Abstract

We present a feature-specific imaging system based on the use of structured illumination. The measurements are defined as inner products between the illumination patterns and the object reflectance function, measured on a single photodetector. The illumination patterns are defined using random binary patterns and thus do not employ prior knowledge about the object. Object estimates are generated using L 1-norm minimization and gradient-projection sparse reconstruction algorithms. The experimental reconstructions show the feasibility of the proposed approach by using 42% fewer measurements than the object dimensionality.

© 2008 Optical Society of America

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References

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  1. Q. Zheng, S. Der, and H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
    [Crossref]
  2. P. Wheel, M. Dobbs, and W. E. Sharp, “Optimization of space borne imaging LADAR sensor for asteroid studies from parameter design,” in Electro-Optical System Design, Simulation, Testing, and Training, R. M. Wasserman and S. L. DeVore, eds., Proc. SPIE4772, 68–77 (2002).
    [Crossref]
  3. S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
    [Crossref]
  4. J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
    [Crossref]
  5. E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vision Comput. 17, 87–97 (1999).
    [Crossref]
  6. M.G.L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
    [Crossref] [PubMed]
  7. J. Ryu, B.K.P. Horn, M.S. Mermelstein, S. Hong, and D.M. Freeman, “Application of Structured Illumination in Nano-Scale Vision,” in IEEE Workshop on Computer Vision for the Nano-Scale, Madison, Wisconsin, 16–22 (2003).
  8. W. T. Cathey and E. R. Dowsky, “New paradigm for imaging systems,” Appl. Opt. 41, 6080–6092 (2002).
    [Crossref] [PubMed]
  9. S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE5108, 1–12 (2003).
    [Crossref]
  10. P. Potuluri, M.R. Fetterman, and D.J. Brady, “High depth of field microscopic imaging using an interferometric camera,” Opt. Express 8, 624–630 (2001).
    [Crossref] [PubMed]
  11. D. J. Brady, “Multiplex sensors and the constant radiance theorem,” Opt. Lett. 27, 16–18 (2002).
    [Crossref]
  12. M. A. Neifeld and P. Shankar, “Feature-specific imaging,” Appl. Opt. 42, 3379–3389 (2003).
    [Crossref] [PubMed]
  13. N. P. Pitsianis, D. J. Brady, and X. Sun, “The Quantized Cosine Transform for sensor-layer image compression,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (OSA, 2005), paper JMA4.
  14. D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).
  15. H. S. Pal, D. Ganotra, and M. A. Neifeld, “Face recognition by using feature-specific imaging,” Appl. Opt. 44, 3784–3794 (2005).
    [Crossref] [PubMed]
  16. M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293–5303 (2007).
    [Crossref] [PubMed]
  17. P. K. Baheti and M. A. Neifeld, “Feature-specific structured imaging,” Appl. Opt. 45, 7382–7391 (2006).
    [Crossref] [PubMed]
  18. E. J. Candès and J. Romberg “Practical signal recovery from random projections,” in Wavelet Applications in Signal and Image Processing XI, Proc. SPIE Conf.5914, (2004).
  19. E. J. Candès, J. Romberg, and T. Tao “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2005).
    [Crossref]
  20. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” (Preprint, 2007). Available: http://www.lx.it.pt/~mtf/GPSR/
  21. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley series in Pure and Applied Optics, 2004).

2007 (1)

2006 (1)

2005 (2)

E. J. Candès, J. Romberg, and T. Tao “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2005).
[Crossref]

H. S. Pal, D. Ganotra, and M. A. Neifeld, “Face recognition by using feature-specific imaging,” Appl. Opt. 44, 3784–3794 (2005).
[Crossref] [PubMed]

2003 (1)

2002 (2)

2001 (2)

P. Potuluri, M.R. Fetterman, and D.J. Brady, “High depth of field microscopic imaging using an interferometric camera,” Opt. Express 8, 624–630 (2001).
[Crossref] [PubMed]

Q. Zheng, S. Der, and H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[Crossref]

2000 (2)

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

M.G.L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref] [PubMed]

1999 (1)

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vision Comput. 17, 87–97 (1999).
[Crossref]

1998 (1)

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[Crossref]

Baheti, P. K.

Baraniuk, R. G.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Baron, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Barrett, H. H.

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley series in Pure and Applied Optics, 2004).

Batlle, J.

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[Crossref]

Brady, D. J.

D. J. Brady, “Multiplex sensors and the constant radiance theorem,” Opt. Lett. 27, 16–18 (2002).
[Crossref]

N. P. Pitsianis, D. J. Brady, and X. Sun, “The Quantized Cosine Transform for sensor-layer image compression,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (OSA, 2005), paper JMA4.

Brady, D.J.

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2005).
[Crossref]

E. J. Candès and J. Romberg “Practical signal recovery from random projections,” in Wavelet Applications in Signal and Image Processing XI, Proc. SPIE Conf.5914, (2004).

Cathey, W. T.

Der, S.

