SPECT with a multi-bang assumption on attenuation. (3rd December 2020)

• Record Type: Journal Article
• Authors: Holman, Sean; Richardson, Philip
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-12-03
• Subjects: multi-bang regularization -- attenuated Radon transform -- SPECT identification problem -- joint recovery -- attenuation correction -- non-convex optimization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abab59
• Languages: English
• ISSNs: 0266-5611

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.