# On Iterative Algorithms for Quantitative Photoacoustic Tomography in the Radiative Transport Regime

## TL;DR

This paper develops and compares iterative algorithms for quantitative photoacoustic tomography using the radiative transfer equation, providing efficient methods for reconstructing optical tissue properties with proven convergence.

## Contribution

It introduces an improved fixed-point iterative method and applies the Barzilai-Borwein method for simultaneous reconstruction of optical coefficients in QPAT based on RTE.

## Key findings

- The fixed-point method converges reliably for absorption coefficient reconstruction.
- The BB method effectively reconstructs both absorption and scattering coefficients.
- Simulation results demonstrate the efficiency of the proposed algorithms.

## Abstract

In this paper, we describe the numerical reconstruction method for quantitative photoacoustic tomography (QPAT) based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and/or scattering coefficient of biological tissues. Given the scattering coefficient, an improved fixed-point iterative method is proposed to retrieve the absorption coefficient for its cheap computational cost. And we prove the convergence. To retrieve two coefficients simultaneously, Barzilai-Borwein (BB) method is applied. Since the reconstruction of optical coefficients involves the solution of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is improved from~\cite{Gao}. Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are the comparative methods for QPAT in two cases.