Q. Zheng, S. Der, and H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[Crossref]

Dobbs, M.

P. Wheel, M. Dobbs, and W. E. Sharp, “Optimization of space borne imaging LADAR sensor for asteroid studies from parameter design,” in Electro-Optical System Design, Simulation, Testing, and Training, R. M. Wasserman and S. L. DeVore, eds., Proc. SPIE4772, 68–77 (2002).
[Crossref]

Dowsky, E. R.

Duarte, M. F.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Felly, K.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Fetterman, M.R.

Figueiredo, M. A. T.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” (Preprint, 2007). Available: http://www.lx.it.pt/~mtf/GPSR/

Freeman, D.M.

J. Ryu, B.K.P. Horn, M.S. Mermelstein, S. Hong, and D.M. Freeman, “Application of Structured Illumination in Nano-Scale Vision,” in IEEE Workshop on Computer Vision for the Nano-Scale, Madison, Wisconsin, 16–22 (2003).

Ganotra, D.

Gustafsson, M.G.L.

M.G.L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref] [PubMed]

Hong, S.

J. Ryu, B.K.P. Horn, M.S. Mermelstein, S. Hong, and D.M. Freeman, “Application of Structured Illumination in Nano-Scale Vision,” in IEEE Workshop on Computer Vision for the Nano-Scale, Madison, Wisconsin, 16–22 (2003).

Horn, B.K.P.

J. Ryu, B.K.P. Horn, M.S. Mermelstein, S. Hong, and D.M. Freeman, “Application of Structured Illumination in Nano-Scale Vision,” in IEEE Workshop on Computer Vision for the Nano-Scale, Madison, Wisconsin, 16–22 (2003).

Horn, E.

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vision Comput. 17, 87–97 (1999).
[Crossref]

Ke, J.

King, B.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

Kiryati, N.

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vision Comput. 17, 87–97 (1999).
[Crossref]

Lai, S.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

Laska, J. N.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Mahmoud, H. I.

Q. Zheng, S. Der, and H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[Crossref]

Mermelstein, M.S.

J. Ryu, B.K.P. Horn, M.S. Mermelstein, S. Hong, and D.M. Freeman, “Application of Structured Illumination in Nano-Scale Vision,” in IEEE Workshop on Computer Vision for the Nano-Scale, Madison, Wisconsin, 16–22 (2003).

Mouaddib, E.

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[Crossref]

Myers, K. J.

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley series in Pure and Applied Optics, 2004).

Neifeld, M. A.

Nowak, R. D.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” (Preprint, 2007). Available: http://www.lx.it.pt/~mtf/GPSR/

Pal, H. S.

Pauca, V. P.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE5108, 1–12 (2003).
[Crossref]

Pitsianis, N. P.

N. P. Pitsianis, D. J. Brady, and X. Sun, “The Quantized Cosine Transform for sensor-layer image compression,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (OSA, 2005), paper JMA4.

Plemmons, R. J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE5108, 1–12 (2003).
[Crossref]

Potuluri, P.

Prasad, S.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE5108, 1–12 (2003).
[Crossref]

Romberg, J.

E. J. Candès, J. Romberg, and T. Tao “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2005).
[Crossref]

E. J. Candès and J. Romberg “Practical signal recovery from random projections,” in Wavelet Applications in Signal and Image Processing XI, Proc. SPIE Conf.5914, (2004).

Ryu, J.

J. Ryu, B.K.P. Horn, M.S. Mermelstein, S. Hong, and D.M. Freeman, “Application of Structured Illumination in Nano-Scale Vision,” in IEEE Workshop on Computer Vision for the Nano-Scale, Madison, Wisconsin, 16–22 (2003).

Salvi, J.

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[Crossref]

Sarvotham, S.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Shankar, P.

Sharp, W. E.

P. Wheel, M. Dobbs, and W. E. Sharp, “Optimization of space borne imaging LADAR sensor for asteroid studies from parameter design,” in Electro-Optical System Design, Simulation, Testing, and Training, R. M. Wasserman and S. L. DeVore, eds., Proc. SPIE4772, 68–77 (2002).
[Crossref]

Sun, X.

N. P. Pitsianis, D. J. Brady, and X. Sun, “The Quantized Cosine Transform for sensor-layer image compression,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (OSA, 2005), paper JMA4.

Takhar, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Tao, T.

E. J. Candès, J. Romberg, and T. Tao “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2005).
[Crossref]

Torgersen, T. C.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE5108, 1–12 (2003).
[Crossref]

van der Gracht, J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE5108, 1–12 (2003).
[Crossref]

Wakin, M. B.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

Wheel, P.

P. Wheel, M. Dobbs, and W. E. Sharp, “Optimization of space borne imaging LADAR sensor for asteroid studies from parameter design,” in Electro-Optical System Design, Simulation, Testing, and Training, R. M. Wasserman and S. L. DeVore, eds., Proc. SPIE4772, 68–77 (2002).
[Crossref]

Wright, S. J.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” (Preprint, 2007). Available: http://www.lx.it.pt/~mtf/GPSR/

Zheng, Q.

