Efficient inclusion of total variation type priors in quantitative photoacoustic tomography

TL;DR

This paper presents an efficient iterative method for solving the inverse problem in quantitative photoacoustic tomography, incorporating total variation type priors to improve high-resolution 3D optical parameter reconstructions.

Contribution

It introduces a novel algorithm combining prior-conditioned LSQR, lagged diffusivity, and linearization, optimized for large-scale 3D photoacoustic inverse problems.

Findings

Accurate high-quality estimates of optical parameters in 3D geometries

Moderate computational time and cost achieved

Method effectively handles complex tissue geometries

Abstract

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the distribution of optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This optical parameter estimation problem is ill-posed and needs to be approached within the framework of inverse problems. Photoacoustic images are three-dimensional and high-resolution. Furthermore, high-resolution reconstructions of the optical parameters are targeted. Therefore, in order to provide a practical method for quantitative photoacoustic tomography, the inversion algorithm needs to be able to perform successfully with problems of prominent size. In this work, an efficient approach for the inverse problem of quantitative photoacoustic tomography is proposed, assuming an edge-preferring prior for the optical parameters. The method is based on iteratively combining priorconditioned LSQR with a lagged diffusivity step and a linearisation of the measurement model, with the needed multiplications by Jacobians performed in a matrix-free manner. The algorithm is tested with three-dimensional numerical simulations. The results show that the approach can be used to produce accurate and high quality estimates of absorption and diffusion in complex three-dimensional geometries with moderate computation time and cost.