Abstract

We present an adaptive feature-specific imaging (AFSI) system for application to an M-class recognition task. The proposed system uses nearest-neighbor-based density estimation to compute the (non- Gaussian) class-conditional densities. We refine the density estimates based on the training data and the knowledge from previous measurements at each step. The projection basis for the AFSI system is also adapted based on the previous measurements at each step. The decision-making process is based on sequential hypothesis testing. We quantify the number of measurements required to achieve a specified probability of error (Pe) and we compare the AFSI system with an adaptive-conventional (ACONV) system. The AFSI system exhibits significant improvement compared to the ACONV system at low signal-to-noise ratio (SNR), and it is shown that, for an M=4 hypotheses, SNR=10dB, and a desired Pe=102, the AFSI system requires 30 times fewer measurements than the ACONV system. Experimental results validating the AFSI system are presented.

© 2009 Optical Society of America

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  1. M. A. Turk and A. P. Pentland, “Face recognition using eigenfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.
    [CrossRef]
  2. P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711-720(1997).
    [CrossRef]
  3. W. Zhao, R. Chellapa, P. J. Phillips, and A. Rosenfeld, “Face recognition: a literature survey,” ACM Comput. Surv. 35, 399-458 (2003).
    [CrossRef]
  4. H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
    [CrossRef]
  5. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139-145 (1964).
    [CrossRef]
  6. A. Mahanalobis, B. V. K. Kumar, S. R. F. Sims, and J. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751-3759 (1994).
    [CrossRef]
  7. B. Javidi, P. Refregier, and P. Willett, “Optimum receiver design for pattern recognition with nonoverlapping target and scene noise,” Opt. Lett. 18, 1660-1662 (1993).
    [CrossRef] [PubMed]
  8. A. Yuille, D. Cohen, and P. Hallinan, “Feature extraction from faces using deformable templates,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 104-109.
  9. S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, “Face recognition: a convolutional neural network approach,” IEEE Trans. Neural Netw. 8, 98-113 (1997).
    [CrossRef] [PubMed]
  10. M. A. Neifeld and P. Shankar, “Feature-specific imaging,” Appl. Opt. 42, 3379-3389 (2003).
    [CrossRef] [PubMed]
  11. P. K. Baheti and M. A. Neifeld, “Feature-specific structured imaging,” Appl. Opt. 45, 7382-7391 (2006).
    [CrossRef] [PubMed]
  12. M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, “Sparse signal detection from incoherent projections,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP, 2006), Vol. 3, pp. 14-19.
  13. D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).
  14. 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, 2005 OSA Technical Digest Series (Optical Society of America, 2005), paper JMA4.
  15. M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293-5303 (2007).
    [CrossRef] [PubMed]
  16. H. S. Pal, D. Ganotra, and M. A. Neifeld, “Face recognition by using feature-specific imaging,” Appl. Opt. 44, 3784-3794(2005).
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  17. P. K. Baheti and M. A. Neifeld, “Adaptive feature-specific imaging: a face recognition example,” Appl. Opt. 47, B21-B31(2008).
    [CrossRef] [PubMed]
  18. A. Wald, “Sequential Analysis of statistical hypotheses,” Ann. Math. Stat. 16, 117-176 (1945).
    [CrossRef]
  19. P. Armitage, “Sequential analysis with more than two alternative hypotheses and its relation to discriminant function analysis,” J. R. Stat. Soc. Ser. B. Methodol. 12, 137-144 (1950).
  20. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).
  21. C. C. Holmes and N. M. Adams, “A probabilistic nearest neighbour method for statistical pattern recognition,” J. R. Stat. Soc. Ser. B. Methodol. 64, 1-12 (2002).
    [CrossRef]
  22. E. Marszalec, B. Martinkauppi, M. Soriano, and M. Pietikäinen, “A physics-based face database for color research,” J. Electron. Imaging 9, 32-38 (2000).
    [CrossRef]
  23. N. A. Goodman, P. R. Venkata, and M. A. Neifeld, “Adaptive waveform design and sequential hypothesis testing for target recognition using cognitive radar,” IEEE J. Sel. Top. Signal Process. 1, 105-113 (2007).
    [CrossRef]
  24. H. H. Barrett and K. J. Myers, Foundations of Image Science, Pure and Applied Optics (Wiley, 2004).
  25. S. Kay, Statistical Signal Processing--Detection Theory (Prentice-Hall PTR, 1998).
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    [CrossRef] [PubMed]

