Abstract

We analyze the performance of feature-specific imaging systems. We study incoherent optical systems that directly measure linear projects of the optical irradiance distribution. Direct feature measurement exploits the multiplex advantage, and for small numbers of projections can provide higher feature-fidelity than those systems that postprocess a conventional image. We examine feature-specific imaging using Wavelet, Karhunen-Loeve (KL), Hadamard, and independent-component features, quantifying feature fidelity in Gaussian-, shot-, and quantization-noise environments. An example of feature-specific imaging based on KL projections is analyzed and demonstrates that within a high-noise environment it is possible to improve image fidelity via direct feature measurement. A candidate optical system is presented and a preliminary implementational study is undertaken.

© 2003 Optical Society of America

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2002

2001

2000

E. Clarkson, H. H. Barrett, “Approximations to ideal-observer performance on signal-detection tasks,” Appl. Opt. 39, 1783–1793 (2000).
[CrossRef]

W. C. Chou, M. A. Neifeld, R. Xuan, “Information-based optical design for binary-valued imagery,” Appl. Opt. 39, 1731–1742 (2000).
[CrossRef]

S. Prasad, “Information capacity of a seeing-limited imaging system,” Opt. Commun. 177, 119–134 (2000).
[CrossRef]

A. Hyvarinen, “Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef] [PubMed]

1999

S. J. Lee, S. B. Jung, J. W. Kwon, S. H. Hong, “Face detection and recognition using PCA,” TENCON 99 Proc. IEEE Region 10 Conference 1, 84–87 (1999).

S. Tucker, W. T. Cathey, E. Dowski, “Extended depth of field and aberration control for inexpensive digital microscope systems,” Optics Express 4, 467–474 (1999).
[CrossRef] [PubMed]

1992

M. Antonini, M. Barlaud, P. Mathieu, I. Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Process. 1, 205–220 (1992).
[CrossRef] [PubMed]

1991

1990

I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
[CrossRef]

1976

1975

A. G. Marshall, M. B. Comisarow, “Fourier and Hadamard transform methods in spectroscopy,” Anal. Chem. 47, 491–504 (1975).

1971

H. J. Landau, D. Slepian, “Some computer experiments in picture processing for bandwidth reduction,” Bell Syst. Tech. J. 50, 1525–1540 (1971).
[CrossRef]

1955

P. B. Fellgett, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 269–407 (1955).
[CrossRef]

Antonini, M.

M. Antonini, M. Barlaud, P. Mathieu, I. Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Process. 1, 205–220 (1992).
[CrossRef] [PubMed]

Athale, R. A.

Aysin, A.

A. Aysin, L. F. Chaparro, I. Grave, V. Shusterman, “Denoising of Non-Stationary Signals Using Optimized Karhunen-Loeve Expansion,” Proc. IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 621–624 (1998).

Barlaud, M.

M. Antonini, M. Barlaud, P. Mathieu, I. Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Process. 1, 205–220 (1992).
[CrossRef] [PubMed]

Barrett, H. H.

Brady, D.

Brady, D. J.

Cathey, W. T.

S. Tucker, W. T. Cathey, E. Dowski, “Extended depth of field and aberration control for inexpensive digital microscope systems,” Optics Express 4, 467–474 (1999).
[CrossRef] [PubMed]

Centurion, M.

Chaparro, L. F.

A. Aysin, L. F. Chaparro, I. Grave, V. Shusterman, “Denoising of Non-Stationary Signals Using Optimized Karhunen-Loeve Expansion,” Proc. IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 621–624 (1998).

Chou, W. C.

Christensen, M. P.

Clarkson, E.

Comisarow, M. B.

A. G. Marshall, M. B. Comisarow, “Fourier and Hadamard transform methods in spectroscopy,” Anal. Chem. 47, 491–504 (1975).

Coyle, K. M.

Daubechies, I.

M. Antonini, M. Barlaud, P. Mathieu, I. Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Process. 1, 205–220 (1992).
[CrossRef] [PubMed]

I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
[CrossRef]

Decker, J. A.

Diamantaras, K. I.

K. I. Diamantaras, S. Y. Kung, Principal Components Neural Networks: Theory and Applications, (Wiley, New York, 1996), pp. 44–73.

Dowski, E.

S. Tucker, W. T. Cathey, E. Dowski, “Extended depth of field and aberration control for inexpensive digital microscope systems,” Optics Express 4, 467–474 (1999).
[CrossRef] [PubMed]

Effros, M.

H. Feng, M. Effros, “On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression,” IEEE Trans. Image Process. 11, 113–122 (2002).
[CrossRef]

Euliss, G. W.

Fellgett, P. B.

P. B. Fellgett, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 269–407 (1955).
[CrossRef]

Feng, H.

H. Feng, M. Effros, “On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression,” IEEE Trans. Image Process. 11, 113–122 (2002).
[CrossRef]

Fetterman, M.

Grave, I.

A. Aysin, L. F. Chaparro, I. Grave, V. Shusterman, “Denoising of Non-Stationary Signals Using Optimized Karhunen-Loeve Expansion,” Proc. IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 621–624 (1998).

