refer to imaging techniques where two modalities with distinct underlying physics are coupled together to achieve the contrast and resolution not attainable separately by each of the modalities involved. This project is concerned with a specific class of hybrid imaging modalities that couple ultrasound imaging with optical imaging to achieve high-resolution imaging of optical properties of heterogeneous media. Our objectives are (i) to develop fast and robust image reconstruction algorithms for these hybrid modalities for practical use, and (ii) to train advanced undergraduate students, graduate students, and postdoctoral researchers on the mathematical and computational research in this field. The main proposed research efforts in this project include, but not limited to: (i) to develop efficient inversion algorithms for multi-coefficient inverse problems in photoacoustic tomography (PAT) with unknown ultrasound properties; (ii) to develop efficient reconstruction algorithms for inverse problems in quantitative fluorescence PAT (fPAT) and two-photon PAT (TP-PAT) for molecular imaging; (iii) to perform mathematical analysis on inverse problems in ultrasound-modulated fluorescence optical tomography (UMfOT) and to develop robust image reconstruction strategies in the same setting; and (iv) to develop fast algorithms for the transport equation for optimization-based iterative image reconstruction strategies for PAT, fPAT, TP-PAT and UMfOT with partial measurements. The mathematical ideas developed in the proposed projects are expected to provide insights on the mathematical and numerical solutions of many similar inverse coefficient problems to partial differential equations that appear in many fields of science and technology.