2008 (2)

2007 (2)

N. A. Goodman, P. R. Venkata, and M. A. Neifeld, “Adaptive waveform design and sequential hypothesis testing for target recognition using cognitive radar,” IEEE J. Sel. Top. Signal Process. 1, 105-113 (2007).
[CrossRef]

M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293-5303 (2007).
[CrossRef] [PubMed]

2006 (2)

P. K. Baheti and M. A. Neifeld, “Feature-specific structured imaging,” Appl. Opt. 45, 7382-7391 (2006).
[CrossRef] [PubMed]

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

2005 (1)

2003 (2)

M. A. Neifeld and P. Shankar, “Feature-specific imaging,” Appl. Opt. 42, 3379-3389 (2003).
[CrossRef] [PubMed]

W. Zhao, R. Chellapa, P. J. Phillips, and A. Rosenfeld, “Face recognition: a literature survey,” ACM Comput. Surv. 35, 399-458 (2003).
[CrossRef]

2002 (1)

C. C. Holmes and N. M. Adams, “A probabilistic nearest neighbour method for statistical pattern recognition,” J. R. Stat. Soc. Ser. B. Methodol. 64, 1-12 (2002).
[CrossRef]

2000 (1)

E. Marszalec, B. Martinkauppi, M. Soriano, and M. Pietikäinen, “A physics-based face database for color research,” J. Electron. Imaging 9, 32-38 (2000).
[CrossRef]

1997 (2)

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711-720(1997).
[CrossRef]

S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, “Face recognition: a convolutional neural network approach,” IEEE Trans. Neural Netw. 8, 98-113 (1997).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

1992 (1)

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

1950 (1)

P. Armitage, “Sequential analysis with more than two alternative hypotheses and its relation to discriminant function analysis,” J. R. Stat. Soc. Ser. B. Methodol. 12, 137-144 (1950).

1945 (1)

A. Wald, “Sequential Analysis of statistical hypotheses,” Ann. Math. Stat. 16, 117-176 (1945).
[CrossRef]

Adams, N. M.

C. C. Holmes and N. M. Adams, “A probabilistic nearest neighbour method for statistical pattern recognition,” J. R. Stat. Soc. Ser. B. Methodol. 64, 1-12 (2002).
[CrossRef]

Armitage, P.

P. Armitage, “Sequential analysis with more than two alternative hypotheses and its relation to discriminant function analysis,” J. R. Stat. Soc. Ser. B. Methodol. 12, 137-144 (1950).

Back, A. D.

S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, “Face recognition: a convolutional neural network approach,” IEEE Trans. Neural Netw. 8, 98-113 (1997).
[CrossRef] [PubMed]

Baheti, P. K.

Baraniuk, R. G.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, “Sparse signal detection from incoherent projections,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP, 2006), Vol. 3, pp. 14-19.

Baron, D.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

Barrett, H. H.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

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

Belhumeur, P.

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711-720(1997).
[CrossRef]

Brady, D. J.

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, 2005 OSA Technical Digest Series (Optical Society of America, 2005), paper JMA4.

Chellapa, R.

W. Zhao, R. Chellapa, P. J. Phillips, and A. Rosenfeld, “Face recognition: a literature survey,” ACM Comput. Surv. 35, 399-458 (2003).
[CrossRef]

Cohen, D.

A. Yuille, D. Cohen, and P. Hallinan, “Feature extraction from faces using deformable templates,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 104-109.

Davenport, M. A.

M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, “Sparse signal detection from incoherent projections,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP, 2006), Vol. 3, pp. 14-19.

Duarte, M. F.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, “Sparse signal detection from incoherent projections,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP, 2006), Vol. 3, pp. 14-19.

Duda, R. O.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

Epperson, J.

Ganotra, D.

Giles, C. L.

S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, “Face recognition: a convolutional neural network approach,” IEEE Trans. Neural Netw. 8, 98-113 (1997).
[CrossRef] [PubMed]

Girodias, K.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

Goodman, N. A.