Haney, M. W.

Harwit, M.

Hong, J.

Hong, S. H.

S. J. Lee, S. B. Jung, J. W. Kwon, S. H. Hong, “Face detection and recognition using PCA,” TENCON 99 Proc. IEEE Region 10 Conference 1, 84–87 (1999).

Hyvarinen, A.

A. Hyvarinen, “Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef] [PubMed]

A. Hyvarinen, “Fast ICA by a fixed-point algorithm that maximizes non-Gaussianity,” Independent Component Analysis: Principles and Practice, R. Stephen, E. Richard, eds. (Cambridge University, Cambridge, UK, 2001), Chap. 2, pp. 71–94.

Johnson, A. J.

Jung, S. B.

S. J. Lee, S. B. Jung, J. W. Kwon, S. H. Hong, “Face detection and recognition using PCA,” TENCON 99 Proc. IEEE Region 10 Conference 1, 84–87 (1999).

Kawamura, T.

H. Saruwatari, T. Kawamura, K. Shikano, “Fast-convergence algorithm for ICA-based blind source separation using array signal processing,” Proc. IEEE 11th Signal Processing Workshop on Statistical Signal Processing, 464–467 (2001).

Kung, S. Y.

K. I. Diamantaras, S. Y. Kung, Principal Components Neural Networks: Theory and Applications, (Wiley, New York, 1996), pp. 44–73.

Kwon, J. W.

S. J. Lee, S. B. Jung, J. W. Kwon, S. H. Hong, “Face detection and recognition using PCA,” TENCON 99 Proc. IEEE Region 10 Conference 1, 84–87 (1999).

Landau, H. J.

H. J. Landau, D. Slepian, “Some computer experiments in picture processing for bandwidth reduction,” Bell Syst. Tech. J. 50, 1525–1540 (1971).
[CrossRef]

Lee, S. J.

S. J. Lee, S. B. Jung, J. W. Kwon, S. H. Hong, “Face detection and recognition using PCA,” TENCON 99 Proc. IEEE Region 10 Conference 1, 84–87 (1999).

Linfoot, E. H.

P. B. Fellgett, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 269–407 (1955).
[CrossRef]

Liu, Z.

Mann, C. K.

Marks, D. L.

Marshall, A. G.

A. G. Marshall, M. B. Comisarow, “Fourier and Hadamard transform methods in spectroscopy,” Anal. Chem. 47, 491–504 (1975).

Mathieu, P.

M. Antonini, M. Barlaud, P. Mathieu, I. Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Process. 1, 205–220 (1992).
[CrossRef] [PubMed]

McFadden, M. J.

Milojkovic, P.

Munson, D. C.

Neifeld, M. A.

Oliver, C. J.

Paganetti, R.

Panotopoulos, G.

Potuluri, P.

Prasad, S.

S. Prasad, “Information capacity of a seeing-limited imaging system,” Opt. Commun. 177, 119–134 (2000).
[CrossRef]

Psaltis, D.

Richard, E.

R. Stephen, E. Richard, Independent Component Analysis: Principles and Practice, R. Stephen, E. Richard, eds. (Cambridge University, Cambridge, UK, 2001), Chap. 1, 1–70.

Saruwatari, H.

H. Saruwatari, T. Kawamura, K. Shikano, “Fast-convergence algorithm for ICA-based blind source separation using array signal processing,” Proc. IEEE 11th Signal Processing Workshop on Statistical Signal Processing, 464–467 (2001).

Shikano, K.

H. Saruwatari, T. Kawamura, K. Shikano, “Fast-convergence algorithm for ICA-based blind source separation using array signal processing,” Proc. IEEE 11th Signal Processing Workshop on Statistical Signal Processing, 464–467 (2001).

Shusterman, V.

A. Aysin, L. F. Chaparro, I. Grave, V. Shusterman, “Denoising of Non-Stationary Signals Using Optimized Karhunen-Loeve Expansion,” Proc. IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 621–624 (1998).

Slepian, D.

H. J. Landau, D. Slepian, “Some computer experiments in picture processing for bandwidth reduction,” Bell Syst. Tech. J. 50, 1525–1540 (1971).
[CrossRef]

Sloane, N. J. A.

M. Harwit, N. J. A. Sloane, Hadamard Transform Optics, (Academic, New York, 1979), pp. 62–70.

Stack, R.

Stephen, R.

R. Stephen, E. Richard, Independent Component Analysis: Principles and Practice, R. Stephen, E. Richard, eds. (Cambridge University, Cambridge, UK, 2001), Chap. 1, 1–70.

Swift, R. D.

Tucker, S.

S. Tucker, W. T. Cathey, E. Dowski, “Extended depth of field and aberration control for inexpensive digital microscope systems,” Optics Express 4, 467–474 (1999).
[CrossRef] [PubMed]

van der Gracht, J.

Vickers, T. J.

Wattson, R. B.

Xuan, R.

Zhu, J.

Anal. Chem.

A. G. Marshall, M. B. Comisarow, “Fourier and Hadamard transform methods in spectroscopy,” Anal. Chem. 47, 491–504 (1975).

