Abstract

In response to “Comments on ‘Design and characterization of thin multiple aperture infrared cameras,’” Appl. Opt. 50, 1584 (2011), I explain how aliasing and regularization impact noise scaling in multiple aperture imagers.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. W. Haney, “Performance scaling in flat imagers,” Appl. Opt. 45, 2901–2910 (2006).
    [CrossRef] [PubMed]
  2. D. J. Brady, M. A. Fiddy, U. Shahid, and T. J. Suleski, Compressive Optical MONTAGE Photography Initiative: Noise and Error Analysis (Optical Society of America, 2005).
  3. A. Portnoy, N. Pitsianis, X. Sun, D. Brady, R. Gibbons, A. Silver, R. Te Kolste, C. Chen, T. Dillon, and D. Prather, “Design and characterization of thin multiple aperture infrared cameras,” Appl. Opt. 48, 2115–2126 (2009).
    [CrossRef] [PubMed]
  4. J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): concept and experimental verification,” Appl. Opt. 40, 1806–1813 (2001).
    [CrossRef]
  5. S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
    [CrossRef]
  6. S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
    [CrossRef]
  7. V. R. Bhakta, M. Somayaji, S. C. Douglas, and M. P. Christensen, “Experimentally validated computational imaging with adaptive multiaperture folded architecture,” Appl. Opt. 49, B51–B58 (2010).
    [CrossRef] [PubMed]
  8. F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
    [CrossRef] [PubMed]
  9. A. V. Kanaev, J. R. Ackerman, E. F. Fleet, and D. A. Scribner, “TOMBO sensor with scene-independent superresolution processing,” Opt. Lett. 32, 2855–2857 (2007).
    [CrossRef] [PubMed]
  10. P. M. Shankar, W. C. Hasenplaugh, R. L. Morrison, R. A. Stack, and M. A. Neifeld, “Multiaperture imaging,” Appl. Opt. 45, 2871–2883 (2006).
    [CrossRef] [PubMed]
  11. F. Champagnat, G. Le Besnerais, and C. Kulcsár, “Statistical performance modeling for superresolution: a discrete data-continuous reconstruction framework,” J. Opt. Soc. Am. A 26, 1730–1746 (2009).
    [CrossRef]
  12. K. Krapels, R. G. Driggers, E. Jacobs, S. Burks, and S. Young, “Characteristics of infrared imaging systems that benefit from superresolution reconstruction,” Appl. Opt. 46, 4594–4603(2007).
    [CrossRef] [PubMed]
  13. M. W. Haney, “Comments on ‘Design and characterization of thin multiple aperture infrared cameras,’” Appl. Opt. , 50, 1584–1586 (2011).
    [CrossRef] [PubMed]
  14. D. J. Brady, Optical Imaging and Spectroscopy, N.J.Hoboken, ed. (Wiley-OSA, 2009).
    [CrossRef]
  15. M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).
  16. A. Ashok, P. K. Baheti, and M. A. Neifeld, “Compressive imaging system design using task-specific information,” Appl. Opt. 47, 4457–4471 (2008).
    [CrossRef] [PubMed]
  17. M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293–5303 (2007).
    [CrossRef] [PubMed]
  18. N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).
  19. N. P. Pitsianis, D. J. Brady, and X. B. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
    [CrossRef]
  20. M. Shankar, N. P. Pitsianis, and D. J. Brady, “Compressive video sensors using multichannel imagers,” Appl. Opt. 49, B9–B17 (2010).
    [CrossRef] [PubMed]
  21. M. E. Gehm, S. T. McCain, N. P. Pitsianis, D. J. Brady, P. Potuluri, and M. E. Sullivan, “Static two-dimensional aperture coding for multimodal multiplex spectroscopy,” Appl. Opt. 45, 2965–2974 (2006).
    [CrossRef] [PubMed]
  22. A. A. Wagadarikar, M. E. Gehm, and D. J. Brady, “Performance comparison of aperture codes for multimodal, multiplex spectroscopy,” Appl. Opt. 46, 4932–4942 (2007).
    [CrossRef] [PubMed]
  23. M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027(2007).
    [CrossRef] [PubMed]
  24. A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
    [CrossRef] [PubMed]
  25. A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47, B76–B85 (2008).
    [CrossRef] [PubMed]
  26. S. Prasad, “Digital superresolution and the generalized sampling theorem,” J. Opt. Soc. Am. A 24, 311–325(2007).
    [CrossRef]

2011 (1)

2010 (3)

2009 (2)

2008 (3)

2007 (6)

2006 (4)

2005 (1)

N. P. Pitsianis, D. J. Brady, and X. B. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

2004 (1)

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[CrossRef]

2003 (1)

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

2001 (1)

Ackerman, J. R.

