Digital superresolution and the generalized sampling theorem

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

Volumn 24, Issue 2, 2007, Pages 311-325

  Prasad, Sudhakar ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DIGITAL SIGNAL PROCESSING; IMAGE RECONSTRUCTION; PIXELS;

DIGITAL SUPERRESOLUTION; RANDOM SUBPIXEL SHIFTS;

IMAGE RESOLUTION;

EID: 33847278920     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.24.000311     Document Type: Article

References (27)

1. R. Tsai and T. Huang, "Multiframe image restoration and registration," in Advances in Computer Vision and Image Processing, T. Huang, ed. (JAI, 1984), Vol. 1, pp. 317-339.
2. S. Kim, N. Bose, and H. Valenzuela, "Recursive reconstruction of high-resolution image from noisy undersampled multiframes," IEEE Trans. Acoust., Speech, Signal Process. 38, 1013-1027 (1990).
3. H. Ur and D. Gross, "Improved resolution from sub-pixel shifted images," CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
4. A. Papoulis, "Generalized sampling expansion," IEEE Trans. Circuits Syst. 24, 652-654 (1977).
5. J. L. Brown, Jr., "Sampling of bandlimited signals," Handbook of Statistics, N. K. Bose and C. R. Rao, eds. (North-Holland, 1993), Vol. 10, pp. 59-101.
6. R. Schulz and R. Stevenson, "Extraction of high-resolution frames from video sequences," IEEE Trans. Image Process. 5, 996-1011 (1996).
7. L. Poletto and P. Nicolosi, "Enhancing the spatial resolution of a two-dimensional array detector," Opt. Eng. (Bellingham) 38, 748-757 (1999).
8. S. Farisu, D. Robinson, M. Elad, and P. Milanfar, "Fast and robust multiframe superresolution," IEEE Trans. Image Process. 13, 1327-1344 (2004).
9. R. Hardie, K. Barnard, and E. Armstrong, "Joint map registration and high-resolution image estimation using a sequence of undersampled images," IEEE Trans. Image Process. 6, 1621-1633 (1997).
10. P. Vandewalle, L. Sbaiz, M. Vetterli, and S. Süsstrunk, "Superresolution from highly undersampled images," in Proceedings IEEE Conference on Image Processing, (IEEE, 2005), Vol. 1, pp. 889-892.
11. M. Elad and A. Feuer, "Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images," IEEE Trans. Image Process. 6, 1646-1658 (1997).
12. D. Rajan and S. Chaudhuri, "Simultaneous estimation of superresolved scene and depth maps from low-resolution defocused observations," IEEE Trans. Pattern Anal. Mach. Intell. 25, 1102-1117 (2003).
13. S. Park, M. Park, and M. Gang, "Superresolution image reconstruction: a technical overview," IEEE Signal Process. Mag. 20, 21-36 (2003).
14. S. Farisu, D. Robinson, M. Elad, and P. Milanfar, "Advances and challenges in superresolution," Int. J. Imaging Syst. Technol. 14, 47-57 (2004).
15. J. Tanida, T. Kumugai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): Concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
16. Y. Kitamura, R. Shogenji, K. Yamada, S. Miyatake, M. Miyamoto, T. Morimoto, Y. Masaki, N. Kondou, D. Miyazaki, J. Tanida, and Y. Ichioka, "Reconstruction of a high-resolution image on a compound-eye image-capturing system," Appl. Opt. 43, 1719-1727 (2004).
17. M. Elad and Y. Hel-Or, "A fast superresolution reconstruction algorithm for pure translational motion and common space-invariant blur," IEEE Trans. Image Process. 10, 1187-1193 (2001).
18. R. Lagendijk and J. Biemond, Iterative Identification and Restoration of Images (Kluwer, 1991).
19. If the HR signal itself is an undersampled, aliased version of an original higher-resolution signal, then it is only the aliased HR signal that can be reconstructed in this way. Indeed, since the undersampled HR signal, but not the original higher-resolution signal, may always be regarded as being critically sampled by the HR array and thus bandlimited to (-B,B), there is no scope for confusion in this statement. Consistent with this picture, the use of the qualifiers LR and HR is favored over aliased and critically sampled throughout this paper.
20. C. Cullen, Matrices and Linear Transformations, 2nd ed. (Dover, 1972), p. 117.
21. D. Robinson and P. Milanfar, "Statistical performance analysis of superresolution," IEEE Trans. Image Process. 15, 1413-1428 (2006).
22. R. Barnard, V. Pauca, T. Torgersen, R. Plemmons, S. Prasad, J. van der Gracht, J. Nagy, J. Chung, G. Behrmann, S. Mathews, and M. Mirotznik, "High-resolution iris image reconstruction from low-resolution imagery," in Advanced Signal Processing Algorithms, Architectures and Implementations XVI, Proc. SPIE 6313, 63130D (2006).
23. This statement is mathematically accurate only when M » L because the (L - 1) vanishing columns of S′ modify (L - 1) of the M blocks from their otherwise identical M(X) form. However, since the inequality M » L is generally true in a practical situation, one need not question the accuracy of the statement in practice.
24. D. Brady, M. Fiddy, U. Shahid, and T. Suleski, "Compressive optical MONTAGE photography initiative: noise and error analysis," presented at the Computational Optical Sensing and Imaging (COSI) Conference, Charlotte, N.C., June 6-8, 2005 (conference proceedings on CD-ROM), paper CMB3.
25. M. Neifeld and A. Ashok, "Imaging using alternate point spread function: lenslets with pseudo-random phase diversity," presented at the Computational Optical Sensing and Imaging (COSI) Conference, Charlotte, N.C., June 6-8, 2005 (conference proceedings on CD-ROM), paper CMB1.
26. P. Morse and H. Feshbach, Methods of Theoretical Physics, Part I (McGraw-Hill, 1953), pp. 466-467.
27. M. Krook, G. Carrier, and C. Pearson, Functions of a Complex Variable (McGraw-Hill, 1966), p. 57.