Image reconstruction: A unifying model for resolution enchancement and data extrapolation. Tutorial

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 23, Issue 2, 2006, Pages 258-266

  Shieh, Hsin M ^a   Byrne, Charles L ^b   Fiddy, Michael A ^c  

^a FENG CHIA UNIVERSITY   (Taiwan)

^b University of Massachusetts Lowell   (United States)

^c UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ESTIMATION; EXTRAPOLATION; IMAGE ENHANCEMENT; ITERATIVE METHODS; MATHEMATICAL MODELS;

DATA EXTRAPOLATION; ITERATIVE SHANNON-ENTROPY-MAXIMATION ALGORITHMS; MINIMUM-WEIGHTED-NORM (MWN) ESTIMATION; RESOLUTION ENHANCEMENT;

IMAGE RECONSTRUCTION;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; STATISTICAL MODEL; THREE DIMENSIONAL IMAGING;

ALGORITHMS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL;

EID: 33644502848     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.23.000258     Document Type: Article

References (27)

1. R. W. Gerchberg, "Super-restoration through error energy reduction," Opt. Acta 21, 709-720 (1974).
2. A. Papoulis, "A new algorithm in spectral analysis and band-limited extrapolation," IEEE Trans. Circuits Syst. 22, 735-742 (1975).
3. J. Burg, "Maximum entropy spectral analysis," presented at the 37th Annual Society of Exploration Geophysicists Meeting, Oklahoma City, Oklahoma, July 1967.
4. J. Burg, "The relationship between maximum entropy spectra and maximum likelihood spectra," Geophysics 37, 375-376 (1972).
5. J. Burg, "Maximum Entropy Spectral Analysis," Ph.D. thesis (Stanford University, Stanford, California, 1975).
6. M. Bertero, "Sampling theory, resolution limits and inversion methods," in Inverse Problems in Scattering and Imaging, M. Bertero and E. R. Pike, eds. (Malvern Physics Series, Adam Hilger, IOP Publishing, 1992), pp. 71-94.
7. C. L. Byrne and R. M. Fitzgerald, "A unifying model for spectrum estimation," presented at the Rome Air Development Center Workshop on Spectrum Estimation, Griffiss Air Force Base, Rome, New York, October 3-5, 1979.
8. H. Stark and Y. Yang, Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets and Optics (Wiley, 1998).
9. H. Cox, "Resolving power and sensitivity to mismatch of optimum array processors," J. Acoust. Soc. Am. 54, 771-785 (1973).
10. C. L. Byrne and R. M. Fitzgerald, "Reconstruction from partial information, with applications to tomography," SIAM J. Appl. Math. 42, 933-940 (1982).
11. C. L. Byrne, R. M. Fitzgerald, M. A. Fiddy, T. J. Hall, and A. M. Darling, "Image restoration and resolution enhancement," J. Opt. Soc. Am. 73, 1481-1487 (1983).
12. T. Poggio and S. Smale, "The mathematics of learning: dealing with data," Not. Am. Math. Soc. 50, 537-544 (2003).
13. R. Gordon, R. Bender, and G. T. Herman, "Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography," J. Theor. Biol. 29, 471-481 (1970).
14. C. L. Byrne, "Iterative image reconstruction algorithms based on cross-entropy minimization," IEEE Trans. Image Process. IP-2, 96-103 (1993).
15. C. L. Byrne, "Erratum and addendum to 'Iterative image reconstruction algorithms based on cross-entropy minimization'," IEEE Trans. Image Process. IP-4, 225-226 (1995).
16. C. L. Byrne and M. A. Fiddy, "Estimation of continuous object distributions from Fourier magnitude measurements," J. Opt. Soc. Am. A 4, 412-417 (1987).
17. M. A. Fiddy, "The phase retrieval problem," in Inverse Optics, A. Devaney, ed., Proc. SPIE 413, 176-181 (1983).
18. J. C. Dainty and M. A. Fiddy, "The essential role of prior knowledge in phase retrieval," Opt. Acta 31, 325-330 (1984).
19. J. Fienup, "Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint," J. Opt. Soc. Am. A 4, 118-123 (1987).
20. R. Lane, "Recovery of complex images from Fourier magnitude," Opt. Commun. 63, 6-10 (1987).
21. J. Cederquist, J. Fienup, C. Wackerman, S. Robinson, and D. Kryskowski, "Wave-front phase estimation from Fourier intensity measurements," J. Opt. Soc. Am. A 6, 1020-1026 (1989).
22. J. Fienup, "Space object imaging through the turbulent atmosphere," Opt. Eng. (Bellingham) 18, 529-534 (1979).
23. C.-W Liao, M. A. Fiddy, and C. L. Byrne, "Imaging from the zero locations of far-field intensity data," J. Opt. Soc. Am. A 14, 3155-3161 (1997).
24. H. M. Shieh, M. E. Testorf, C. L. Byrne, and M. A. Fiddy, "Iterative image reconstruction using prior knowledge," submitted to J. Opt. Soc. Am. A.
25. C. L. Byrne, Signal Processing: A Mathematical Approach (AK Peters, 2005).
26. C. L. Byrne and M. A. Fiddy, "Images as power spectra; reconstruction as Wiener filter approximation," Inverse Probl. 4, 399-409 (1988).
27. C. L. Byrne and R. M. Fitzgerald, "Spectral estimators that extend the maximum entropy and maximum likelihood methods," SIAM J. Appl. Math. 44, 425-442 (1984).