Abstract

We propose a novel approach to imaging that is not based on traditional optical imaging architecture. With the new approach, the image is reconstructed and visualized from random projections of the input object. The random projections are implemented within a single exposure by using a random phase mask which can be placed on a lens. For objects that have sparse representation in some known domain (e.g., Fourier or wavelet), the novel imaging systems have larger effective space–bandwidth product than conventional imaging systems. This implies, for example, that more object pixels may be reconstructed and visualized than the number of pixels of the image sensor. We present simulation results on the utility of the new approach. The proposed approach can have broad applications in efficient imaging capture, visualization, and display given ever increasing demands for larger and higher resolution images, faster image communications, and multidimensional image communications such as 3-D TV and display.

© 2007 IEEE

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References

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  1. Three Dimensional Television, Video, and Display Technologies (Springer-Verlag, 2002).
  2. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory 52, 1289-1306 (2006).
  3. E. J. Candes, J. Romberg, T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory 52, 489-509 (2006).
  4. Y. Tsaig, D. L. Donoho, "Extensions to compressed sensing," Signal Process. 86, 549-571 (2006).
  5. D. Takhar, J. N. Laska, M. B. Wakin, M. F. Durate, D. Baron, S. Sarvotham, K. F. Kelly, R. G. Baraniuk, "A new compressive imaging camera architecture using optical-domain compression," Computational Imaging IV at SPIE Electronic Imaging San JoseCA (2006).
  6. M. F. Duarte, M. B. Wakin, R. G. Baraniuk, "Fast reconstruction of piecewise smooth signals from random projections," Online Proc. Workshop on Signal process. with Adaptive Sparse Structured Representations (SPARS) (2005).
  7. T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, "Image reconstruction from compressed encrypted digital hologram," Opt. Eng. 44, 75801-75809 (2005).
  8. T. J. Naughton, Y. Frauel, B. Javidi, E. Tajahuerce, "Compression of digital holograms for three-dimensional object reconstruction and recognition," Appl. Opt. 41, 4124-4132 (2002).
  9. T. J. Naughton, J. B. McDonald, B. Javidi, "Efficient compression of digital holograms for Internet transmission of three-dimensional images," Appl. Opt. 42, 4758-4764 (2003).
  10. Selected Papers on Automatic Target Recognition (SPIE Press, 1999).
  11. H. Kwon, N. M. Nasrabadi, "Kernel RX-algorithm: A nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).
  12. R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).
  13. S. K. Yeom, A. Stern, B. Javidi, "Compression of 3-D color integral images," Opt. Expr. 12, 1632-1642 (2004).
  14. A. Mahalanobis, "Processing of multi-sensor data using correlation filters," Proc. SPIE 3466, 56-64 (1998).
  15. M. Elad, A. M. Bruckstein, "A generalized uncertainty principle and sparse representation in pairs of RN bases," IEEE Trans. Inf. Theory 48, 2558-2567 (2002).
  16. D. L. Donoho, M. Elad, "Optimally sparse representation from overcomplete dictionaries via ${\rm l}^{1}$ norm minimization," Proc. Nat. Acad. Sci. USA 100, 2197-2002 (2003).
  17. S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1999).
  18. S. Mallat, Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process. 41, 3397-3415 (1993).
  19. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1984).
  20. J. W. Goodman, Statistical Optics (Wiley, 1985).

2006 (3)

D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory 52, 1289-1306 (2006).

E. J. Candes, J. Romberg, T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory 52, 489-509 (2006).

Y. Tsaig, D. L. Donoho, "Extensions to compressed sensing," Signal Process. 86, 549-571 (2006).

2005 (2)

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, "Image reconstruction from compressed encrypted digital hologram," Opt. Eng. 44, 75801-75809 (2005).

H. Kwon, N. M. Nasrabadi, "Kernel RX-algorithm: A nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).

2004 (2)

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).

