Abstract

In optical imaging, the resolution of the imaging system is not only limited by the aperture and imperfection of the lens, but also by the CCD nonzero pixel size and separation between the two consecutive pixels. We deal only with the geometric superresolution and assume that the size of the CCD pixels is much smaller in comparison with the separation between the pixels. The separation between the pixels limits the resolution of the CCD camera. Our object is to address this problem. In the proposal, we focus on exceeding the geometric resolution with a new approach in which no moving element of the imaging system is used, but only a mask is placed at the Fourier transform plane. This mask encodes the input data. The encoded image is captured by the CCD. The captured image is then Fourier transformed and a decoding mask is used to nullify the effect of undersampling by the CCD. Mathematical modeling and simulation in one dimension are presented.

© 2010 Optical Society of America

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References

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  2. S. Peleg, D. Keren, and L. Schweitzer, “Improving image resolution using subpixel motion,” Phys. Rev. Lett. 5, 223–226(1987).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
    [CrossRef]

2008

2007

K. Yu, N. Park, D. Lee, and O. Solgaard, “Super-resolution digital image enhancement by subpixel image translation with a scanning micromirror,” IEEE J. Sel. Top. Quantum Electron. 13, 304–311 (2007).
[CrossRef]

2006

M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
[CrossRef]

S. K. Nayar, “Computational cameras: redefining the image,” IEEE Computer 39, 30–38 (2006).
[CrossRef]

Z. Zalevsky, P. García-Martínez, and J. García, “Superresolution using gray level coding,” Opt. Express 14, 5178–5182(2006).
[CrossRef] [PubMed]

2005

2003

2000

Z. Zalevsky, D. Mendelovic, and A. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

1999

1992

1987

S. Peleg, D. Keren, and L. Schweitzer, “Improving image resolution using subpixel motion,” Phys. Rev. Lett. 5, 223–226(1987).

Brada, R.

D. Keren, S. Peleg, and R. Brada, “Image sequence enhancement using sub-pixel displacements,” in Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition ’88 (IEEE, 1988), pp. 742–746.
[CrossRef]

Brady, D. J.

Bramberger, M.

M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
[CrossRef]

Doblander, A.

M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
[CrossRef]

Eldeniz, C.

Garcia, J.

García, J.

García-Martínez, P.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd international ed. (McGraw-Hill, 1996), pp. 101–104.

Keren, D.

S. Peleg, D. Keren, and L. Schweitzer, “Improving image resolution using subpixel motion,” Phys. Rev. Lett. 5, 223–226(1987).

D. Keren, S. Peleg, and R. Brada, “Image sequence enhancement using sub-pixel displacements,” in Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition ’88 (IEEE, 1988), pp. 742–746.
[CrossRef]

Kim, C.

Kim, J.

Lee, D.

K. Yu, N. Park, D. Lee, and O. Solgaard, “Super-resolution digital image enhancement by subpixel image translation with a scanning micromirror,” IEEE J. Sel. Top. Quantum Electron. 13, 304–311 (2007).
[CrossRef]

Leith, E. N.

Maier, A.

M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
[CrossRef]

Marcia, R. F.

Marom, A.

Z. Zalevsky, D. Mendelovic, and A. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

Martinez, P. G.

Mendelovic, D.

Z. Zalevsky, D. Mendelovic, and A. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

Mendlovic, D.

Nayar, S. K.

S. K. Nayar, “Computational cameras: redefining the image,” IEEE Computer 39, 30–38 (2006).
[CrossRef]

Park, N.

K. Yu, N. Park, D. Lee, and O. Solgaard, “Super-resolution digital image enhancement by subpixel image translation with a scanning micromirror,” IEEE J. Sel. Top. Quantum Electron. 13, 304–311 (2007).
[CrossRef]

Peleg, S.

S. Peleg, D. Keren, and L. Schweitzer, “Improving image resolution using subpixel motion,” Phys. Rev. Lett. 5, 223–226(1987).

D. Keren, S. Peleg, and R. Brada, “Image sequence enhancement using sub-pixel displacements,” in Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition ’88 (IEEE, 1988), pp. 742–746.
[CrossRef]

Rinner, B.

M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
[CrossRef]

Schilling, D. L.

H. Taub and D. L. Schilling, Principles of Communication Systems, 2nd ed. (McGraw-Hill, 1986).

Schwabach, H.

M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
[CrossRef]

Schweitzer, L.

S. Peleg, D. Keren, and L. Schweitzer, “Improving image resolution using subpixel motion,” Phys. Rev. Lett. 5, 223–226(1987).

Shemer, A.

Solgaard, O.

