Abstract
We consider the identification problem which arises in single photon emission computed tomography (SPECT) of joint reconstruction of both attenuation a and source density f. Assuming that a takes only finitely many values and we are able to characterise singularities appearing in the attenuated Radon transform R a f, which models SPECT data. Using this characterisation we prove that both a and f can be determined in some circumstances from R a f. We also propose a numerical algorithm to jointly compute a and f from R a f based on a weakly convex regularizer when a only takes values from a known finite list, and show that this algorithm performs well on some synthetic examples.
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