Abstract

Compressive sensing is a relatively new measurement paradigm which seeks to capture the “essential” aspects of a high-dimensional object using as few measurements as possible. In this work we demonstrate successful application of compressive sensing framework to digital Fresnel holography. It is shown that when applying compressive sensing approach to Fresnel fields a special sampling scheme should be adopted for improved results.

© 2010 IEEE

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2009

I. Moon, M. Daneshpanah, B. Javidi, A. Stern, "Automated three dimensional identification and tracking of micro/nanobiological organisms by computational holographic microscopy," Proc. IEEE 97, 990-1010 (2009).

D. Brady, K. Choi, D. Marks, R. Horisaki, S. Lim, "Compressive holography," Opt. Express 17, 13040-13049 (2009).

2008

A. M. Bruckstein, M. Elad, M. Zibulevsky, "A non-negative and sparse enough solution of an underdetermined linear system of equations is unique," IEEE Trans. Inf. Theory 54, 4813-4820 (2008).

E. Candes, M. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag. 25, 21-30 (2008).

2007

2006

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proc. IEEE 94, 636-654 (2006).

2004

2000

Z. Zalevsky, D. Mendlovic, A. W. Lohmann, "Understanding superresolution in Wigner space," J. Opt. Soc. Amer. A 17, 2422-2430 (2000).

1999

1997

Appl. Opt.

IEEE Signal Process. Mag.

E. Candes, M. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag. 25, 21-30 (2008).

IEEE Trans. Inf. Theory

A. M. Bruckstein, M. Elad, M. Zibulevsky, "A non-negative and sparse enough solution of an underdetermined linear system of equations is unique," IEEE Trans. Inf. Theory 54, 4813-4820 (2008).

Inverse Problems

E. Candès, J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems 23, 969-985 (2007).

J. Display Technol.

J. Opt. Soc. Amer. A

Z. Zalevsky, D. Mendlovic, A. W. Lohmann, "Understanding superresolution in Wigner space," J. Opt. Soc. Amer. A 17, 2422-2430 (2000).

Opt. Commun.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, F. Marinho, "Fast algorithms for free-space diffraction patterns calculation," Opt. Commun. 164, 233-245 (1999).

Opt. Express

Opt. Lett.

Proc. IEEE

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proc. IEEE 94, 636-654 (2006).

I. Moon, M. Daneshpanah, B. Javidi, A. Stern, "Automated three dimensional identification and tracking of micro/nanobiological organisms by computational holographic microscopy," Proc. IEEE 97, 990-1010 (2009).

Other

M. Lustig, Sparse MRI Ph.D. dissertation Dept. Elect. Eng., Stanford Univ.Palo AltoCA (2008).

A. Lohmann, M. E. Testorf, J. Ojeda-Castaneda, The Art and Science of Holography, A Tribute to Elmmett Leith and Yuri Denisyuk (SPIE Press, 2004) pp. 129-144.

R. Fergus, A. Torralba, W. T. Freeman, “Random lens imaging,” Computer Science and Artificial Intell. Lab., MITCambridgeMA Tech. Rep. MIT-CSAIL-TR-2006-058 (2006).

R. Marcia, R. Willett, "Compressive coded aperture superresolution image reconstruction," Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., ICASSP (2008).

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