A Multi-Grid Iterative Method for Photoacoustic Tomography

TL;DR

This paper introduces a multigrid iterative method for faster photoacoustic tomography image reconstruction in heterogeneous media, leveraging adaptive search directions and analytical adjoints to enhance efficiency.

Contribution

It proposes a novel multigrid line search method that adaptively chooses between gradient and error correction, improving reconstruction speed in PAT.

Findings

Significant speed-up in iterative image reconstruction.

Effective integration of absorption and dispersion effects.

Enhanced performance of ISTA and FISTA algorithms.

Abstract

Inspired by the recent advances on minimizing nonsmooth or bound-constrained convex functions on models using varying degrees of fidelity, we propose a line search multigrid (MG) method for full-wave iterative image reconstruction in photoacoustic tomography (PAT) in heterogeneous media. To compute the search direction at each iteration, we decide between the gradient at the target level, or alternatively an approximate error correction at a coarser level, relying on some predefined criteria. To incorporate absorption and dispersion, we derive the analytical adjoint directly from the first-order acoustic wave system. The effectiveness of the proposed method is tested on a total-variation penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated variant (FISTA), which have been used in many studies of image reconstruction in PAT. The results show the great potential of the proposed method in improving speed of iterative image reconstruction.