THERMOACOUSTIC TOMOGRAPHY AND THE CIRCULAR RADON TRANSFORM: EXACT INVERSION FORMULA

Abstract

Thermoacoustic computed tomography (TACT) is an emerging hybrid imaging method for non-invasive medical diagnosis and fully three-dimensional visualization of biological probes. Within this modality electromagnetic illumination is used to induce acoustic waves inside an object of interest. In this paper, we assume that a cylindrical array of line detectors is used to record the acoustical data. This leads to the mathematical problem of inverting the circular Radon transform.The circular Radon transform arises in several other up-to-date imaging modalities, such as RADAR imaging or ultrasound tomography. In this paper we prove a novel stable formula for recovering a planar function from its circular Radon transform. We apply this formula to obtain an exact three-dimensional imaging algorithm for TACT. Numerical reconstructions from real and synthetic data demonstrate the potential and robustness of our algorithm.