OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 6 — Jun. 1, 2012
  • pp: 1003–1016

Objective assessment of image quality. V. Photon-counting detectors and list-mode data

Luca Caucci and Harrison H. Barrett  »View Author Affiliations


JOSA A, Vol. 29, Issue 6, pp. 1003-1016 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001003


View Full Text Article

Enhanced HTML    Acrobat PDF (328 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A theoretical framework for detection or discrimination tasks with list-mode data is developed. The object and imaging system are rigorously modeled via three random mechanisms: randomness of the object being imaged, randomness in the attribute vectors, and, finally, randomness in the attribute vector estimates due to noise in the detector outputs. By considering the list-mode data themselves, the theory developed in this paper yields a manageable expression for the likelihood of the list-mode data given the object being imaged. This, in turn, leads to an expression for the optimal Bayesian discriminant. Figures of merit for detection tasks via the ideal and optimal linear observers are derived. A concrete example discusses detection performance of the optimal linear observer for the case of a known signal buried in a random lumpy background.

© 2012 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(040.1880) Detectors : Detection
(110.3000) Imaging systems : Image quality assessment
(110.4280) Imaging systems : Noise in imaging systems
(170.0110) Medical optics and biotechnology : Imaging systems
(330.1880) Vision, color, and visual optics : Detection

ToC Category:
Imaging Systems

History
Original Manuscript: January 13, 2012
Manuscript Accepted: March 9, 2012
Published: May 25, 2012

Citation
Luca Caucci and Harrison H. Barrett, "Objective assessment of image quality. V. Photon-counting detectors and list-mode data," J. Opt. Soc. Am. A 29, 1003-1016 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-6-1003


