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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    [CrossRef]
  2. P. Wheel, M. Dobbs and W. E. Sharp, "Optimization of space borne imaging LADAR sensor for asteroid studies from parameter design," Proc. SPIE 4772, 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).
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    [CrossRef] [PubMed]
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    [CrossRef]
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  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 IV SPIE Electronic Imaging 6065, San Jose, CA (2006).
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    [CrossRef] [PubMed]
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    [CrossRef]
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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]

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," Proc. SPIE 4772, 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," Proc. SPIE 5108, 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 IV SPIE Electronic Imaging 6065, 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 Appl. Opt., 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 } ,

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