Attenuation correction in SPECT using consistency conditions for the exponential ray transform

Using data consistency conditions for the exponential ray transform, a method is derived to correct SPECT data for attenuation effects. No transmission measurements are required, and no operator-defined contours are needed. Furthermore, any 3D parallel-ray geometry can be considered for SPECT data acquisition, even unconventional geometries which do not lead to a set of 2D parallel-beam sinograms. The method is presented for both the 2D parallel-beam geometry and a particular 3D case, called the rotating slant hole geometry. Full details of the algorithms are given. Implementation has been carried out and results are presented in 2D and in 3D using simulated data.