N. A. Goodman, P. R. Venkata, and M. A. Neifeld, “Adaptive waveform design and sequential hypothesis testing for target recognition using cognitive radar,” IEEE J. Sel. Top. Signal Process. 1, 105-113 (2007).
[CrossRef]

Gooley, T.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

Hallinan, P.

A. Yuille, D. Cohen, and P. Hallinan, “Feature extraction from faces using deformable templates,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 104-109.

Hart, P. E.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

Hespanha, J.

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711-720(1997).
[CrossRef]

Holmes, C. C.

C. C. Holmes and N. M. Adams, “A probabilistic nearest neighbour method for statistical pattern recognition,” J. R. Stat. Soc. Ser. B. Methodol. 64, 1-12 (2002).
[CrossRef]

Javidi, B.

Kay, S.

S. Kay, Statistical Signal Processing--Detection Theory (Prentice-Hall PTR, 1998).

Ke, J.

Kelly, K.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

Kriegman, D.

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711-720(1997).
[CrossRef]

Kumar, B. V. K.

Lao, J.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

Laska, J. N.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

Lawrence, S.

S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, “Face recognition: a convolutional neural network approach,” IEEE Trans. Neural Netw. 8, 98-113 (1997).
[CrossRef] [PubMed]

Mahanalobis, A.

Marszalec, E.

E. Marszalec, B. Martinkauppi, M. Soriano, and M. Pietikäinen, “A physics-based face database for color research,” J. Electron. Imaging 9, 32-38 (2000).
[CrossRef]

Martinkauppi, B.

E. Marszalec, B. Martinkauppi, M. Soriano, and M. Pietikäinen, “A physics-based face database for color research,” J. Electron. Imaging 9, 32-38 (2000).
[CrossRef]

Myers, K. J.

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

Neifeld, M. A.

Pal, H. S.

Pentland, A. P.

M. A. Turk and A. P. Pentland, “Face recognition using eigenfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.
[CrossRef]

Phillips, P. J.

W. Zhao, R. Chellapa, P. J. Phillips, and A. Rosenfeld, “Face recognition: a literature survey,” ACM Comput. Surv. 35, 399-458 (2003).
[CrossRef]

Pietikäinen, M.

E. Marszalec, B. Martinkauppi, M. Soriano, and M. Pietikäinen, “A physics-based face database for color research,” J. Electron. Imaging 9, 32-38 (2000).
[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, 2005 OSA Technical Digest Series (Optical Society of America, 2005), paper JMA4.

Refregier, P.

Rolland, J.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

Rosenfeld, A.

W. Zhao, R. Chellapa, P. J. Phillips, and A. Rosenfeld, “Face recognition: a literature survey,” ACM Comput. Surv. 35, 399-458 (2003).
[CrossRef]

Sarvotham, S.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

Shankar, P.

Sims, S. R. F.

Soriano, M.

E. Marszalec, B. Martinkauppi, M. Soriano, and M. Pietikäinen, “A physics-based face database for color research,” J. Electron. Imaging 9, 32-38 (2000).
[CrossRef]

Stork, D. G.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

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, 2005 OSA Technical Digest Series (Optical Society of America, 2005), paper JMA4.

Takhar, D.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

Tsoi, A. C.

S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, “Face recognition: a convolutional neural network approach,” IEEE Trans. Neural Netw. 8, 98-113 (1997).
[CrossRef] [PubMed]

Turk, M. A.

M. A. Turk and A. P. Pentland, “Face recognition using eigenfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.
[CrossRef]

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

Venkata, P. R.

N. A. Goodman, P. R. Venkata, and M. A. Neifeld, “Adaptive waveform design and sequential hypothesis testing for target recognition using cognitive radar,” IEEE J. Sel. Top. Signal Process. 1, 105-113 (2007).
[CrossRef]

Wakin, M. B.

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, “Sparse signal detection from incoherent projections,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP, 2006), Vol. 3, pp. 14-19.

Wald, A.

A. Wald, “Sequential Analysis of statistical hypotheses,” Ann. Math. Stat. 16, 117-176 (1945).
[CrossRef]

White, T.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

Willett, P.

