Direct Quantitative Photoacoustic Tomography for realistic acoustic media

TL;DR

This paper introduces a direct quantitative photoacoustic tomography method that accounts for realistic acoustic media with heterogeneous properties, using advanced optimisation algorithms to improve reconstruction accuracy.

Contribution

It develops two Krylov-subspace inexact-Newton algorithms for direct QPAT in complex media, outperforming traditional gradient-based methods in computational efficiency.

Findings

Inexact Newton algorithms outperform Quasi-Newton methods in accuracy.

The methods effectively handle heterogeneous acoustic properties.

The approach demonstrates improved reconstruction quality in realistic tissue-like media.

Abstract

Quantitative photo-acoustic tomography (QPAT) seeks to reconstruct a distribution of optical attenuation coefficients inside a sample from a set of time series of pressure data that is measured outside the sample. The associated inverse problems involve two steps, namely acoustic and optical, which can be solved separately or as a direct composite problem. We adopt the latter approach for realistic acoustic media that possess heterogeneous and often not accurately known distributions for sound speed and ambient density, as well as an attenuation following a frequency power law that is evident in tissue media. We use a Diffusion Approximation (DA) model for the optical portion of the problem. We solve the corresponding composite inverse problem using three total variation (TV) regularised optimisation approaches. Accordingly, we develop two Krylov-subspace inexact-Newton algorithms that utilise the Jacobian matrix in a matrix-free manner in order to handle the computational cost. Additionally, we use a gradient-based algorithm that computes a search direction using the L-BFGS method, and applies a TV regularisation based on the Alternating Direction Method of Multipliers (ADMM) as a benchmark, because this method is popular for QPAT and direct QPAT. The results indicate the superiority of the developed inexact Newton algorithms over gradient-based Quasi-Newton approaches for a comparable computational complexity.