Determination of x-ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation

Medical Physics

Volumn 34, Issue 3, 2007, Pages 994-1006

  Delgado, Víctor ^a,b  

^a UNIVERSIDAD NACIONAL DE CÓRDOBA   (Argentina)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Attenuation curve; Deconvolution; X ray spectra

Indexed keywords

DECONVOLUTION; IMAGE SEGMENTATION; MAXIMUM PRINCIPLE; X RAY SPECTROGRAPHS;

ATTENUATION CURVE; ATTENUATION MEASUREMENTS; EXPECTATION-MAXIMIZATION METHOD; EXPERIMENTAL VALIDATIONS; GENERALIZED MOMENTS; ILL CONDITIONED PROBLEMS; SPECTRAL DISTRIBUTION; X-RAY SPECTRA;

X RAYS;

ARTICLE; ATTENUATION; EXPERIMENT; PRIORITY JOURNAL; ROENTGEN SPECTROSCOPY; SIMULATION; THEORY VALIDATION; VALIDATION STUDY;

EID: 33847667857     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.2436971     Document Type: Article

References (48)

1. L. Silberstein, " Determination of the spectral composition of x-ray radiation from filtration data., " J. Opt. Soc. Am. 22, 265-280 (1932).
2. L. Silberstein, " Spectral composition of an x-ray radiation determined from its filtration curve., " Philos. Mag. XV, No. 98, Suppl., Feb., 375-394 (1933).
3. J. R. Greening, " The determination of x-ray wavelength distribution from absorption data., " Proc. Phys. Soc., London, Sect. A 63, 1227-1234 (1950).
4. J. W. Twidell, " The mathematical method for determining kVp from x-ray attenuation measurements., " Med. Phys. 2, 201-207 (1975).
5. P. M. Joseph, and L. C. Baird, " X-ray spectra vs attenuation data: A theoretical analysis., " Med. Phys. 8, 319-323 (1981).
6. P. H. Huang, K. R. Kase, and B. E. Bjarngard, " Spectral characterization of 4 MV bremsstrahlung by attenuation analysis., " Med. Phys. 8, 368-374 (1981).
7. S. Tominaga, " The estimation of x-ray spectral distribution from attenuation data by means of iterative computation., " Nucl. Instrum. Methods 192, 415-421 (1982).
8. P.-H. Huang, K. R. Kase, and B. E. Bjarngard, " Simulation studies of 4 MV x-ray spectral reconstruction by numerical analysis of transmission data., " Med. Phys. 9, 695-702 (1982).
9. H. M. Kramer and H. Von Seggern, " The determination of x-ray spectra from attenuation data: Part I: The potentials of various methods., " Nucl. Instrum. Methods 213, 373-380 (1983).
10. H. M. Kramer, " The determination of x-ray spectra from attenuation data: Part II: Experimental results., " Nucl. Instrum. Methods 214, 445-450 (1983).
11. P. H. Huang, T. S. Cheng, and K. R. Kase, " Reconstruction of diagnostic x-ray spectra by numerical analysis of transmission data., " Med. Phys. 13, 707-710 (1986).
12. P. Francois, A. Catala, and Ch. Scouarnec, " Simulation of x-ray spectral reconstruction from transmission data by direct resolution of the numerical system AF=T., " Med. Phys. 20, 1695-1703 (1993).
13. P. Francois, A. Catala, J. Bonnet, and Ch. Scouarnec, " Reconstruction of 12 MV bremsstrahlung spectra from measured transmission data by direct resolution of the numeric system AF=T., " Med. Phys. 22 (1995).
14. M. Krmar, J. Slivka, I. Bikit, M. Veskovic, and Lj. Conkic, " Evaluation of bremstrahlung spectra generated by a 4 MeV linear accelerator., " Med. Phys. 23, 651-654 (1996).
15. P. Francois, F. Coste, J. Bonnet, and O. Caselles, " Validation of reconstructed bremsstrahlung spectra between 6 MV and 25 MV from measured transmission data., " Med. Phys. 24, 769-773 (1997).
16. R. G. Waggener, M. M. Blough, J. A. Terry, D. Chen, N. E. Lee, S. Zhang, and W. D. McDavid, " X-ray spectra estimation using attenuation measurements from 25 kVp to 18 MV., " Med. Phys. 26, 1269-1278 (1999).
17. M. Stampanoni, M. Fix, P. Francois, and P. Ruegsegger, " Computer algebra for x-ray spectral reconstruction between 6 and 25 MV., " Med. Phys. 28, 325-327 (2001).
18. W. H. Hinson and J. D. Bourland, " Spectral reconstruction of high energy photon beams for kernel based dose calculations., " Med. Phys. 29, 1789-1796 (2002).
19. B. Armbruster, R. J. Hamilton, and A. K. Kuehl, " Spectrum reconstruction from dose measurements as a linear inverse problem., " Phys. Med. Biol. 49, 5087-5099 (2004).
20. J. M. Boone, " Equivalent spectra as a measure of beam quality., " Med. Phys. 13, 861-868 (1986).
21. J. M. Boone, " The three parameter equivalent spectra as an index of beam quality., " Med. Phys. 15, 304-310 (1990).
