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

@article{Luo2014AdjointSM,
  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.},
  year={2014},
  volume={7},
  pages={696-715}
}
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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UNIVERSIDAD DE CHILE FACULTAD DE CIENCIAS FÍSICAS Y MATEMÁTICAS DEPARTAMENTO DE INGENIERÍA MATEMÁTICA MATHEMATICAL MODELING AND INVERSE PROBLEMS IN BIOMEDICAL IMAGING TESIS PARA OPTAR AL GRADO DE DOCTORA EN CIENCIAS DE LA INGENIERÍA, MENCIÓN MODELACIÓN MATEMÁTICA EVELYN GABRIELA CUEVA JARAMI

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