Error bounds in nonsmooth image deblurring

SIAM Journal on Mathematical Analysis

Volumn 28, Issue 3, 1997, Pages 656-668

  Carasso, Alfred S ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

Error bounds; Ill posed problems; Image deblurring; Infinitely smoothing operators; Nonsmooth images; PET imaging; SECB restoration; Tikhonov Miller restoration

Indexed keywords

EID: 0031531628     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141095290215     Document Type: Article

References (27)

1. H. C. ANDREWS AND B. R. HUNT, Digital Image Restoration, Prentice-Hall, Englewcod Cliffs, NJ, 1977.
2. M. BANISH, R. CLARK, AND A. KATHMAN, A validated code to predict the performance of onboard broadband optical seekers through a turbulent transonic flow, AIAA 92-2792, in Proc. 1992 AIAA SDIO Annual Interceptor Technology Conference, American Institute of Aeronautics and Astronautics, Washington, DC, 1992.
3. A. S. CARASSO, Overcoming Hölder continuity in ill-posed continuation problems, SIAM J. Numer. Anal., 31 (1994), pp. 1535-1557.
4. K. A. COSTELLO, V. W. AEBI, AND H. F. MACMILLAN, Imaging GaAs vacuum photodiode with 40% quantum efficiency at 530 nm, SPIE Proc., 1243 (1990), pp. 99-106.
5. W. FELLER, An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd ed., John Wiley, New York, 1971.
6. J. N. FRANKLIN, On Tikhonov's method for ill-posed problems, Math. Comp., 28 (1974), pp. 889-907.
7. R. C. GONZALEZ AND P. WINTZ, Digital Image Processing, 2nd ed., Addison-Wesley, Reading, MA, 1987.
8. Y. HIGASHIDA, K. D. DOI, AND H. B. MACMAHON, Dual-film cassette technique for studying the effect of radiographic image quality on diagnostic accuracy, Med. Phys., 11 (1984), pp. 646-652.
9. F. JOHN, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math., 13 (1960), pp. 551-585.
10. C. B. JOHNSON, Classification of electron-optical device modulation transfer function, Adv. Electron. Electron Phys., 33B (1972), pp. 579-584.
11. C. B. JOHNSON, S. B. PATTON, AND E. BENDER, High resolution microchannel plate image tube development, SPIE Proc., 1449 (1991), pp. 2-12.
12. P. KARPUR AND B. G. FROCK, Two-dimensional pseudo-Wiener filtering in ultrasonic imaging for nondestructive evaluation applications, in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 8A, Plenum Press, New York, 1989, pp. 743-750.
13. H. KUHN AND W. KNUPFER, Imaging characteristics of different mammographic screens, Med. Phys., 19 (1992), pp. 449-457.
14. R. L. LAGENDIJK AND J. BIEMOND, Iterative Identification and Restoration of Images, Kluwer Academic Publishers, Norwell, MA, 1991.
15. B. A. MAIR, Tikhonov regularization for finitely and infinitely smoothing operators, SIAM J. Math. Anal., 25 (1994), pp. 135-147.
16. K. MILLER, Least squares methods for ill-posed problems with a prescribed bound, SIAM J. Math. Anal., 1 (1970), pp. 52-74.
17. S. M. MOHAPATRA, J. D. TURLEY, J. R. PRINCE, J. C. BLECHINGER, AND D. A. WILSON, Transfer function measurement and analysis for a magnetic resonance imager, Med. Phys., 18 (1991) pp. 1141-1144.
18. E. L. NICKOLOFF AND R. RILEY, A simplified approach for modulation transfer function determinations in computed tomography, Med. Phys., 12 (1985), pp. 437-442.
19. P. J. PAPIN AND H. K. HUANG, A prototype amorphous selenium imaging plate, Med. Phys., 14 (1987), pp. 322-329.
20. K. S. PENTLOW, M. C. GRAHAM, R. M. LAMBRECHT, K. V. CHEUNG, AND S. M. LARSON, Quantitative imaging of I-124 using positron emission tomography with applications to radioimmunodiagnosis and radioimmunotherapy, Med. Phys., 18 (1991), pp. 357-366.
21. W. K. PRATT, Digital Image Processing, 2nd ed., John Wiley, New York, 1991.
22. U. RAFF, D. N. STROUD, AND W. R. HENDEE, Improvement of lesion detection in scintigraphic images by SVD techniques for resolution recovery, IEEE Trans. Med. Imaging, MI-5 (1986), pp. 35-44.
23. S. RUDIN, D. BEDNAREK, AND R. WONG, Improving fluoroscopic image quality with continuously variable zoom magnification, Med. Phys., 19 (1991), pp. 972-977.
24. M. TAKAHASHI, S. YOSHIOKA, H. BUSSAKA, Y. HIGASHIDA, M. KAMIYA, AND M. TSUNEOKA, Digital TV tomography: Description and physical assessment, Med. Phys., 17 (1990), pp. 681-685.
25. F. C. WAGNER, A. MACOVSKI, AND D. G. NISHIMURA, A characterization of scatter point spread functions in terms of air gaps, IEEE Trans. Med. Imaging, 7 (1988), pp. 337-344.
26. J. C. WYANT, ED., Imaging through the atmosphere, SPIE Proc., 75 (1976).
27. H. T. YURA, Imaging in clear ocean water, Appl. Optics, 12 (1973), pp. 1061-1066.