A variational model for SPECT reconstruction with a nonlinearly transformed attenuation prototype

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In single photon emission computed tomography (SPECT) reconstruction, the objective is to reconstruct the density of a radioactive marker inside a patient from projections. In this work, state-of-the-art reconstruction models for SPECT reconstruction with a so-called attenuation prototype are discussed. A multimodal correspondence problem is brought up and a novel variational model for SPECT reconstruction is presented that addresses the correspondence problem. This is followed by a description of a numerical realization. Numerical results show the necessity of the proposed SPECT reconstruction model.