SPECT with a multi-bang assumption on attenuation

Sean Holman, Philip Richardson

Research output: Contribution to journalArticlepeer-review


We consider the problem of joint reconstruction of both attenuation a and source density f in emission tomography in two dimensions. This is sometimes called the Single Photon Emission Computed Tomography (SPECT) identification problem. Assuming that a takes only finitely many values and f is once differentiable with compact support, we are able to characterise singularities appearing in the Attenuated Radon Transform Raf, which models SPECT data. Using this characterisation we prove that both a and f can be determined in some circumstances from Raf. We also propose a numerical algorithm to jointly compute a and f from Raf 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.
Original languageEnglish
Article number125005
JournalInverse Problems
Issue number12
Early online date31 Jul 2020
Publication statusPublished - Dec 2020


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