22. J. M. Boone, " X-ray spectral reconstruction from attenuation data using neural networks., " Med. Phys. 17, 647-650 (1990).
23. B. R. Archer and L. K. Wagner, " A Laplace transform pair model for spectral reconstruction., " Med. Phys. 9, 844-847 (1982).
24. M. Rubio and R. T. Mainardi, " Determination of x-ray spectra including characteristic line intensities from attenuation data., " Phys. Med. Biol. 29, 1371-1376 (1984).
25. B. R. Archer, P. R. Almond, and L. K. Wagner, " Application of a Laplace transform pair model for high-energy x-ray spectral reconstruction., " Med. Phys. 12, 630-633 (1985).
26. B. R. Archer, and L. K. Wagner, " Determination of diagnostic x-ray spectra with characteristic radiation using attenuation analysis., " Med. Phys. 15, 637-643 (1988).
27. B. R. Archer and L. K. Wagner, " A modified x-ray spectra reconstruction technique., " Phys. Med. Biol. 33, 1399-1406 (1988).
28. B. R. Archer, and L. K. Wagner, " A modified x-ray spectra reconstruction technique., " Phys. Med. Biol. 34, 539-539 (1989).
29. B. R. Archer, T. R. Fewell, and L. K. Wagner, " Laplace reconstruction of experimental diagnostic x-ray spectra., " Med. Phys. 15, 832-837 (1988).
30. G. M. Wing and J. D. Zahrt. A Primer on Integral Equations of the First Kind (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1991).
31. V. Delgado and P. Ortiz, " The narrow beam attenuation curve as a functional description of a low energy x-ray beam., " X-Ray Spectrom. 20, 343-344 (1991).
32. P. Ortiz and V. Delgado, " The narrow beam attenuation curve as a mean of assessing the energy imparted to a phantom by a low energy x-ray beam., " Radiat. Prot. Dosim. 49 (1-3), 349-351 (1993).
33. P. Ortiz, Doctoral thesis, Universidad Complutense, Madrid, Spain (1993).
34. V. Delgado and P. Ortiz, " Determination of the energy fluence of diagnostic x-ray beams from field measurements of attenuation curves., " Med. Phys. 24, 1089-1095 (1997).
35. V. Delgado, " Comparison between measured and predicted attenuation curves of x-ray beams., " Med. Phys. 26, 2183-2189 (1999).
36. M. Pruksch and F. Fleischmann, " Positive iterative deconvolution in comparison to Richardson-Lucy like algorithms., " Astronomical Data-Analysis Software and Systems VII ASP Conference Series, Vol. 145,, R. Albrecht,,, R. N. Hook,, and, H. A. Bushouse,, Astronomical Society of the Pacific, 496-499 (1998).
37. E. Y. Sidky, Yu Lifeng, Pan Xiaochuan, Zou Yu, and M. Vannier, " A robust method of x-ray source spectrum estimation from transmission measurements: Demonstrated on computer simulated, scatter-free transmission data., " J. Appl. Phys. 97, 124701-1-124701-11 (2005).
38. L. D. Paniak and P. M. Charland, " Enhanced bremsstrahlung spectrum reconstruction from depth dose gradients., " Phys. Med. Biol. 50, 3245-3261 (2005).
39. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series, Vol. 55, Dover, New York (1965).
40. J. H. Hubbell and S. M. Seltzer, " Tables of x-ray mass attenuation coefficients and mass energy-absorption coefficients from 1 keV to 20 MeV for elements Z=1 to 92 and 48 Additional Substances of Dosimetric Interes., " NISTIR 5632 (http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html) Ionizing Radiation Division, Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (1996).
41. Mathcad. Mathsoft Engineering, www.mathsoft.com
42. See EPAPS Document No. E-MPHYA6-34-003703 for supplementary figures and tables. This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/ epaps.html).
43. J. Reilly and D. Sutton, " Report 78 spectrum processor., " IPEM Report (1997).
44. V. Delgado and P. Ortiz, " Calculation of integral quantities from the narrow beam attenuation curve of a low energy x-ray beam., " Radiat. Prot. Dosim. 48, 273-277 (1993).
45. V. Delgado and P. Ortiz, " Energy imparted to a phantom by a low energy x-ray beam: Calculation from its narrow beam attenuation curve and comparison with experiments., " Appl. Radiat. Isot. 46, 437-438 (1995).
46. G. J. Michael, " Determination of equivalent x-ray spectra from attenuation data., " Prog. Semicond. 18, 124-32 (1995).
47. L. B. Lucy, " Image restoration of high photometric quality., " in Proc., Restoration of HST Images and Spectra,, R. J. Hanisch, and, R. L. White,, Eds. STSci, pp. 79-85 (1994).
48. R. Molina, J. Nuñez, F. Cortijo, and J. Mateos " Image restoration in astronomy. A Bayesian perspective., " IEEE Signal Process. Mag. 18, 11-29 (2001).