SPECT with a multi-bang assumption on attenuation

Abstract

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 f ∈ C c 1 ( R 2 ) 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.