Mathematical extrapolation of image spectrum for constraint-set design and set-theoretic superresolution

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

Volumn 20, Issue 8, 2003, Pages 1516-1527

  Bhattacharjee, Supratik ^a   Sundareshan, Malur K ^a  

^a University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFRACTIVE OPTICS; EXTRAPOLATION; IMAGE ENHANCEMENT; IMAGE RECONSTRUCTION; IMAGE SENSORS; SPECTRUM ANALYSIS;

SUPERRESOLUTION;

IMAGING TECHNIQUES;

EID: 0041930997     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.20.001516     Document Type: Article

References (36)

1. B. R. Hunt, "Super-resolution of images: algorithms, principles, and performance," Int. J. Imaging Syst. Technol. 6, 297-304 (1995).
2. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
3. C. K. Rushforth and J. L. Harris, "Restoration, resolution, and noise," J. Opt. Soc. Am. 58, 539-545 (1968).
4. D. L. Snyder and M. I. Miller, Random Point Processes in Time and Space, 2nd ed. (Springer-Verlag, New York, 1991).
5. D. Slepian and H. O. Pollack, "Prolate spheroidal wave functions, Fourier analysis and uncertainty - I," Bell Syst. Tech. J. 40, 43-62 (1961).
6. B. R. Frieden, "Band-unlimited reconstruction of optical objects and spectral sources," J. Opt. Soc. Am. 57, 1013-1019 (1967).
7. B. R. Frieden, "Restoring with maximum likelihood and maximum entropy," J. Opt. Soc. Am. 62, 51-55 (1972).
8. W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-60 (1972).
9. L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 79, 745-759 (1974).
10. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. R. Stat. Soc. Ser, B. Methodol. 39, 1-38 (1977).
11. L. Shepp and Y. Vardi, "Maximum likelihood reconstruction for emission tomography," IEEE Trans. Med. Imaging 1, 113-122 (1982).
12. B. R. Hunt, "Bayesian methods in digital image restoration," IEEE Trans. Comput. C-26, 219-229 (1977).
13. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721-741 (1984).
14. R. K. Pina and R. C. Puetter, "Bayesian image reconstruction: the pixon and optimal image modeling," Publ. Astron. Soc. Pac. 105, 630-637 (1993).
15. H. H. Barrett, D. W. Wilson, and B. M. W. Tsui, "Noise properties of the EM algorithm: 1. Theory," Phys. Med. Biol. 39, 833-846 (1994).
16. H. Y. Pang, M. K. Sundareshan, and S. Amphay, "Optimized maximum-likelihood algorithms for superresohition of passive millimeter-wave imagery," in Passive Millimeter-Wave Imaging Technology II, R. Smith, ed., Proc. SPIE 3378, 148-160 (1998).
17. H. Y. Pang, M. K. Sundareshan, and S. Amphay, "Superresolution of millimeter-wave images by iterative blind maximum-likelihood restoration," in Passive Millimeter-Wave Imaging Technology, R. Smith, ed., Proc. SPIE 3084, 227-238 (1997).
18. R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
19. A. Papoulis, "A new algorithm in spectral analysis and band-limited extrapolation," IEEE Trans. Circuits Syst. CAS-22, 735-742 (1975).
20. L. G. Gubin, B. T. Polak, and E. V. Raik, "The method of projection for finding the common point of convex sets," USSR Comput. Math. Math. Phys. 7, 1-24 (1967).
21. A. Lent and H. Tuy, "An iterative method for extrapolation of band-limited functions," J. Math. Anal. Appl. 83, 544-565 (1981).
22. D. C. Youla, "Generalized image restoration by the method of alternating orthogonal projections," IEEE Trans. Circuits Syst. 25, 694-702 (1978).
23. D. C. Youla and H. Webb, "Image restoration by the method of convex projections: Part 1. Theory," IEEE Trans. Med. Imaging MI-1, 81-94 (1982).
24. M. I. Sezan and H. Stark, "Image restoration by the method of convex projections: Part 2. Application and numerical results," IEEE Trans. Med. Imaging MI-1, 95-101 (1982).
25. P. L. Combettes, "The foundations of set theoretic estimation, " Proc. IEEE 81, 182-208 (1993).
26. H. Stark, ed. Image Recovery; Theory and Application (Academic, San Diego, Calif., 1987).
27. M. I. Sezan, "An overview of convex projections theory and its application to image recovery problems," Ultramicroscopy 40, 55-67 (1992).
28. G. Crombez, "Image recovery by convex combinations of projections," J. Math. Anal. Appl. 15, 413-419 (1991).
29. P. L. Combettes and H. Puh, "Iterations of parallel convex projections in Hubert spaces," Numer. Functi. Analy. Optim. 15, 225-243 (1994).
30. S. Bhattacharjee and M. K. Sundareshan, "Hybrid Bayesian and convex set projection algorithms for restoration and resolution enhancement of digital images," in Applications of Digital Image Processing XXIII, A. G. Tescher, ed., Proc. SPIE 4115, 12-22 (2000).
31. M. K. Sundareshan and S. Bhattacharjee, "Superresolution of passive millimeter-wave images using a combined maximum-likelihood optimization and projection-onto-convex-sets approach," in Passive Millimeter-Wave Imaging Technology V, R. Smith and R. Appleby, eds., Proc. SPIE 4373, 105-116 (2001).
32. D. Terzopoulos, "Regularization of the inverse visual problem involving discontinuities," IEEE Trans. Pattern Anal. Mach. Intell. 1, 413-424 (1986).
33. E. L. Kosarev, "Shannon's super-resolution limit for signal recovery," Inverse Probl. 6, 55-76 (1990).
34. M. K. Sundareshan and P. Zegers, "Role of over-sampled data in superresolution processing and a progressive up-sampling scheme for optimized implementations of iterative restoration algorithms," in Passive Millimeter-Wave Imaging Technology III, R. Smith, ed., Proc. SPIE 3703, 155-166 (1999).
35. P. J. Sementilli, B. R. Hunt, and M. S. Nadar, "An analysis of the limit to superresolution in incoherent imaging," J. Opt. Soc. Am. A 10, 2265-2276 (1993).
36. J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 372-381 (1986).