Ashok, A.

Baheti, P. K.

Bhakta, V. R.

Brady, D.

Brady, D. J.

M. Shankar, N. P. Pitsianis, and D. J. Brady, “Compressive video sensors using multichannel imagers,” Appl. Opt. 49, B9–B17 (2010).
[CrossRef] [PubMed]

A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47, B76–B85 (2008).
[CrossRef] [PubMed]

M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027(2007).
[CrossRef] [PubMed]

A. A. Wagadarikar, M. E. Gehm, and D. J. Brady, “Performance comparison of aperture codes for multimodal, multiplex spectroscopy,” Appl. Opt. 46, 4932–4942 (2007).
[CrossRef] [PubMed]

M. E. Gehm, S. T. McCain, N. P. Pitsianis, D. J. Brady, P. Potuluri, and M. E. Sullivan, “Static two-dimensional aperture coding for multimodal multiplex spectroscopy,” Appl. Opt. 45, 2965–2974 (2006).
[CrossRef] [PubMed]

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).

N. P. Pitsianis, D. J. Brady, and X. B. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

D. J. Brady, Optical Imaging and Spectroscopy, N.J.Hoboken, ed. (Wiley-OSA, 2009).
[CrossRef]

D. J. Brady, M. A. Fiddy, U. Shahid, and T. J. Suleski, Compressive Optical MONTAGE Photography Initiative: Noise and Error Analysis (Optical Society of America, 2005).

Burks, S.

Champagnat, F.

Chen, C.

Christensen, M. P.

de la Barrière, F.

Deschamps, J.

Dillon, T.

Douglas, S. C.

Driggers, R. G.

Druart, G.

Elad, M.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[CrossRef]

Farsiu, S.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[CrossRef]

Feldman, M. R.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).

Fiddy, M. A.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).

D. J. Brady, M. A. Fiddy, U. Shahid, and T. J. Suleski, Compressive Optical MONTAGE Photography Initiative: Noise and Error Analysis (Optical Society of America, 2005).

Fleet, E. F.

Gehm, M. E.

Gibbons, R.

Guérineau, N.

Haney, M. W.

Harwit, M.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Hasenplaugh, W. C.

Ichioka, Y.

Ishida, K.

Jacobs, E.

John, R.

Kanaev, A. V.

Kang, M. G.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Ke, J.

Kondou, N.

Krapels, K.

Kulcsár, C.

Kumagai, T.

Le Besnerais, G.

McCain, S. T.

Milanfar, P.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[CrossRef]

Miyatake, S.

Miyazaki, D.

Morimoto, T.

Morrison, R. L.

Neifeld, M. A.

Park, M. K.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Park, S. C.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Pitsianis, N.

Pitsianis, N. P.

Portnoy, A.

A. Portnoy, N. Pitsianis, X. Sun, D. Brady, R. Gibbons, A. Silver, R. Te Kolste, C. Chen, T. Dillon, and D. Prather, “Design and characterization of thin multiple aperture infrared cameras,” Appl. Opt. 48, 2115–2126 (2009).
[CrossRef] [PubMed]

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).

Portnoy, A. D.

Potuluri, P.

Prasad, S.

Prather, D.

Primot, J.

Robinson, D.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[CrossRef]

Schulz, T. J.

Scribner, D. A.

Shahid, U.

D. J. Brady, M. A. Fiddy, U. Shahid, and T. J. Suleski, Compressive Optical MONTAGE Photography Initiative: Noise and Error Analysis (Optical Society of America, 2005).

Shankar, M.

Shankar, P. M.

Silver, A.

Sloane, N. J. A.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Somayaji, M.

Stack, R. A.

Suleski, T.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).

Suleski, T. J.

D. J. Brady, M. A. Fiddy, U. Shahid, and T. J. Suleski, Compressive Optical MONTAGE Photography Initiative: Noise and Error Analysis (Optical Society of America, 2005).

Sullivan, M. E.