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. H. Barrett, “Objective assessment of image quality: effects of quantum noise and object variability,” J. Opt. Soc. Am. A 7, 1266–1278 (1990). [CrossRef]
  2. H. H. Barrett, J. L. Denny, R. F. Wagner, and K. J. Myers, “Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995). [CrossRef]
  3. H. H. Barrett, C. K. Abbey, and E. Clarkson, “Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions,” J. Opt. Soc. Am. A 15, 1520–1535 (1998). [CrossRef]
  4. H. H. Barrett, K. J. Myers, N. Devaney, and C. Dainty, “Objective assessment of image quality. IV. Application to adaptive optics,” J. Opt. Soc. Am. A 23, 3080–3105 (2006). [CrossRef]
  5. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley-Interscience, 2004).
  6. K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, “Effect of noise correlation on detectability of disk signals in medical imaging,” J. Opt. Soc. Am. A 2, 1752–1759 (1985). [CrossRef]
  7. W. E. Smith and H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am. A 3, 717–725 (1986). [CrossRef]
  8. R. D. Fiete, H. H. Barrett, W. E. Smith, and K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987). [CrossRef]
  9. K. M. Hanson, “Method of evaluating image-recovery algorithms based on task performance,” J. Opt. Soc. Am. A 7, 1294–1304 (1990). [CrossRef]
  10. A. E. Burgess, “Statistically defined backgrounds: performance of a modified nonprewhitening observer model,” J. Opt. Soc. Am. A 11, 1237–1242 (1994). [CrossRef]
  11. A. E. Burgess, X. Li, and C. K. Abbey, “Visual signal detectability with two noise components: anomalous masking effects,” J. Opt. Soc. Am. A 14, 2420–2442 (1997). [CrossRef]
  12. F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds,” J. Opt. Soc. Am. A 17, 193–205 (2000). [CrossRef]
  13. C. K. Abbey and M. P. Eckstein, “Derivation of a detectability index for correlated responses in multiple-alternative forced-choice experiments,” J. Opt. Soc. Am. A 17, 2101–2104 (2000). [CrossRef]
  14. M. P. Eckstein, C. K. Abbey, and F. O. Bochud, “Visual signal detection in structured backgrounds. IV. Figures of merit for model performance in multiple-alternative forced-choice detection tasks with correlated responses,” J. Opt. Soc. Am. A 17, 206–217 (2000). [CrossRef]
  15. M. A. Kupinski, J. W. Hoppin, E. Clarkson, and H. H. Barrett, “Ideal-observer computation in medical imaging with use of Markov-chain Monte Carlo techniques,” J. Opt. Soc. Am. A 20, 430–438 (2003). [CrossRef]
  16. L. Chen and H. H. Barrett, “Task-based lens design with application to digital mammography,” J. Opt. Soc. Am. A 22, 148–167 (2005). [CrossRef]
  17. J. Rolland, J. O’Daniel, C. Akcay, T. DeLemos, K. S. Lee, K.-I. Cheong, E. Clarkson, R. Chakrabarti, and R. Ferris, “Task-based optimization and performance assessment in optical coherence imaging,” J. Opt. Soc. Am. A 22, 1132–1142 (2005). [CrossRef]
  18. L. Caucci, H. H. Barrett, N. Devaney, and J. J. Rodríguez, “Application of the Hotelling and ideal observers to detection and localization of exoplanets,” J. Opt. Soc. Am. A 24, B13–B24 (2007). [CrossRef]
  19. A. E. Burgess and P. F. Judy, “Signal detection in power-law noise: effect of spectrum exponents,” J. Opt. Soc. Am. A 24, B52–B60 (2007). [CrossRef]
  20. C. K. Abbey and M. P. Eckstein, “Classification images for simple detection and discrimination tasks in correlated noise,” J. Opt. Soc. Am. A 24, B110–B124 (2007). [CrossRef]
  21. T. D. Dixon, E. F. Canga, S. G. Nikolov, T. Troscianko, J. M. Noyes, C. N. Canagarajah, and D. R. Bull, “Selection of image fusion quality measures: objective, subjective, and metric assessment,” J. Opt. Soc. Am. A 24, B125–B135 (2007). [CrossRef]
  22. L. Platiša, B. Goossens, E. Vansteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized Hotelling observers for the assessment of volumetric imaging data sets,” J. Opt. Soc. Am. A 28, 1145–1163 (2011). [CrossRef]
  23. R. F. Wagner and D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985). [CrossRef]
