Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic Tomography

TL;DR

This paper introduces stochastic proximal gradient algorithms for multi-source quantitative photoacoustic tomography, including a novel multilinear formulation that bypasses solving the radiative transfer equation, improving computational efficiency.

Contribution

The paper presents the first stochastic proximal gradient methods for multi-source QPAT and introduces a new multilinear formulation that avoids explicitly solving the RTE.

Findings

Algorithms demonstrate improved efficiency over standard methods.

Numerical results validate the effectiveness of the new approaches.

Multilinear formulation simplifies the inverse problem.

Abstract

The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as accurate model for light transport. The tissue parameters are jointly reconstructed from the acoustical data measured for each of the applied sources. We develop stochastic proximal gradient methods for multi-source QPAT, which are more efficient than standard proximal gradient methods in which a single iterative update has complexity proportional to the number applies sources. Additionally, we introduce a completely new formulation of QPAT as multilinear (MULL) inverse problem which avoids explicitly solving the RTE. The MULL formulation of QPAT is again addressed with stochastic proximal gradient methods. Numerical results for both approaches are presented. Besides the introduction of stochastic proximal gradient algorithms to QPAT, we consider the new MULL formulation of QPAT as main contribution of this paper.