Appl. Opt.

Appl. Spectrosc.

Bell Syst. Tech. J.

H. J. Landau, D. Slepian, “Some computer experiments in picture processing for bandwidth reduction,” Bell Syst. Tech. J. 50, 1525–1540 (1971).
[CrossRef]

IEEE Trans. Image Process.

M. Antonini, M. Barlaud, P. Mathieu, I. Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Process. 1, 205–220 (1992).
[CrossRef] [PubMed]

H. Feng, M. Effros, “On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression,” IEEE Trans. Image Process. 11, 113–122 (2002).
[CrossRef]

IEEE Trans. Inf. Theory

I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
[CrossRef]

Neural Comput.

A. Hyvarinen, “Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef] [PubMed]

Opt. Commun.

S. Prasad, “Information capacity of a seeing-limited imaging system,” Opt. Commun. 177, 119–134 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Optics Express

S. Tucker, W. T. Cathey, E. Dowski, “Extended depth of field and aberration control for inexpensive digital microscope systems,” Optics Express 4, 467–474 (1999).
[CrossRef] [PubMed]

Philos. Trans. R. Soc. London

P. B. Fellgett, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 269–407 (1955).
[CrossRef]

TENCON 99 Proc. IEEE Region 10 Conference

S. J. Lee, S. B. Jung, J. W. Kwon, S. H. Hong, “Face detection and recognition using PCA,” TENCON 99 Proc. IEEE Region 10 Conference 1, 84–87 (1999).

Other

A. Aysin, L. F. Chaparro, I. Grave, V. Shusterman, “Denoising of Non-Stationary Signals Using Optimized Karhunen-Loeve Expansion,” Proc. IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 621–624 (1998).

H. Saruwatari, T. Kawamura, K. Shikano, “Fast-convergence algorithm for ICA-based blind source separation using array signal processing,” Proc. IEEE 11th Signal Processing Workshop on Statistical Signal Processing, 464–467 (2001).

A. Hyvarinen, “Fast ICA by a fixed-point algorithm that maximizes non-Gaussianity,” Independent Component Analysis: Principles and Practice, R. Stephen, E. Richard, eds. (Cambridge University, Cambridge, UK, 2001), Chap. 2, pp. 71–94.

M. Harwit, N. J. A. Sloane, Hadamard Transform Optics, (Academic, New York, 1979), pp. 62–70.

K. I. Diamantaras, S. Y. Kung, Principal Components Neural Networks: Theory and Applications, (Wiley, New York, 1996), pp. 44–73.

R. Stephen, E. Richard, Independent Component Analysis: Principles and Practice, R. Stephen, E. Richard, eds. (Cambridge University, Cambridge, UK, 2001), Chap. 1, 1–70.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of (a) a conventional imager, (b) a feature-specific imager.

Fig. 2
Fig. 2

Hadamard projection matricies of order 8 with: (a) natural ordering, (b) sequential ordering.

Fig. 3
Fig. 3

Wavelet projection matricies of order 8: (a) Integer-valued Haar wavelets, (b) real-valued DAUB4 wavelets.

Fig. 4
Fig. 4

(a) Ten faces used for training the KL and ICA features, (b) first 16 KL features computed using N = 64. Each 64-dimensional feature appears as an 8 × 8 image, (c) first 16 ICA features computed using N = 64. These features are rendered as in (b).

Fig. 5
Fig. 5

(a) Relative feature fidelity (i.e., η) versus number of features (M) under AWGN noise model described in the text for N = 64. (b) η versus fractional number of KL features under AWGN model for N = 36, 49, 64, and 81. η versus M under (c) shot-noise, and (d) quantization noise models described in the text for N = 64.

Fig. 6
Fig. 6

Reconstructed images obtained with (a) conventional imaging (MSE d = 500), (b) feature-specific imaging (MSEkl = 154). AWGN corrupts all measurements with σ2 = 500 and the feature-specific imager used M = 4 and N = 64.

Fig. 7
Fig. 7

Reconstruction MSE for KL feature-specific imaging corrupted by AWGN. (a) MSE versus number of features for σ2 = 500 and N = 16, 36, and 64. (b) Minimum MSE versus blocksize for σ2 = 500. (c) Optimum KL feature-specific imaging performance versus noise standard deviation.

Fig. 8
Fig. 8

Test images for evaluating training-set-sensitivity of KL feature-specific imaging: (a) Man, (b) Dog, (c) Desk, (d) Car, and (e) Goldhill.

Fig. 9
Fig. 9

Candidate feature-specific imaging architecture: PBS = polarizing beamsplitter, SPM = spatial polarization modulator, D1+ and D1- are detectors for the positive and negative components of the 1st feature measurement and D2+ and D2- are for the 2nd feature.

Fig. 10
Fig. 10

SPM response function used in optical system tolerancing study.

Tables (1)

Tables Icon

Table 1 Crossover Noise Costa

Equations (2)

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

MSEkl=1Ni=M+1N λi+Mσ2NC+k2+C-1-k2,
MSEkl=1Ni=M+1N λi+σ2Ni=1MC+aai2+C-bbi2.

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