A simple Fourier transform-based reconstruction formula for photoacoustic computed tomography with a circular or spherical measurement geometry

TL;DR

This paper introduces a simple, exact Fourier transform-based reconstruction formula for photoacoustic computed tomography with circular or spherical measurement geometries, offering improved computational efficiency and insights into the frequency domain relationship.

Contribution

It presents a new hybrid reconstruction formula that is mathematically exact, simpler than previous methods, and significantly more computationally efficient for 2D and 3D PACT.

Findings

The formula explicitly links spatial and temporal frequency components.

It is two orders of magnitude faster than filtered backprojection algorithms.

The method is robust and easy to implement numerically.

Abstract

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging modality that has great potential for a wide range of biomedical imaging applications. In this Note, we derive a hybrid reconstruction formula that is mathematically exact and operates on a data function that is expressed in the temporal frequency and spatial domains. This formula explicitly reveals new insights into how the spatial frequency components of the sought-after object function are determined by the temporal frequency components of the data function measured with a circular or spherical measurement geometry in two- and three-dimensional implementations of PACT, respectively. The structure of the reconstruction formula is surprisingly simple compared with existing Fourier-domain reconstruction formulae. It also yields a straightforward numerical implementation that is robust and two orders of magnitude more computationally efficient than filtered backprojection algorithms.