Yuille, A.

A. Yuille, D. Cohen, and P. Hallinan, “Feature extraction from faces using deformable templates,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 104-109.

Zhao, W.

W. Zhao, R. Chellapa, P. J. Phillips, and A. Rosenfeld, “Face recognition: a literature survey,” ACM Comput. Surv. 35, 399-458 (2003).
[CrossRef]

ACM Comput. Surv. (1)

W. Zhao, R. Chellapa, P. J. Phillips, and A. Rosenfeld, “Face recognition: a literature survey,” ACM Comput. Surv. 35, 399-458 (2003).
[CrossRef]

Ann. Math. Stat. (1)

A. Wald, “Sequential Analysis of statistical hypotheses,” Ann. Math. Stat. 16, 117-176 (1945).
[CrossRef]

Appl. Opt. (6)

IEEE J. Sel. Top. Signal Process. (1)

N. A. Goodman, P. R. Venkata, and M. A. Neifeld, “Adaptive waveform design and sequential hypothesis testing for target recognition using cognitive radar,” IEEE J. Sel. Top. Signal Process. 1, 105-113 (2007).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

IEEE Trans. Neural Netw. (1)

S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, “Face recognition: a convolutional neural network approach,” IEEE Trans. Neural Netw. 8, 98-113 (1997).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711-720(1997).
[CrossRef]

Image Vision Comput. (1)

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, and J. Lao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451-460 (1992).
[CrossRef]

J. Electron. Imaging (1)

E. Marszalec, B. Martinkauppi, M. Soriano, and M. Pietikäinen, “A physics-based face database for color research,” J. Electron. Imaging 9, 32-38 (2000).
[CrossRef]

J. R. Stat. Soc. Ser. B. Methodol. (2)

C. C. Holmes and N. M. Adams, “A probabilistic nearest neighbour method for statistical pattern recognition,” J. R. Stat. Soc. Ser. B. Methodol. 64, 1-12 (2002).
[CrossRef]

P. Armitage, “Sequential analysis with more than two alternative hypotheses and its relation to discriminant function analysis,” J. R. Stat. Soc. Ser. B. Methodol. 12, 137-144 (1950).

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

D. Takhar, J. N. 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,” Proc. SPIE 6065, 43-52 (2006).

Other (7)

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, 2005 OSA Technical Digest Series (Optical Society of America, 2005), paper JMA4.

M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, “Sparse signal detection from incoherent projections,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP, 2006), Vol. 3, pp. 14-19.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

A. Yuille, D. Cohen, and P. Hallinan, “Feature extraction from faces using deformable templates,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 104-109.

M. A. Turk and A. P. Pentland, “Face recognition using eigenfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.
[CrossRef]

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

S. Kay, Statistical Signal Processing--Detection Theory (Prentice-Hall PTR, 1998).

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Figures (16)

Fig. 1
Fig. 1

Schematic representation of (a) feature extraction after measuring a conventional image and (b) optical feature extraction using a feature-specific imager.

Fig. 2
Fig. 2

Example optical implementation for FSI system.

Fig. 3
Fig. 3

Training examples from M = 4 hypotheses; each row represents a different hypothesis and each column represents a different perspective example.

Fig. 4
Fig. 4

System flow diagram for MVG-AFSI and NN-AFSI.

Fig. 5
Fig. 5

Example to demonstrate the update of posterior probabilities for a sample experiment where a test object corresponding to the fourth hypothesis was actually chosen.

Fig. 6
Fig. 6

Comparison of MVG-AFSI and NN-AFSI ( n = 11 301 ) for M = 4 , P e = 10 2 , σ 2 = 10 , and L = 1 .

Fig. 7
Fig. 7

(a) Comparisons of NN-AFSI with different values of T int for M = 4 , P e = 10 2 , σ 2 = 10 , and L = 1 . (b) Relative improvement (by increasing n from 11 to 301) of NN-AFSI as a function of T int .

Fig. 8
Fig. 8

Comparison of MVG-AFSI and NN-AFSI ( n = 201 ) for M = 4 , P e = 10 2 , σ 2 = 10 , and L = 1 3 .