Q. Zheng, S. Der, and H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[Crossref]

Appl. Opt. (5)

Comm. Pure Appl. Math. (1)

E. J. Candès, J. Romberg, and T. Tao “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2005).
[Crossref]

IEEE Trans. Image Process. (1)

Q. Zheng, S. Der, and H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[Crossref]

Image Vision Comput. (1)

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vision Comput. 17, 87–97 (1999).
[Crossref]

J. Microsc. (1)

M.G.L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref] [PubMed]

Opt. Commun. (1)

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Pattern Recogn. (1)

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[Crossref]

Other (8)

P. Wheel, M. Dobbs, and W. E. Sharp, “Optimization of space borne imaging LADAR sensor for asteroid studies from parameter design,” in Electro-Optical System Design, Simulation, Testing, and Training, R. M. Wasserman and S. L. DeVore, eds., Proc. SPIE4772, 68–77 (2002).
[Crossref]

J. Ryu, B.K.P. Horn, M.S. Mermelstein, S. Hong, and D.M. Freeman, “Application of Structured Illumination in Nano-Scale Vision,” in IEEE Workshop on Computer Vision for the Nano-Scale, Madison, Wisconsin, 16–22 (2003).

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE5108, 1–12 (2003).
[Crossref]

N. P. Pitsianis, D. J. Brady, and X. Sun, “The Quantized Cosine Transform for sensor-layer image compression,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (OSA, 2005), paper JMA4.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Felly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Proc. of Computational Imaging IVSPIE Electronic Imaging6065, San Jose, CA (2006).

E. J. Candès and J. Romberg “Practical signal recovery from random projections,” in Wavelet Applications in Signal and Image Processing XI, Proc. SPIE Conf.5914, (2004).

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” (Preprint, 2007). Available: http://www.lx.it.pt/~mtf/GPSR/

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley series in Pure and Applied Optics, 2004).

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Figures (9)

Fig. 1.
Fig. 1.

System diagram for the RFSSI approach.

Fig. 2.
Fig. 2.

(a) Two example 32×32 binary sparse objects with M=160. (b) Two example 32×32 gray-scale truck objects. (c) Plot of coefficient vector α representing leftmost object from (b) in wavelet basis V̿ DW . (d) Estimated object reflectance G trunc obtained by retaining the dominant 250 coefficients from (c).

Fig. 3.
Fig. 3.

(a) Example of 32×32 binary sparse object with M=160. (b) L1 reconstructed estimate of the object in (a) for K=350 and K=450 (Simulation data). (c) Example of a 32×32 gray-scale truck object that is “mostly-sparse” in the basis V̿ DW . (d) L1 reconstructed estimate of the object in (d) for K=350 and K=450 (Simulation data). (e) Plot of RMSE versus K resulting from applying L1 to the random projection measurements (curves with ‘circles’ and ‘squares’ represent the objects in figs. 4(a) and 4(c) respectively).

Fig. 4.
Fig. 4.

Simulation example: (a) GPSR reconstructed estimate of the object in fig. 3(a), with noise (σo =2) added to the projection measurements), for K=450 and K=600. (b) Plot of RMSE versus K resulting from applying GPSR to the noisy random projection measurements (σo =2). (c) Estimates obtained by retaining only M=160 dominant values of the object estimates in fig. 4(a).

Fig. 5.
Fig. 5.

Experimental setup for the RFSSI system.

Fig. 6.
Fig. 6.

(a) Two of 4000 example truck objects used to generate a PC basis. (b) Explicitly-sparse in the PC basis (with M=160) versions of the objects in (a).

Fig. 7.
Fig. 7.

(a) Five training objects used for calibration. (b) Plot of first 100 entries of R and R exp corresponding to the leftmost object in (a). (c) Plot of first 100 entries of R and R calib corresponding to the leftmost object in (a).

Fig. 8.
Fig. 8.

Experimental results: (a) Two binary objects along with their respective estimates. (b) Two explicitly-sparse objects in V̿ PC along with their estimates. (c) Two mostly-sparse truck objects in V̿ PC along with their estimates. d) Two mostly-sparse truck objects in V̿ DW along with their respective estimates.

Fig. 9.
Fig. 9.

RMSE comparison between theory and experiment for RFSSI system.

Tables (1)

Tables Icon

Table 1. Comparison of KRFSSI and KFSSI for several values of RMSE (σo =2)

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

R = i = 1 N 2 [ P ] i [ G ] i .
R = P = G ,
RMSE = 1 N G G ̂ L 2 ,
min G ̂ N 2 V = T G ̂ L 1 subject to P = G ̂ = R .
R = P = G + n ,
min G ̂ N 2 V = T G ̂ L 1 such that P = G ̂ R L 2 σ .
RMSE FSSI = 1 N Tr { R s R s P = PC T [ P = PC R S P = PC T + σ o 2 [ I ] ] 1 P = PC R S } ,

Metrics