Random projections imaging with extended space ... - CiteSeerX

Preprint. To appear IEEE/OSA Journal of Display Technology , vol.3 no.3 Sept 2007


2λz1 L

13. (A11)

and

1 1 1 ∆ o >> ρz1  + −   z1 fl z2  .

(A12) Thus we conclude that if the conditions (A9), (A11) and (A12) hold then the columns of Φ are uncorrelated.

14. 15.

16. REFERENCES B. Javidi and F. Okano eds, “Three Dimensional Television, Video, and Display Technologies," Springer Verlag Berlin, 2002. 2. D. L. Donoho, “Compressed sensing”, Manuscript (2004). http://wwwstat.stanford.edu/%7Edonoho/Reports/2004/CompressedS ensing091604.pdf. 3. E. J. Candes, J. Romberg and T. Tao, “Robust uncertainty Principles: Exact signal reconstruction from highly incomplete frequency information”, manuscript (2004).. 4. Y. Tsaig and D. L. Donoho, “Extensions to compressed sensing”, Signal Processing, vol 86, 549-571, March 2006. 5. D. Takhar, J. N. Laska, M. B. Wakin. M. F. Durate, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression”, presented at Proc. of Computational Imaging IV at SPIE Electronic Imaging, San Jose, CA, Jan. 2006 . 6. M. F. Duarte, M. B. Wakin, and R. G. Baraniuk, “Fast reconstruction of piecewise smooth signals from random projections,” in Proc. SPARS05, (Rennes, France), (2005). T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, and 7. B. Javidi, “Image reconstruction from compressed encrypted digital hologram,” Opt. Eng. Vol. 44, 2005. 8. 9. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. vol. 41, 4124-4132, 2002. 9. T.J. Naughton, J.B. McDonald, and B. Javidi, "Efficient compression of digital holograms for Internet transmission of three-dimensional images," Applied Optics, vol. 42, 4758-4764, August 2003. 10. F. Sadjadi, ed., "Selected Papers on Automatic Target Recognition," SPIE Press, 1999. 11. H. Kwon and N. M. Nasrabadi, “Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens., vol. 43, 388-397, (2005). 12. R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express, vol. 12, 1.

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5237-5242 Oct. 2004., http://www.opticsinfobase.org/abstract.cfm?URI=oe-1221-5237. S. K. Yeom, A. Stern, and B. Javidi, “Compression of 3D color integral images,” Optics Express, on-line Journal of the Optical Society of America, vol. 12, 1632-1642, April 2004. A. Mahalanobis, “Processing of multi-sensor data using correlation filters,” Proc. SPIE 3466, 56–64 (1998). M. Elad and A. M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of RN bases”, IEEE Trans. on Information Theory, vol. 48, 2558–2567 (2002). D. L. Donoho and M. Elad,” Optimally sparse representation from overcomplete dictionaries via l1 norm minimization,” Proc. Natl. Acad. Sci. USA, vol 100,2197-2002, March 2003. S. Mallat, A wavelet tour of signal processing, (Academic Press. 2’nd edition, 1999). S. Mallat, and Z. Zhang, “Matching Pursuits with TimeFrequency Dictionaries”, IEEE Trans. Sig. Proc., 41 (12), 3397-3415 (1993). A. Papoulis, Probability, random variables and stochastic processes, (McGraww-Hill, 2’nd edition, Chp. 9, 1984). Joseph W. Goodman. Statistical Optics, (John Wiley & Sons, chp. 8.3, 1985).

Adrian Stern received his B.Sc., M. Sc. (cum laude) and PhD degrees from Ben-Gurion University of the Negev, Israel, in 1988,1997 and 2003 respectively, all in Electrical and Computer Engineering. During 2002-2003 he was a post-doctoral fellow in the Electrical and Computer Engineering Department at University of Connecticut. He is now with department of Electro-Optical Engineering at Ben-Gurion University of the Negev, Israel. His current research interests include sequences of images processing, image restoration, image and video compression, three dimensional imaging, bio-medical imaging, optical encryption, non conventional imaging. Bahram Javidi (Fellow, IEEE) received the B.S. degree in electrical engineering from George Washington University, Washington, D.C., and the M.S. and Ph.D. degrees in electrical engineering from the Pennsylvania State University, University Park. He is Board of Trustees Distinguished Professor at the University of Connecticut, Storrs. He has supervised over 80 masters and doctoral graduate students, postdoctoral students, and visiting professors during his academic career. He has published over 230 technical articles in major journals. He has published over 270 conference proceedings, including over 100 invited conference papers, and 60 invited presentations. His papers have been cited over 3200 times, according to the citation index of WEB of Science. His papers have appeared in Physics Today and Nature, and his research has been cited in the Frontiers in Engineering Newsletter, published by the National Academy of Engineering, IEEE Spectrum, Science, New Scientist, and National Science Foundation Newsletter. He has completed eight books including, Physics of Automatic Target Recognition (Springer 2007); "Optical

Preprint. To appear IEEE/OSA Journal of Display Technology , vol.3 no.3 Sept 2007< Imaging Sensors and Systems for Homeland Security Applications (Springer, 2005); Optical and Digital Techniques For Information Security (Springer, 2005); Image Recognition: Algorithms, Systems, and Applications (Marcel Dekker, 2002); Three Dimensional Television, Video, and Display Technologies (Springer-Verlag, 2002); Smart Imaging Systems (SPIE Press, 2001). He is currently on the Board of Editors of the Proceedings of the IEEE Journal, the Editor in Chief of the Springer Verlag series on Advanced Science and Technologies for Security Applications, and the IEEE/OSA journal of Display Technologies. He has served as topical editor for Springer-Verlag, Marcel Dekker publishing company, Optical Engineering Journal, and IEEE/SPIE Press Series on Imaging Science and Engineering. He has held visiting positions during his sabbatical leave at Massachusetts Institute of Technology, United States Air Force Rome Lab at Hanscom Base, and Thomson-CSF Research Labs in Orsay, France. He is a consultant to industry in the areas of optical systems, image recognition systems, and 3-D optical imaging systems. Dr. Javidi is Fellow of six professional societies, including the IEEE. He was awarded the Dennis Gabor Award in Diffractive Wave Technologies by the SPIE in 2005. He was the recipient of the IEEE Lasers and ElectroOptics Society Distinguished Lecturer Award twice in 2003 and 2004. He has been awarded the University of Connecticut Board Of Trustees Distinguished Professor Award, the School Of Engineering Distinguished Professor Award, University of Connecticut Alumni Association Excellence in Research Award, the Chancellor's Research Excellence Award, and the first Electrical and Computer Engineering Department Outstanding Research Award. In 1990, the National Science Foundation named him a Presidential Young Investigator.

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Preprint. To appear IEEE/OSA Journal of Display Technology , vol.3 no.3 Sept 2007
M ≥ K .

Object plane

Image plane

z1

Ψ

z2

Random phase mask Fig. 2. One possible optical setup to implement the image acquisition in Fig. 1.

fˆ p

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Preprint. To appear IEEE/OSA Journal of Display Technology , vol.3 no.3 Sept 2007