Inversion of the V-line transform for breast cancer detection with Compton camera

Abstract

Abstract-In the recent past, Compton camera became an attractive alternative to the Anger camera in scintimammography, known as nuclear medicine breast imaging or molecular breast imaging. This novel imaging modality leads to the use of the V-line transform, which integrates a function along coupled rays with a common vertex. In previous works the attenuation phenomena was mostly neglected. However, in scintimammography ignoring the effect of the attenuation of photon can significantly degrade the quality of the reconstruction image. In this paper, we introduce the attenuated V-line transform and establish a new integral relation between the attenuated V-line transform and the exponential Radon transform. The results are not only interesting as original mathematical discoveries, but also can be useful in challenging applications e.g., in breast imaging for tumor detection close to the chest wall.Keywords-V-line transform; attenuated V-line transform; imaging of breast cancer; breast cancer detection; Compton camera.