  24. E. C. Frey, K. L. Gilland, and B. M. W. Tsui, “Application of task-based measures of image quality to optimization and evaluation of three-dimensional reconstruction-based compensation methods in myocardial perfusion SPECT,” IEEE Trans. Med. Imag. 21, 1040–1050 (2002). [CrossRef]
  25. X. He, E. C. Frey, J. M. Links, K. L. Gilland, W. P. Segars, and B. M. W. Tsui, “A mathematical observer study for the evaluation and optimization of compensation methods for myocardial SPECT using a phantom population that realistically models patient variability,” IEEE Trans. Nucl. Sci. 51, 218–224(2004). [CrossRef]
  26. G. J. Gang, J. Lee, J. L. Prince, J. W. Stayman, D. J. Tward, W. Zbijewski, and J. H. Siewerdsen, “Analysis of Fourier-domain task-based detectability index in tomosynthesis and cone-beam CT in relation to human observer performance,” Med. Phys. 38, 1754–1768 (2011). [CrossRef]
  27. H. Hotelling, “The generalization of student’s ratio,” Ann. Math. Stat. 2, 360–378 (1931). [CrossRef]
  28. K. J. Myers and H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987). [CrossRef]
  29. C. Papaliolios and L. Mertz, “New two-dimensional photon camera,” Proc. SPIE 331, 360–369 (1982).
  30. C. Papaliolios, P. Nisenson, and S. Ebstein, “Speckle imaging with the PAPA detector,” Appl. Opt. 24, 287–292 (1985). [CrossRef]
  31. J. G. Timothy, J. S. Morgan, D. C. Slater, D. B. Kasle, and R. L. Bybee, “MAMA detector systems: a status report,” Proc. SPIE 1158, 104–117 (1989).
  32. J. G. Timothy, “Optical detectors for spectroscopy,” Pub. Astron. Soc. Pac. 95, 810–834 (1983). [CrossRef]
  33. P. Bruyndonckx, C. Lemaître, D. Schaart, M. Maas, D. J. van der Laan, M. Krieguer, O. Devroede, and S. Tavernier, “Towards a continuous crystal APD-based PET detector design,” Nucl. Instrum. Methods Phys. Res. A 571, 182–186 (2007). [CrossRef]
  34. K. A. Bostroem, A. Aloisi, R. Bohlin, R. Diaz, V. Dixon, P. Goudfrooij, P. Hodge, D. Lennon, C. Long, S. Niemi, R. Osten, C. Proffitt, N. Walborn, T. Wheeler, M. Wolfe, B. York, and W. Zheng, STIS Instrument Handbook, Version 10.0 (Space Telescope Science Institute, 2010).
  35. H. O. Anger, “Scintillation camera,” Rev. Sci. Instrum. 29, 27–33 (1958). [CrossRef]
  36. M. N. Wernick and J. N. Aarsvold, Emission Tomography: The Fundamentals of PET and SPECT (Elsevier Academic, 2004).
  37. P. C. Johns, J. Dubeau, D. G. Gobbi, M. Li, and M. S. Dixit, “Photon-counting detectors for digital radiography and x-ray computed tomography,” Proc. SPIE TD01, 367–369 (2002).
  38. P. M. Shikhaliev, T. Xu, and S. Molloi, “Photon counting computed tomography: concept and initial results,” Med. Phys. 32, 427–436 (2005). [CrossRef]
  39. W. C. J. Hunter, H. H. Barrett, and L. R. Furenlid, “Calibration method for ML estimation of 3D interaction position in a thick gamma-ray detector,” IEEE Trans. Nucl. Sci. 56, 189–196 (2009). [CrossRef]
  40. J. Y. Hesterman, L. Caucci, M. A. Kupinski, H. H. Barrett, and L. R. Furenlid, “Maximum-likelihood estimation with a contracting-grid search algorithm,” IEEE Trans. Nucl. Sci. 57, 1077–1084 (2010). [CrossRef]
  41. T. Takahashi, K. Nakazawa, T. Kamae, H. Tajima, Y. Fukazawa, M. Nomachi, and M. Kokubun, “High resolution CdTe detectors for the next-generation multi-Compton gamma-ray telescope,” Proc. SPIE 4851, 1228–1235 (2002). [CrossRef]
  42. E. C. Bellm, S. E. Boggs, M. S. Bandstra, J. D. Bowen, D. Perez-Becker, C. B. Wunderer, A. Zoglauer, M. Amman, P. N. Luke, H.-K. Chang, J.-L. Chiu, J.-S. Liang, Y.-H. Chang, Z.-K. Liu, W.-C. Hung, C.-H. Lin, M. A. Huang, and P. Jean, “Overview of the nuclear Compton telescope,” IEEE Trans. Nucl. Sci. 56, 1250–1256 (2009). [CrossRef]
  43. A. Zoglauer, R. Andritschke, and G. Kanbach, “Data analysis for the MEGA prototype,” New Astron. Rev. 48, 231–235 (2004). [CrossRef]
  44. G. K. Kitaeva and A. N. Penin, “Spontaneous parametric down-conversion,” JETP Lett. 82, 350–355 (2005). [CrossRef]
  45. A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photon. 2, 238–241 (2008). [CrossRef]