Fig. 9
Fig. 9

(a) Comparison of NN-AFSI ( n = 201 ) and ACONV ( n = 201 ) for M = 4 , P e = 10 2 , σ 2 = 10 , and L = 1 , 2, and 3. (b) Left image, example test object; center image, example image measured (using CONV) at T int = 1 and σ 2 = 10 ; right image, example image measured (using CONV) measured at T int = 8 and σ 2 = 10 .

Fig. 10
Fig. 10

Comparison of NN-AFSI with L = 1 and ACONV with L = 3 for n = 101 , 201, and 301, M = 4 , P e = 10 2 , and σ 2 = 10 .

Fig. 11
Fig. 11

Average detection time for NN-AFSI ( L = 1 ) and ACONV ( L = 3 ) with M = 4 , P e = 10 2 , σ 2 = 10 , and n = 101 , 201, and 301.

Fig. 12
Fig. 12

Study of NN-AFSI (with L = 1 ) for M = 4 class problem in presence of SLM imperfections. Simulation details are σ 2 = 10 and T int = 1 .

Fig. 13
Fig. 13

(a) AFSI system diagram and (b) experimental setup of the AFSI system.

Fig. 14
Fig. 14

Comparison of interclass separation between the four hypotheses using theoretical feature measurements (solid curves) and interclass separation between the four hypotheses using the calibrated experimental feature measurements (dashed curves).

Fig. 15
Fig. 15

Comparison of experimental recognition performance for NN-AFSI and SFSI with n = 11 and comparison of NN-AFSI for n = 5 , 11, and 21.

Fig. 16
Fig. 16

Example to demonstrate the update of posterior probabilities for a sample experiment using the NN-AFSI setup in Fig. 13b, where a test object corresponding to the second hypothesis was actually chosen.

Tables (1)

Tables Icon

Table 1 List of First Five Indices Corresponding to the Nearest Neighbors in Each Hypothesis as Experiment Progresses a

Equations (18)

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r conv = P conv T ( T int G + n conv ) ,
r FSI = P FSI T G + n FSI ,
max l { j = 1 L | [ P FSI ] l j | } = T int .
r FSI k = P FSI k T G + n FSI ,
r conv k = P conv k T ( T int G + n conv ) .
P e = i = 1 M Pr ( H 1 , H i 1 , H i + 1 , H M | H i ) P i .
p ( G | H i ) = 1 ( 2 π ) N / 2 ( det ( Σ i ) ) 1 / 2 exp ( ( G μ i ) T Σ i 1 ( G μ i ) 2 ) ,
μ i = 1 S j = 1 S G i , j , Σ i = 1 S j = 1 S [ ( G i , j μ i ) ( G i , j μ i ) T ] .
p ( r FSI ( k ) | H i ) = 1 ( 2 π ) k L / 2 ( det ( Σ FSI i , k ) ) 1 / 2 exp ( ( r FSI ( k ) μ FSI i , k ) T Σ FSI i , k 1 ( r FSI ( k ) μ FSI i , k ) 2 ) ,
p ( r FSI ( k ) | H i ) = 1 n · j = 1 G ˜ j R FSI i ( k ) n 1 ( 2 π · 2 σ 2 ) k L / 2 exp ( ( P FSI ( k ) ) T G ˜ j r FSI ( k ) 2 L 2 4 σ 2 ) .
λ i , j k = p i , k p j , k · P i P j ,
Σ W k = m = 1 M P m k Σ m ,
Σ B k = m = 1 M P m k [ ( μ m μ ) ( μ m μ ) T ] ,
P j k = p ( r ( k ) | H j ) P j k 1 m = 1 M p ( r ( k ) | H m ) P m k 1 ,
J ( P FSI k + 1 ) = det ( P FSI k + 1 T Σ B k P FSI k + 1 T ) det ( P FSI k + 1 T Σ W k P FSI k + 1 T ) .
E [ K ; n = 11 ] E [ K ; n = 301 ] E [ K ; n = 11 ] ,
p ( r conv ( k ) | H i ) = 1 n ( 2 π σ 2 ) k L / 2 j = 1 n exp ( d ˜ i , j ( k ) / 2 σ 2 ) ,
# of correct decisions # of trials .

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