Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenuated X-Ray Transform

  title={Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenuated X-Ray Transform},
  author={Songting Luo and Jianliang Qian and Plamen Stefanov},
  journal={SIAM J. Imaging Sci.},
Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply efficient fast sweeping methods to solve static transport equations and adjoint state equations… 
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