Exact inversion of the exponential x-ray transform for rotating slant-hole (RSH) SPECT.

The RSH SPECT scanner provides parallel-beam attenuated projections for a fully 3D acquisition geometry. The geometry can be represented by circles on the unit sphere of projection directions, one circle for each position of the detector head. Unlike most other fully 3D geometries this one is particularly challenging because there are no 2D subsets in the data. When no attenuation is present, it is well known that an unmeasured projection can be synthesized if it lies inside one of the measured circles. The main result of this work is that under some assumptions on the attenuation distribution, attenuated projections within a circle can be synthesized from available attenuated projections. One consequence is that RSH SPECT projections can be rebinned into a conventional SPECT geometry for which analytic attenuation correction techniques are available.