Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

TL;DR

This paper introduces an efficient numerical algorithm for thermoacoustic tomography with detectors on an open curve, enabling accurate image reconstruction in scenarios where the region cannot be fully surrounded by detectors, such as in breast imaging.

Contribution

The paper presents a novel numerical method based on plane wave approximation and layer potentials, applicable in 2-D and extendable to 3-D, with complexity comparable to classical Radon transform algorithms.

Findings

Produces highly accurate reconstructions with precise and well-sampled data

Demonstrates stability against noise in the data

Applicable to practical imaging scenarios with incomplete detector coverage

Abstract

Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and 3-D) because frequently the region of interest cannot be completely surrounded by the detectors, as it happens, for example, in breast imaging. We present an efficient numerical algorithm for solving this problem in 2-D (similar methods are applicable in the 3-D case). Our method is based on the numerical approximation of plane waves by certain single layer potentials related to the acquisition geometry. After the densities of these potentials have been precomputed, each subsequent image reconstruction has the complexity of the regular filtration backprojection algorithm for the classical Radon transform. The peformance of the method is demonstrated in several numerical examples: one can see that the algorithm produces very accurate reconstructions if the data are accurate and sufficiently well sampled, on the other hand, it is sufficiently stable with respect to noise in the data.