K. Yu, N. Park, D. Lee, and O. Solgaard, “Super-resolution digital image enhancement by subpixel image translation with a scanning micromirror,” IEEE J. Sel. Top. Quantum Electron. 13, 304–311 (2007).
[CrossRef]

Solomon, J.

Sun, P. C.

Taub, H.

H. Taub and D. L. Schilling, Principles of Communication Systems, 2nd ed. (McGraw-Hill, 1986).

Willett, R. M.

Yu, K.

K. Yu, N. Park, D. Lee, and O. Solgaard, “Super-resolution digital image enhancement by subpixel image translation with a scanning micromirror,” IEEE J. Sel. Top. Quantum Electron. 13, 304–311 (2007).
[CrossRef]

Zalevsky, Z.

Appl. Opt.

Computer

M. Bramberger, A. Doblander, A. Maier, B. Rinner, and H. Schwabach, “Distributed embedded smart cameras for surveillance applications,” Computer 39, 68–75 (2006).
[CrossRef]

IEEE Computer

S. K. Nayar, “Computational cameras: redefining the image,” IEEE Computer 39, 30–38 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Yu, N. Park, D. Lee, and O. Solgaard, “Super-resolution digital image enhancement by subpixel image translation with a scanning micromirror,” IEEE J. Sel. Top. Quantum Electron. 13, 304–311 (2007).
[CrossRef]

Opt. Eng.

Z. Zalevsky, D. Mendelovic, and A. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

S. Peleg, D. Keren, and L. Schweitzer, “Improving image resolution using subpixel motion,” Phys. Rev. Lett. 5, 223–226(1987).

Other

D. Keren, S. Peleg, and R. Brada, “Image sequence enhancement using sub-pixel displacements,” in Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition ’88 (IEEE, 1988), pp. 742–746.
[CrossRef]

H. Taub and D. L. Schilling, Principles of Communication Systems, 2nd ed. (McGraw-Hill, 1986).

J. Goodman, Introduction to Fourier Optics, 2nd international ed. (McGraw-Hill, 1996), pp. 101–104.

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Figures (7)

Fig. 1
Fig. 1

Delta function with spacing p.

Fig. 2
Fig. 2

Signal after the multiplication with the optical mask in the frequency domain.

Fig. 3
Fig. 3

Replicas before the decoding mask.

Fig. 4
Fig. 4

Replicas after the decoding mask.

Fig. 5
Fig. 5

Multiplication of two delta functions yields one delta function.

Fig. 6
Fig. 6

(a) The unoverlapped multiple copies of the input spectrum; (b) represents the filter, and (c) selects the central copy from the incoming multiple input spectrum.

Fig. 7
Fig. 7

(a) Input object. (b) Fourier transform of the input object. (c) Optical mask. (d) Multiplication of (b) and (c). (e) Inverse of (d) is the image, which is at the CCD plane. (f) Image captured by the CCD. (g) Fourier transform of (f). (h) Multiplication of optical mask and (g). (i) Multiplication of the filter with (h) to select the central copy of the spectrum. (j) Interpolation of (i). (k) Inverse of (j) gives the output image. (l) Original input object.

Equations (14)

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G ( v ) = J { g ( x ) } .
O ˜ ( v ) = G ( v ) O M ˜ ( v ) .
O M ˜ ( v ) = k = δ ( v k p ) ,
O ˜ ( v ) = G ( v ) k = δ ( v k p ) .
O ( x ) = J 1 { O ˜ ( v ) } = J 1 { G ( v ) k = δ ( v k p ) } .
S ( x ) = O ( x ) CCD ( x ) = J 1 { G ( v ) k = δ ( v k p ) } n = δ ( x n X ) ,
CCD ( x ) = n = δ ( x n X ) .
S ˜ ( v ) = J [ J 1 { G ( v ) k = δ ( v k p ) } n = δ ( x n X ) ] ,
J [ n = δ ( x n X ) ] = n = δ [ v n ( Δ v + p 2 ) ] ,
S ˜ ( v ) = { G ( v ) k = δ ( v k p ) } n = δ [ v n ( Δ v + p 2 ) ] .
S ˜ ( v ) = n = [ G { v n ( Δ v + p 2 ) } k = δ { v k p n ( Δ v + p 2 ) } ] .
R ˜ ( v ) = k = n = [ G { v n ( Δ v + p 2 ) } δ { v k p n ( Δ v + p 2 ) } ] O M ˜ ( v ) , R ˜ ( v ) = m = k = n = [ G ( v n Δ v n p 2 ) δ { v n Δ v ( n 2 + k ) p } ] δ ( v m p ) .
R ˜ ( v ) = n = even k = G ( v n Δ v n p 2 ) δ { v n Δ v ( n 2 + k ) p } .
R ˜ ( v ) = k = G ( v ) δ ( v k p ) .

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