S. K. Yeom, A. Stern, B. Javidi, "Compression of 3-D color integral images," Opt. Expr. 12, 1632-1642 (2004).

2003 (2)

T. J. Naughton, J. B. McDonald, B. Javidi, "Efficient compression of digital holograms for Internet transmission of three-dimensional images," Appl. Opt. 42, 4758-4764 (2003).

D. L. Donoho, M. Elad, "Optimally sparse representation from overcomplete dictionaries via ${\rm l}^{1}$ norm minimization," Proc. Nat. Acad. Sci. USA 100, 2197-2002 (2003).

2002 (2)

M. Elad, A. M. Bruckstein, "A generalized uncertainty principle and sparse representation in pairs of RN bases," IEEE Trans. Inf. Theory 48, 2558-2567 (2002).

T. J. Naughton, Y. Frauel, B. Javidi, E. Tajahuerce, "Compression of digital holograms for three-dimensional object reconstruction and recognition," Appl. Opt. 41, 4124-4132 (2002).

1998 (1)

A. Mahalanobis, "Processing of multi-sensor data using correlation filters," Proc. SPIE 3466, 56-64 (1998).

1993 (1)

S. Mallat, Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process. 41, 3397-3415 (1993).

Appl. Opt. (2)

T. J. Naughton, Y. Frauel, B. Javidi, E. Tajahuerce, "Compression of digital holograms for three-dimensional object reconstruction and recognition," Appl. Opt. 41, 4124-4132 (2002).

T. J. Naughton, J. B. McDonald, B. Javidi, "Efficient compression of digital holograms for Internet transmission of three-dimensional images," Appl. Opt. 42, 4758-4764 (2003).

IEEE Trans. Inf. Theory (2)

D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory 52, 1289-1306 (2006).

E. J. Candes, J. Romberg, T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory 52, 489-509 (2006).

IEEE Trans. Geosci. Remote Sens. (1)

H. Kwon, N. M. Nasrabadi, "Kernel RX-algorithm: A nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).

IEEE Trans. Inf. Theory (1)

M. Elad, A. M. Bruckstein, "A generalized uncertainty principle and sparse representation in pairs of RN bases," IEEE Trans. Inf. Theory 48, 2558-2567 (2002).

IEEE Trans. Signal Process. (1)

S. Mallat, Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process. 41, 3397-3415 (1993).

Opt. Express (1)

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).

Opt. Eng. (1)

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, "Image reconstruction from compressed encrypted digital hologram," Opt. Eng. 44, 75801-75809 (2005).

Opt. Expr. (1)

S. K. Yeom, A. Stern, B. Javidi, "Compression of 3-D color integral images," Opt. Expr. 12, 1632-1642 (2004).

Proc. Nat. Acad. Sci. USA (1)

D. L. Donoho, M. Elad, "Optimally sparse representation from overcomplete dictionaries via ${\rm l}^{1}$ norm minimization," Proc. Nat. Acad. Sci. USA 100, 2197-2002 (2003).

Proc. SPIE (1)

A. Mahalanobis, "Processing of multi-sensor data using correlation filters," Proc. SPIE 3466, 56-64 (1998).

Signal Process. (1)

Y. Tsaig, D. L. Donoho, "Extensions to compressed sensing," Signal Process. 86, 549-571 (2006).

Other (7)

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Durate, D. Baron, S. Sarvotham, K. F. Kelly, R. G. Baraniuk, "A new compressive imaging camera architecture using optical-domain compression," Computational Imaging IV at SPIE Electronic Imaging San JoseCA (2006).

M. F. Duarte, M. B. Wakin, R. G. Baraniuk, "Fast reconstruction of piecewise smooth signals from random projections," Online Proc. Workshop on Signal process. with Adaptive Sparse Structured Representations (SPARS) (2005).

Three Dimensional Television, Video, and Display Technologies (Springer-Verlag, 2002).

Selected Papers on Automatic Target Recognition (SPIE Press, 1999).

S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1999).

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1984).

J. W. Goodman, Statistical Optics (Wiley, 1985).

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