  46. M. B. Nasr, O. Minaeva, G. N. Goltsman, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Submicron axial resolution in an ultrabroadband two-photon interferometer using superconducting single-photon detect,” Opt. Express 16, 15104–15108(2008). [CrossRef]
  47. A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004). [CrossRef]
  48. A. J. Reader, S. Ally, F. Bakatselos, R. Manavaki, R. J. Walledge, A. P. Jeavons, P. J. Julyan, S. Zhao, D. L. Hastings, and J. Zweit, “One-pass list-mode EM algorithm for high-resolution 3-D PET image reconstruction into large arrays,” IEEE Trans. Nucl. Sci. 49, 693–699 (2002). [CrossRef]
  49. P. Khurd, I.-T. Hsiao, A. Rangarajan, and G. Gindi, “A globally convergent regularized ordered-subset EM algorithm for list-mode reconstruction,” IEEE Trans. Nucl. Sci. 51, 719–725 (2004). [CrossRef]
  50. A. J. Reader, K. Erlandsson, R. J. Ott, and M. A. Flower, “Attenuation and scatter correction of list-mode data driven iterative and analytic image reconstruction algorithms for rotating 3D PET systems,” IEEE Trans. Nucl. Sci. 46, 2218–2226 (1999). [CrossRef]
  51. L. Parra and H. H. Barrett, “List-mode likelihood: EM algorithm and image quality estimation demonstrated on 2-D PET,” IEEE Trans. Med. Imag. 17, 228–235 (1998). [CrossRef]
  52. D. L. Snyder, and D. G. Politte, “Image reconstruction from list-mode data in an emission tomography system having time-of-flight measurements,” IEEE Trans. Nucl. Sci. 30, 1843–1849 (1983). [CrossRef]
  53. A. J. Reader, K. Erlandsson, M. A. Flower, and R. J. Ott, “Fast accurate iterative reconstruction for low-statistics positron volume imaging,” Phys. Med. Biol. 43, 835–846 (1998). [CrossRef]
  54. C. Byrne, “Likelihood maximization for list-mode emission tomographic image reconstruction,” IEEE Trans. Med. Imag. 20, 1084–1092 (2001). [CrossRef]
  55. R. H. Huesman, G. J. Klein, W. W. Moses, J. Qi, B. W. Reutter, and P. R. G. Virador, “List-mode maximum-likelihood reconstruction applied to positron emission mammography (PEM) with irregular sampling,” IEEE Trans. Med. Imag. 19, 532–537 (2000). [CrossRef]
  56. R. Levkovitz, D. Falikman, M. Zibulevsky, A. Ben-Tal, and A. Nemirovski, “The design and implementation of COSEN, an iterative algorithm for fully 3-D listmode data,” IEEE Trans. Med. Imag. 20, 633–642 (2001). [CrossRef]
  57. H. H. Barrett, T. White, and L. C. Parra, “List-mode likelihood,” J. Opt. Soc. Am. A 14, 2914–2923 (1997). [CrossRef]
  58. S. Surti, J. S. Karp, L. M. Popescu, M. E. Daube-Witherspoon, and M. Werner, “Investigation of image quality and NEC in a TOF-capable PET scanner,” in IEEE Nuclear Science Symposium Conference Record (IEEE, 2004), pp. 4032–4037.
  59. B. Guérin and G. E. Fakhri, “Novel scatter compensation of list-mode PET data using spatial and energy dependent corrections,” IEEE Trans. Med. Imag. 30, 759–773 (2011). [CrossRef]
  60. D. L. Snyder, “Parameter estimation for dynamic studies in emission-tomography systems having list-mode data,” IEEE Trans. Nucl. Sci. 31, 925–931 (1984). [CrossRef]
  61. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, “Introducing Markov chain Monte Carlo,” in Markov Chain Monte Carlo in Practice, W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, eds. (Chapman & Hall/CRC, 1996), Chap. 1.
  62. R. M. Neal, “Probabilistic inference using Markov chain Monte Carlo methods,” Tech. Rep. CRG-TR-93-1 (Department of Computer Science, University of Toronto, 1993).
  63. A. Lehovich, “List-mode SPECT reconstruction using empirical likelihood,” Ph.D. thesis (University of Arizona, 2005).
  64. S. Korpar, P. Križan, R. Pestotnik, A. Gorišek, A. Stanovnik, M. Starič, and D. Škrk, “Multianode photomultipliers as position-sensitive detectors of single photons,” Nucl. Instrum. Methods Phys. Res. A 442, 316–321 (2000). [CrossRef]
  65. J. P. Rolland and H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992). [CrossRef]
  66. Z. X. Wang and D. R. Guo, Special Functions (World Scientific, 1989).
  67. A. Apelblat, Table of Definite and Infinite Integrals (Elsevier Scientific, 1983).
  68. G. E. Andrews, R. Askey, and R. Roy, Special Functions(Cambridge University, 2000).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited