Non-Bayesian detection and detectability of anomalies from a few noisy tomographic projections

IEEE Transactions on Signal Processing

Volumn 55, Issue 2, 2007, Pages 401-413

  Fillatre, Lionel ^a   Nikiforov, Igor ^b  

^a ECOLE DES MINES DE NANTES   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE TROYES   (France)

Author keywords

Anomaly detectability; Anomaly detection; Computerized tomography; Deterministic nuisance parameter; Non Bayesian parametric approach; Optimal hypotheses testing

Indexed keywords

COMPUTERIZED TOMOGRAPHY; POLYNOMIALS; SIGNAL NOISE MEASUREMENT; SPURIOUS SIGNAL NOISE; STATISTICAL TESTS;

ANOMALY DETECTABILITY; ANOMALY DETECTION; DETERMINISTIC NUISANCE PARAMETER; NON-BAYESIAN PARAMETRIC APPROACH; OPTIMAL HYPOTHESES TESTING;

SIGNAL DETECTION;

EID: 33847648018     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2006.885693     Document Type: Article

References (42)

1. Y. Bresler and A. Macovski, "Three-dimensional reconstruction from projections with incomplete and noisy data by object estimation," IEEE Trans. Acoust., Speech, Signal Process., vol. 35, pp. 1139-1151, Aug. 1987.
2. J. Idier, Approche Bayésienne pour les problèmes inverses, ser. Traité IC2, Traitement du signal et de l'image. Paris, France: Hermès, 2001.
3. L. E. Bryant, Nondestructive Tesing Handbook, 2nd ed. Columbus, OH: Amer. Soc. for Nondestructive Testing, 1985, vol. 3, Radiography & Testing.
4. A. Rius, G. Ruffini, and L. Cucurull, "Improving the vertical resolution of ionospheric tomography with GPS occultations," Geophys. Res. Lett., vol. 24, pp. 2291-2294, 1997.
5. D. J. Rossi and A. S. Willsky, "Reconstruction from projections based on detection and estimation of objects - Parts I and II: Performance analysis and robustness analysis," IEEE Trans. Acoust., Speech, Signal Process., vol. 32, pp. 886-906, Aug. 1984.
6. A. Frakt, W. Karl, and A. Willsky, "A multiscale hypothesis testing approach to anomaly detection and localization from noisy tomographic data," IEEE Trans. Image Process., vol. 7, pp. 825-837, Jun. 1998.
7. E. Clarkson and H. H. Barrett, "Approximations to ideal-observer performance on signal-detection tasks," Appl. Opt., vol. 39, no. 11, pp. 1783-1793, 2000.
8. M. D. Wheeler and I. Katsushi, "Sensor modeling, probabilistic hypothesis generation, and robust localization for object recognition," IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, no. 3, pp. 252-265, Mar. 1995.
9. D. Mery, T. Jaeger, and D. Filbert, "A review of methods for automated recognition of casting defects," J. Br. Inst. Non-Destruct. Test., vol. 44, no. 7, pp. 428-436, 2002.
10. I. Kazantsev, I. Lemahieu, G. Salov, and R. Denys, "Statistical detection of defects in radiographic images in nondestructive testing," Signal Process., vol. 82, no. 5, pp. 791-801, 2002.
11. G. Wang and T. W. Liao, "Automatic identification of different types of welding defects in radiographic images," NDT&E Int., vol. 35, no. 8, pp. 519-528, 2002.
12. H. Boerner and H. Strecker, "Automated x-ray inspection of aluminium casting," IEEE Trans. Pattern Anal. Mach. Intell., vol. 10, no. 1, pp. 79-91, 1988.
13. A. Kehoe and G. Parker, "An intelligent knowledge based approach for the automated radiographic inspection of castings," NDT&E Int., vol. 25, no. 1, pp. 23-36, 1992.
14. S. Lawson and G. Parker, "Intelligent segmentation of industrial radiographic images using neural networks," in Machine Vision Applications Systems Integration III, Proc. SPIE, 1994, vol. 2347, pp. 245-255.
15. A. Gayer, A. Saya, and A. Shiloh, "Automatic recognition of welding defects in real-time radiography," NDT&E Int., vol. 23, no. 4, pp. 131-136, 1990.
16. D. Mery and D. Filbert, "Automated flaw detection in aluminum castings based on the tracking of potential defects in a radioscopic image sequence," IEEE Trans. Robot. Automat., vol. 18, pp. 890-901, 2002.