Sun, X.

Sun, X. B.

N. P. Pitsianis, D. J. Brady, and X. B. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

Taboury, J.

Tanida, J.

Te Kolste, R.

TeKolste, R. D.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).

Wagadarikar, A.

Wagadarikar, A. A.

Willett, R.

Willett, R. M.

Yamada, K.

Young, S.

Appl. Opt. (15)

M. W. Haney, “Performance scaling in flat imagers,” Appl. Opt. 45, 2901–2910 (2006).
[CrossRef] [PubMed]

A. Portnoy, N. Pitsianis, X. Sun, D. Brady, R. Gibbons, A. Silver, R. Te Kolste, C. Chen, T. Dillon, and D. Prather, “Design and characterization of thin multiple aperture infrared cameras,” Appl. Opt. 48, 2115–2126 (2009).
[CrossRef] [PubMed]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): concept and experimental verification,” Appl. Opt. 40, 1806–1813 (2001).
[CrossRef]

V. R. Bhakta, M. Somayaji, S. C. Douglas, and M. P. Christensen, “Experimentally validated computational imaging with adaptive multiaperture folded architecture,” Appl. Opt. 49, B51–B58 (2010).
[CrossRef] [PubMed]

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

P. M. Shankar, W. C. Hasenplaugh, R. L. Morrison, R. A. Stack, and M. A. Neifeld, “Multiaperture imaging,” Appl. Opt. 45, 2871–2883 (2006).
[CrossRef] [PubMed]

K. Krapels, R. G. Driggers, E. Jacobs, S. Burks, and S. Young, “Characteristics of infrared imaging systems that benefit from superresolution reconstruction,” Appl. Opt. 46, 4594–4603(2007).
[CrossRef] [PubMed]

M. W. Haney, “Comments on ‘Design and characterization of thin multiple aperture infrared cameras,’” Appl. Opt. , 50, 1584–1586 (2011).
[CrossRef] [PubMed]

A. Ashok, P. K. Baheti, and M. A. Neifeld, “Compressive imaging system design using task-specific information,” Appl. Opt. 47, 4457–4471 (2008).
[CrossRef] [PubMed]

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

M. Shankar, N. P. Pitsianis, and D. J. Brady, “Compressive video sensors using multichannel imagers,” Appl. Opt. 49, B9–B17 (2010).
[CrossRef] [PubMed]

M. E. Gehm, S. T. McCain, N. P. Pitsianis, D. J. Brady, P. Potuluri, and M. E. Sullivan, “Static two-dimensional aperture coding for multimodal multiplex spectroscopy,” Appl. Opt. 45, 2965–2974 (2006).
[CrossRef] [PubMed]

A. A. Wagadarikar, M. E. Gehm, and D. J. Brady, “Performance comparison of aperture codes for multimodal, multiplex spectroscopy,” Appl. Opt. 46, 4932–4942 (2007).
[CrossRef] [PubMed]

A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
[CrossRef] [PubMed]

A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47, B76–B85 (2008).
[CrossRef] [PubMed]

IEEE Signal Process. Mag. (1)

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

N. P. Pitsianis, D. J. Brady, and X. B. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

Other (4)

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, 6232, A2320(2006).

D. J. Brady, Optical Imaging and Spectroscopy, N.J.Hoboken, ed. (Wiley-OSA, 2009).
[CrossRef]

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

D. J. Brady, M. A. Fiddy, U. Shahid, and T. J. Suleski, Compressive Optical MONTAGE Photography Initiative: Noise and Error Analysis (Optical Society of America, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Sampling matrix, object side singular vectors and singular value spectra for the 15 × 15 Hadamard S matrix and for a 15 × 15 unipolar random matrix.

Fig. 2
Fig. 2

System transfer function along the u axis for pixel transfer function dominated multiple aperture imaging systems. The vertical line at u = 1 / 2 Δ is the aliasing boundary.

Equations (6)

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

g = H f + n
f est = ( H H ) 1 H ( g n ¯ ) ,
σ est 2 = σ 2 N trace ( ( H H ) 1 ) ,
σ est 2 = n 2 σ 2 trace ( ( H ^ H ^ ) 1 ) .
f est = P H ^ f + i = 1 r u i · n λ i v i ,
STF ( u , v ) = | sinc ( n u Δ ) sinc ( n v Δ ) | ,

Metrics