A study of modeling x-ray transmittance for material decomposition without contrast agents

Okkyun Lee, Steffen Kappler, Christoph Polster, Katsuyuki Taguchi

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


This study concerns how to model x-ray transmittance, exp ( - ∫ μa(r, E) dr), of the object using a small number of energy-dependent bases, which plays an important role for estimating basis line-integrals in photon counting detector (PCD)-based computed tomography (CT). Recently, we found that low-order polynomials can model the smooth x-ray transmittance, i.e. object without contrast agents, with sufficient accuracy, and developed a computationally efficient three-step estimator. The algorithm estimates the polynomial coefficients in the first step, estimates the basis line-integrals in the second step, and corrects for bias in the third step. We showed that the three-step estimator was ∼1,500 times faster than conventional maximum likelihood (ML) estimator while it provided comparable bias and noise. The three-step estimator was derived based on the modeling of x-ray transmittance; thus, the accurate modeling of x-ray transmittance is an important issue. For this purpose, we introduce a modeling of the x-ray transmittance via dictionary learning approach. We show that the relative modeling error of dictionary learning-based approach is smaller than that of the low-order polynomials.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2017
Subtitle of host publicationPhysics of Medical Imaging
ISBN (Electronic)9781510607095
StatePublished - 2017
EventMedical Imaging 2017: Physics of Medical Imaging - Orlando, United States
Duration: Feb 13 2017Feb 16 2017


OtherMedical Imaging 2017: Physics of Medical Imaging
CountryUnited States


  • Dictionary learning
  • Low-order polynomial
  • Photon counting
  • X-ray transmittance

ASJC Scopus subject areas

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

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