A Hybrid Reconstruction Method for Quantitative PAT

作者：Ren Kui^*; Gao Hao; Zhao Hongkai

来源：SIAM Journal on Imaging Sciences, 2013, 6(1): 32-55.

DOI：10.1137/120866130

• quantitative photoacoustic tomography
• diffusion equation
• inverse problem
• interior data
• boundary Cauchy data
• hybrid reconstruction algorithm
• numerical minimization
• vector field method
• diffuse optical tomography

The objective of quantitative photoacoustic tomography (qPAT) is to reconstruct the diffusion and absorption properties of a medium from data of absorbed energy distribution inside the medium. Mathematically, qPAT can be formulated as an inverse coefficient problem for the diffusion equation. Past research showed that if the boundary values of the coefficients are known, then the interior values of the coefficients can be uniquely and stably reconstructed with two well-chosen data sets. We propose a hybrid numerical reconstruction procedure for qPAT that uses both interior energy data and boundary current data. We show that these data allow the unique reconstruction of the boundary and interior values of the coefficients. The numerical implementation is based on reformulating the inverse coefficient problem as a nonlinear optimization problem. An explicit reconstruction scheme is utilized to eliminate the unknown coefficients inside the medium so that we need only minimize over the boundary values, which have significantly fewer degrees of freedom. Numerical simulations with synthetic data are presented to validate the method.

• 出版日期2013