title: Pulse pileup statistics for energy discriminating photon counting x-ray detectors.
abstract: OBJECTIVE
  Energy discriminating photon counting x-ray detectors can be subject to a wide range of flux rates if applied in clinical settings. Even when the incident rate is a small fraction of the detector's maximum periodic rate No, pulse pileup leads to count rate losses and spectral distortion. Although the deterministic effects can be corrected, the detrimental effect of pileup on image noise is not well understood and may limit the performance of photon counting systems. Therefore, the authors devise a method to determine the detector count statistics and imaging performance.
  
  
  METHODS
  The detector count statistics are derived analytically for an idealized pileup model with delta pulses of a nonparalyzable detector. These statistics are then used to compute the performance (e.g., contrast-to-noise ratio) for both single material and material decomposition contrast detection tasks via the Cramdr-Rao lower bound (CRLB) as a function of the detector input count rate. With more realistic unipolar and bipolar pulse pileup models of a nonparalyzable detector, the imaging task performance is determined by Monte Carlo simulations and also approximated by a multinomial method based solely on the mean detected output spectrum. Photon counting performance at different count rates is compared with ideal energy integration, which is unaffected by count rate.
  
  
  RESULTS
  The authors found that an ideal photon counting detector with perfect energy resolution outperforms energy integration for our contrast detection tasks, but when the input count rate exceeds 20% N0, many of these benefits disappear. The benefit with iodine contrast falls rapidly with increased count rate while water contrast is not as sensitive to count rates. The performance with a delta pulse model is overoptimistic when compared to the more realistic bipolar pulse model. The multinomial approximation predicts imaging performance very close to the prediction from Monte Carlo simulations. The monoenergetic image with maximum contrast-to-noise ratio from dual energy imaging with ideal photon counting is only slightly better than with dual kVp energy integration, and with a bipolar pulse model, energy integration outperforms photon counting for this particular metric because of the count rate losses. However, the material resolving capability of photon counting can be superior to energy integration with dual kVp even in the presence of pileup because of the energy information available to photon counting.
  
  
  CONCLUSIONS
  A computationally efficient multinomial approximation of the count statistics that is based on the mean output spectrum can accurately predict imaging performance. This enables photon counting system designers to directly relate the effect of pileup to its impact on imaging statistics and how to best take advantage of the benefits of energy discriminating photon counting detectors, such as material separation with spectral imaging.
authors.affiliation: Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA. adamwang@stanford.edu
authors.forename: Adam S
authors.initials: AS
authors.lastname: Wang
authors.forename: Daniel
authors.initials: D
authors.lastname: Harrison
authors.forename: Vladimir
authors.initials: V
authors.lastname: Lobastov
authors.forename: J Eric
authors.initials: JE
authors.lastname: Tkaczyk
mesh_terms: D000465:Algorithms; D003627:Data Interpretation, Statistical; D018499:Linear Energy Transfer; D017785:Photons; D011829:Radiation Dosage; D011874:Radiometry / Q000379:methods*; D012815:Signal Processing, Computer-Assisted; D014965:X-Rays