  The Compton camera is a promising alternative to the Anger camera for imaging
gamma radiation, with the potential to significantly increase the sensitivity
of SPECT. Two-dimensional Compton camera image reconstruction can be
implemented by inversion of the V-line transform, which integrates the emission
distribution over V-lines (unions of two half-lines), that have vertices on a
surrounding detector array. Inversion of the V-line transform without
attenuation has recently been addressed by several authors. However, it is well
known from standard SPECT that ignoring attenuation can significantly degrade
the quality of the reconstructed image. In this paper we address this issue and
study the attenuated V-line transform accounting for attenuation of photons in
SPECT with Compton cameras. We derive an analytic inversion approach based on
circular harmonics expansion, and show uniqueness of reconstruction for the
attenuated V-line transform. We further develop a discrete image reconstruction
algorithm based on our analytic studies, and present numerical results that
demonstrate the effectiveness of our algorithm.

Numerical Analysis