Abstract
We give formulae describing the simplest statistical properties of single-photon emissioncomputed tomography (SPECT) data modelled as the attenuated ray transform withPoisson noise. To obtain some of these formulae we obtain and use an inequality relatingthe even and odd parts of the attenuated ray transform without noise. Preciseequations relating the even and odd parts of this transform are also discussed.Using these results we propose new possibilities for improving the stability ofSPECT imaging based on the explicit inversion formula for the attenuated raytransformation with respect to the Poisson noise in the emission data. Numericalexamples illustrating some of the theoretical conclusions of the present work aregiven.
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