title: An analytical model of the effects of pulse pileup on the energy spectrum recorded by energy resolved photon counting x-ray detectors.
abstract: OBJECTIVE
  Recently, novel CdTe photon counting x-ray detectors (PCXDs) with energy discrimination capabilities have been developed. When such detectors are operated under a high x-ray flux, however, coincident pulses distort the recorded energy spectrum. These distortions are called pulse pileup effects. It is essential to compensate for these effects on the recorded energy spectrum in order to take full advantage of spectral information PCXDs provide. Such compensation can be achieved by incorporating a pileup model into the image reconstruction process for computed tomography, that is, as a part of the forward imaging process, and iteratively estimating either the imaged object or the line integrals using, e.g., a maximum likelihood approach. The aim of this study was to develop a new analytical pulse pileup model for both peak and tail pileup effects for nonparalyzable detectors.
  
  
  METHODS
  The model takes into account the following factors: The bipolar shape of the pulse, the distribution function of time intervals between random events, and the input probability density function of photon energies. The authors used Monte Carlo simulations to evaluate the model.
  
  
  RESULTS
  The recorded spectra estimated by the model were in an excellent agreement with those obtained by Monte Carlo simulations for various levels of pulse pileup effects. The coefficients of variation (i.e., the root mean square difference divided by the mean of measurements) were 5.3%-10.0% for deadtime losses of 1%-50% with a polychromatic incident x-ray spectrum.
  
  
  CONCLUSIONS
  The proposed pulse pileup model can predict recorded spectrum with relatively good accuracy.
authors.affiliation: Russell H. Morgan Department of Radiology and Radiological Sciences, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA. ktaguchi@jhmi.edu
authors.forename: Katsuyuki
authors.initials: K
authors.lastname: Taguchi
authors.forename: Eric C
authors.initials: EC
authors.lastname: Frey
authors.forename: Xiaolan
authors.initials: X
authors.lastname: Wang
authors.forename: Jan S
authors.initials: JS
authors.lastname: Iwanczyk
authors.forename: William C
authors.initials: WC
authors.lastname: Barber
mesh_terms: D003198:Computer Simulation; D017076:Computer-Aided Design; D004735:Energy Transfer; D004867:Equipment Design; D019544:Equipment Failure Analysis; D008962:Models, Theoretical; D010783:Photometry / Q000295:instrumentation*; D017785:Photons; D011859:Radiography / Q000295:instrumentation*; D012815:Signal Processing, Computer-Assisted / Q000295:instrumentation*; D014057:Tomography, X-Ray Computed / Q000295:instrumentation*; D014159:Transducers; D014965:X-Rays