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

Using data consistency conditions for the exponential ray transform, a meth od is derived to correct SPECT data for attenuation effects. No transmissio n measurements are required, and no operator-defined contours are needed. F urthermore, any 3D parallel-ray geometry can be considered for SPECT data a cquisition, 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 geom etry. Full details of the algorithms are given. Implementation has been car ried out and results are presented in 2D and in 3D using simulated data.