title: The Generalized NEQ and Detectability Index for Tomosynthesis and Cone-Beam CT: From Cascaded Systems Analysis to Human Observers.
abstract: OBJECTIVE
  In the early development of new imaging modalities - such as tomosynthesis and cone-beam CT (CBCT) - an accurate predictive model for imaging performance is particularly valuable in identifying the physical factors that govern image quality and guiding system optimization. In this work, a task-based cascaded systems model for detectability index is proposed that describes not only the signal and noise propagation in the 2D (projection) and 3D (reconstruction) imaging chain but also the influence of background anatomical noise. The extent to which generalized detectability index provides a valid metric for imaging performance was assessed through direct comparison to human observer experiments.
  
  
  METHODS
  Detectability index (d') was generalized to include anatomical background noise in the same manner as the generalized noise-equivalent quanta (NEQ) proposed by Barrett et al. (Proc. SPIE Med. Imaging, Vol. 1090, 1989). Anatomical background noise was measured from a custom phantom designed to present power-law spectral density comparable to various anatomical sites (e.g., breast and lung). Theoretical calculations ofd'as a function of the source-detector orbital extent (θtot) was obtained from a 3D cascaded systems analysis model for tomosynthesis and cone-beam CT (CBCT). Four model observers were considered in the calculation ofd': prewhitening (PW), non-prewhitening (NPW), prewhitening with eye filter and internal noise (PWE), and non-prewhitening with eye filter and internal noise (NPWE). Human observer performance was measured from 9AFC tests for a variety of idealized imaging tasks presented within a clutter phantom. Theoretical results (d') were converted to area under the ROC curve (Az) and compared directly to human observer performance as a function of imaging task and orbital extent.
  
  
  RESULTS
  Theoretical results demonstrated reasonable correspondence with human observer response for all tasks across the continuum in θtotranging from low-angle tomosynthesis (θtot~10°) to CBCT (θtot~180°). Both theoretical and experimentalAzwere found to increase with acquisition angle, consistent with increased rejection of out-of-plane clutter for larger tomosynthesis angle. Of the four theoretical model observers considered, the prewhitening models tended to overestimate real observer performance, while the non-prewhitening models demonstrated reasonable agreement.
  
  
  CONCLUSIONS
  Generalized detectability index was shown to provide a meaningful metric for imaging performance, helping to bridge the gap between real observer performance and prevalent Fourier-based metrics based in first principles of spatial-frequency-dependent NEQ and imaging task.
authors.affiliation: Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto ON, Canada M5G2M9.
authors.forename: G J
authors.initials: GJ
authors.lastname: Gang
authors.forename: J
authors.initials: J
authors.lastname: Lee
authors.forename: J W
authors.initials: JW
authors.lastname: Stayman
authors.forename: D J
authors.initials: DJ
authors.lastname: Tward
authors.forename: W
authors.initials: W
authors.lastname: Zbijewski
authors.forename: J L
authors.initials: JL
authors.lastname: Prince
authors.forename: J H
authors.initials: JH
authors.lastname: Siewerdsen
keywords: anatomical clutter; anatomical noise; cascaded systems analysis; cone-beam CT; detectability index; noise-equivalent quanta; noise-power spectrum