A Galerkin least squares approach for photoacoustic tomography

TL;DR

This paper introduces a Galerkin least squares method for photoacoustic tomography in circular geometry, providing a fast, accurate, and convergent algorithm that leverages translation invariant spaces for improved image reconstruction.

Contribution

It develops an efficient Galerkin least squares approach using translation invariant spaces, including Kaiser-Bessel functions, with proven convergence and demonstrated numerical accuracy.

Findings

The method achieves high accuracy in image reconstruction.

The algorithm is computationally efficient and scalable.

Numerical simulations confirm the convergence and effectiveness.

Abstract

The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin least squares method for that purpose. For approximating the function to be recovered we use subspaces of translation invariant spaces generated by a single Funktion. This includes many systems that have previously been employed in PAT such as generalized Kaiser-Bessel basis functions or the natural pixel basis. By exploiting an isometry property of the forward problem we are able to efficiently set up the Galerkin equation for a wide class of generating functions and Devise efficient algorithms for its solution. We establish a convergence analysis and present numerical simulations that demonstrate the efficiency and accuracy of the derived algorithm.