Abstract
Circular arc Radon (CAR) transforms associate to a function, its integrals along arcs of circles. The inversion of such transforms is of natural interest in several imaging modalities such as thermoacoustic and photoacoustic tomography, ultrasound, and intravascular imaging. Unlike the full circle counterpart—the circular Radon transform—which has attracted significant attention in recent years, the CAR transforms are scarcely studied objects.In this paper, we present an efficient algorithm for the numerical inversion of the CAR transform with fixed angular span, for the cases in which the support of the function lies entirely inside or outside the acquisition circle. The numerical algorithm is noniterative and is very efficient as the entire scheme, once processed,can be stored and used repeatedly for reconstruction of images. A modified numerical inversion algorithm is also presented to reduce the artifacts in the reconstructed image which are induced due to the limited angular span.