Inverse problems in photoacoustic imaging : analysis and computation
MetadataShow full item record
Inverse problems in photoacoustic imaging (PAT) have been extensively studied in recent years due to their importance in applications. This thesis addresses three important aspects of PAT inverse problems mathematically and computationally. First, we present a detailed mathematical and numerical analysis of quantitative fluorescence PAT, a variant of PAT for applications in molecular imaging. We develop uniqueness and stability theory on quantitative reconstructions based on the radiative transport model of light propagation and present numerical simulations to validate the mathematical theory. Second, we develop a fast numerical algorithm for solving the radiative transport equation, the model of light propagation in PAT applications on tissue imaging, in isotropic media. Our method is based on an integral equation formulation of the radiative transport equation and a fast multipole method for accelerating matrix-vector multiplications for the discretized system. Third, we perform mathematical analysis on PAT reconstruction problem with unknown ultrasound speed. We prove local uniqueness and stability results on the simultaneous reconstruction of the ultrasound speed, the acoustic attenuation coefficient as well as the optical absorption coefficients.