17. K. Castleman, Digital Image Processing, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.
18. F. Natterer, The Mathematics of Computerized Tomography. New York: Wiley, 1986.
19. G. Demoment, "Image reconstruction and restoration: Overview of common estimation structures and problems," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 12, pp. 2024-2036, 1989.
20. M. Davidson, "The ill-conditionned nature of the limited angle tomography problem," SIAM J. Appl. Math., vol. 42, no. 3, pp. 428-448, 1983.
21. E. Miller and A. Willsky, "Multiscale, statistical anomaly detection analysis and algorithms for linearized inverse scattering problems," Multidimens. Syst. Signal Process., vol. 8, pp. 151-184, 1997.
22. H. H. Barrett and K. J. Myers, Foundations of Image Science. New York: Wiley, 2004.
23. L. Fillatre and I. Nikiforov, "A statistical detection of an anomaly from a few noisy tomographic projections," J. Appl. Signal Process. (Special Issue on Advances in Intelligent Vision Systems: Methods and Applications-Part II), no. 14, pp. 2215-2228, 2005.
24. G. R. Tillack, C. Nockemann, and C. Bellon, "X-ray modelling for industrial applications," NDT&E Int., vol. 33, no. 1, pp. 481-488, 2000.
25. B. Chalmond, F. Coldefy, and B. Lavayssiere, "Tomographic reconstruction from non-calibrated noisy projections in non-destructive evaluation," Inverse Problems, vol. 15, no. 2, pp. 399-411, 1999.
26. F. Retraint, "Contrôle non destructif de pièces industrielles par radiographie: Caractérisation quantitative et reconstruction 3-D à partir d'un nombre limité de vues," Ph.D. dissertation, INSA, Lyon, France, 1998.
27. I. Elbakri and J. Fessler, "Statistical image for reconstruction for polyenergetic X-ray computed tomography," IEEE Trans. Med. Imag., vol. 21, pp. 89-99, 2002.
28. D. Parker, "Optimal short scan convolution reconstruction for ban-beam CT," Med. Phys., vol. 9, pp. 254-257, 1982.
29. A. Naparstek, "Short-scan fan-beam algorithm for CT," IEEE Trans. Nucl. Sci., vol. ns27, pp. 1112-1120, 1980.
30. T. Peters and R. Lewitt, "Computed tomography with fan-beam geometry," J. Comput. Assist. Tomogr., vol. 1, pp. 429-436, 1977.
31. K. M. Hanson and G. W. Wecksung, "Local basis-function approach to computed tomography," Appl. Opt., vol. 24, pp. 4028-4039, 1985.
32. L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Trans. Signal Process., vol. 42, pp. 2146-2157, 1994.
33. M. Fouladirad and I. Nikiforov, "Optimal statistical fault detection with nuisance parameters," Automatica, vol. 41, no. 7, pp. 1157-1171, Jul. 2005.
34. L. Scharf, Statistical Signal Processing. Detection, Estimation, and Time Series Analysis. Reading, MA: Addison-Wesley, 1991.
35. C. Rao, Linear Statistical Inference and its Applications, second ed. New York: Wiley, 1973.
36. A. A. Borovkov, Mathematical Statistics. Amsterdam, The Netherlands: Gordon and Breach Sciences Publishers, 1998.
37. E. Lehman, Testing Statistical Hypotheses, 2nd ed. London, UK.: Chapman & Hall, 1986.
38. A. Wald, "Tests of statistical hypotheses concerning several parameters when the number of observations is large," Trans. Amer. Math. Soc., vol. 54, pp. 426-482, 1943.
39. M. Basseville and I. V. Nikiforov, Detection of Abrupt Changes: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1993.
40. M. Shahram and P. Milanfar, "Imaging below the diffraction limit: A statistical analysis," IEEE Trans. Image Process., vol. 13, pp. 677-689, May 2004.
41. R. Palenichka, A. Alekseichuk, and U. Zscherpel, "Flaw detection in radiographic images by structure-adaptive binary segmentation," in International Symposium on Computerized Tomography for Industrial Applications and Image Processing in Radiology, ser. Proceedings. Berlin, Germany: DGZfP, 1999, pp. 221-232.
42. D. A. Harville, Matrix Algebra from a Statistician's Perspective. New York: Springer-Verlag, 1997.