A Poisson likelihood iterative reconstruction algorithm for material decomposition in CT

Jingyan Xu, Eric C. Frey, Katsuyuki Taguchi, Benjamin M.W. Tsui

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations


Emerging photon-counting detectors with energy discrimination ability for x-ray CT perform binning according to the energy of the incoming photons. Multiple output channels with different energy thresholds can be obtained in one irradiation. The energy dependency of attenuation coefficients can be described by a linear combination of basis functions, e.g., Compton scatter and photo-electric effect; their individual contributions can be differentiated by using the multiple energy channels hence material characterization is made possible. Conventional analytic approach is a two-step process. First decompose in the projection domain to obtain the sinograms corresponding to the coefficients of the basis functions, then apply FBP to obtain the individual material components. This two-step process may have poor quality and quantitative accuracy due to the lower counts in the separate energy channels and approximation errors propagated to the image domain from projection domain decomposition. In this work we modeled the energy dependency of linear attenuation coefficients in our problem formulation and applied the optimality transfer principle to derive a Poisson-likelihood based algorithm for material decomposition from multiple energy channels. Our algorithm reconstructs the coefficients of the basis functions directly therefore the separate non-linear estimation step in the projection domain as in conventional approaches is avoided. We performed simulations to study the accuracy and noise properties of our method. We synthesized the linear attenuation coefficients at a reference energy and compared with standard attenuation values provided by NIST. We also synthesized the attenuation maps at different effective energy bin centers corresponding to the different energy channels and compared the synthesized images with reconstructions from standard fan-beam FBP methods. Preliminary simulations showed that our reconstructed images have much better noise properties.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2007
Subtitle of host publicationPhysics of Medical Imaging
EditionPART 2
StatePublished - 2007
EventMedical Imaging 2007: Physics of Medical Imaging - San Diego, CA, United States
Duration: Feb 18 2007Feb 22 2007

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
NumberPART 2
ISSN (Print)1605-7422


OtherMedical Imaging 2007: Physics of Medical Imaging
Country/TerritoryUnited States
CitySan Diego, CA


  • Computed tomography
  • Iterative reconstruction
  • Material decomposition
  • Poisson likelihood

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


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