Abstract

Localization information of moving and changing objects, as commonly extracted from video sequences, is typically very sparse with respect to the full data frames, thus fulfilling one of the basic conditions of compressive sensing theory. Motivated by this observation, we developed an optical compressive change and motion-sensing technique that detects the location of moving objects by using a significantly fewer samples than conventionally taken. We present examples of motion detection and motion tracking with over two orders of magnitude fewer samples than required with conventional systems.

© 2012 Optical Society of America

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  5. D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.
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    [CrossRef]
  16. D. Brady, K. Choi, D. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
    [CrossRef]
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    [CrossRef]
  21. J. M. Bioucas-Dias, and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
    [CrossRef]

2012 (1)

2011 (4)

2010 (2)

2009 (2)

2008 (1)

2007 (3)

A. Stern, “Compressed imaging system with linear sensors,” Opt. Lett. 32, 3077–3079 (2007).
[CrossRef]

J. M. Bioucas-Dias, and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

2006 (2)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

1986 (1)

Abolbashari, M.

Araújo, F. M.

Baraniuk, R. G.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Baron, D.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias, and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

Brady, D.

Candès, E.

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Choi, K.

Correia, M. V.

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Duarte, M. F.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Eldar, Y. C.

Evladov, S.

Farahi, F.

Figueiredo, M. A. T.

J. M. Bioucas-Dias, and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

Gazit, S.

Gehm, M. E.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Harmany, Z. T.

R. F. Marcia, Z. T. Harmany, and R. M. Willet, “Compressive coded aperture imaging,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2009), vol. 7245.

Horisaki, R.

Jain, A. K.

A. K. Jain, Fundamentals of Image Processing (Prentice-Hall, 1989).

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18, 15094–15103 (2010).
[CrossRef]

A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

John, R.

Kelly, K.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Laska, J.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Levi, O.

Lim, S.

Magalhães, F.

Marcia, R. F.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

R. F. Marcia, Z. T. Harmany, and R. M. Willet, “Compressive coded aperture imaging,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2009), vol. 7245.

Mariano, A.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Marks, D.

Nichols, J. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Osman, T.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Poon, P. K.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Rivenson, Y.

Y. Rivenson, A. Stern, and J. Rosen, “Compressive multiple view projection incoherent holography,” Opt. Express 19, 6109–6118 (2011).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18, 15094–15103 (2010).
[CrossRef]

Y. Rivenson and A. Stern, “An efficient method for multi-dimensional compressive imaging,” in Computational Optical Sensing and Imaging, Technical Digest (CD) (Optical Society of America, 2009), paper CTuA4.

Romberg, J.

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Rosen, J.

Sarvotham, S.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Segev, M.

Shechtman, Y.

Shori, R. K.

Steier, W. H.

Stenner, M.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Stern, A.

S. Evladov, O. Levi, and A. Stern, “Progressive compressive imaging from Radon projections,” Opt. Express 20, 4260–4271 (2012).
[CrossRef]

Y. Rivenson, A. Stern, and J. Rosen, “Compressive multiple view projection incoherent holography,” Opt. Express 19, 6109–6118 (2011).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18, 15094–15103 (2010).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

A. Stern, “Compressed imaging system with linear sensors,” Opt. Lett. 32, 3077–3079 (2007).
[CrossRef]

A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

Y. Rivenson and A. Stern, “An efficient method for multi-dimensional compressive imaging,” in Computational Optical Sensing and Imaging, Technical Digest (CD) (Optical Society of America, 2009), paper CTuA4.

Szameit, A.

Takhar, D.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Tao, T.

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Townsend, D.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Wagadarikar, A.

Wakin, M. B.

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

Wehrwein, S.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Willet, R. M.

R. F. Marcia, Z. T. Harmany, and R. M. Willet, “Compressive coded aperture imaging,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2009), vol. 7245.

Willett, R.

Willett, R. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias, and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

IEEE Trans. Inf. Theory (2)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

J. Disp. Technol. (2)

A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

Opt. Eng. (1)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Other (5)

R. F. Marcia, Z. T. Harmany, and R. M. Willet, “Compressive coded aperture imaging,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2009), vol. 7245.

T. Osman, P. K. Poon, D. Townsend, S. Wehrwein, A. Mariano, M. Stenner, and M. E. Gehm, “Experimental demonstration of compressive target tracking,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMB2.

Y. Rivenson and A. Stern, “An efficient method for multi-dimensional compressive imaging,” in Computational Optical Sensing and Imaging, Technical Digest (CD) (Optical Society of America, 2009), paper CTuA4.

A. K. Jain, Fundamentals of Image Processing (Prentice-Hall, 1989).

D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proceedings of SPIE-IS&T on Electronic Imaging (IEEE, 2006), pp. 43.

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Figures (9)

Fig. 1.
Fig. 1.

Motion-location detection (c) from two consecutive video frames, (a) and (b).

Fig. 2.
Fig. 2.

Schematic diagram of compressive imaging [3].

Fig. 3.
Fig. 3.

Schematic illustration of Radon projection at θ=90°, sampled by a linear sensor with respect to field angles.

Fig. 4.
Fig. 4.

(a), (b) Two Radon projections, p1(r) and p2(r), of two consecutive frames taken at instants tn and tn+1; (c) change-location detection estimated from absolute value differences (solid line) of the respective radon projections; (d) difference signals d1(r;tn+1) and d2(r;tn+1) marked on two perpendicular linear array sensors S1 and S2 in the image plane. Location of the moving object is obtained from the intersection of the back-projected lines R1 and R2.

Fig. 5.
Fig. 5.

(a) Original image; (b) reconstructed image from four Radon projections (total 2000 samples); (c) image obtained using conventional imaging system, consisting of 2025 samples.

Fig. 6.
Fig. 6.

Optical implementation: (a) four co-planar cylindrical lenses with annular stop; (b) entire setup: C=cylindrical lenses ensemble; R=relay optics; and f(x,y) and g(x,y) are the intensities in the object and image plane, respectively; (c) photograph of the system.

Fig. 7.
Fig. 7.

Block diagram of capturing process.

Fig. 8.
Fig. 8.

(a) and (b) measured projections pl(r), l=1, 2, 3, 4 taken along the four strips in the image plane (b); (d) four temporal difference vectors dl(r), l=1, 2, 3, 4 and their respective location in the image plane.

Fig. 9.
Fig. 9.

Detection of the moving person in the frames shown in Figs. 1(a) and 1(b) obtained with the compressive-change detector capturing 2000pixels/frame (a), compared to that from a regular video capturing 500×500pixels/frame (b).

Equations (3)

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minα1,subject tog=Ωα,
gS=(f*h)·M,
p1(mΔ,tn)=gS(0,m),p2(n2Δ,tn)=gS(n,n),p3(nΔ,tn)=gS(n,0),p4(n2Δ,tn)=gS(n,n).

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