Abstract

In digital imaging, resolution is mostly limited by the nonzero pixel size of the CCD detector. The pixel averages out all the spatial variations falling over it and reduces the overall resolution of the digital image. This Letter introduces a geometric superresolution technique for resolving a pixel into N number of subpixels in one dimension by scanning a mask over it while keeping the imager and scene relatively fixed.

© 2010 Optical Society of America

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References

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  1. A. Borkowski, Z. Zalevsky, and B. Javidi, J. Opt. Soc. Am. A 26, 589 (2009).
    [CrossRef]
  2. Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, Opt. Express 14, 5178 (2006).
    [CrossRef] [PubMed]
  3. Z. Zalevsky and B. Javidi, “A novel approach to attaining high-resolution imaging,” SPIE Electronic Imaging & Signal Processing Newsletter (9 March 2009).
  4. D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
    [CrossRef]
  5. M. Sohail and A. A. Mudassar, Appl. Opt. 49, 3000 (2010).
    [CrossRef] [PubMed]
  6. J. Solomon, Z. Zalevsky, and D. Mendlovic, Appl. Opt. 44, 32, 2005.
    [PubMed]
  7. S. S. Young and R. G. Driggers, Appl. Opt. 45, 5073 (2006).
    [CrossRef] [PubMed]
  8. S. S. Young and R. G. Driggers, Proc. SPIE 5784, 114 (2005).
    [CrossRef]
  9. Z. Zalevsky, D. Mendlovic, and E. Marom, Opt. Eng. 39, 1936 (2000).
    [CrossRef]
  10. Z. Zalevsky, N. Shamir, and D. Mendlovic, Opt. Eng. 43, 1401 (2004).
    [CrossRef]
  11. Z. Zalevsky and D. Mendlovic, Optical Superresolution, 1st ed., Springer Series in Optical Sciences (Springer, 2003).

2010 (1)

2009 (1)

2007 (1)

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
[CrossRef]

2006 (2)

2005 (2)

J. Solomon, Z. Zalevsky, and D. Mendlovic, Appl. Opt. 44, 32, 2005.
[PubMed]

S. S. Young and R. G. Driggers, Proc. SPIE 5784, 114 (2005).
[CrossRef]

2004 (1)

Z. Zalevsky, N. Shamir, and D. Mendlovic, Opt. Eng. 43, 1401 (2004).
[CrossRef]

2000 (1)

Z. Zalevsky, D. Mendlovic, and E. Marom, Opt. Eng. 39, 1936 (2000).
[CrossRef]

Borkowski, A.

Deutsch, M.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
[CrossRef]

Driggers, R. G.

S. S. Young and R. G. Driggers, Appl. Opt. 45, 5073 (2006).
[CrossRef] [PubMed]

S. S. Young and R. G. Driggers, Proc. SPIE 5784, 114 (2005).
[CrossRef]

Fixler, D.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
[CrossRef]

Garcia, J.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
[CrossRef]

Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, Opt. Express 14, 5178 (2006).
[CrossRef] [PubMed]

Garcia-Martinez, P.

Javidi, B.

Z. Zalevsky and B. Javidi, “A novel approach to attaining high-resolution imaging,” SPIE Electronic Imaging & Signal Processing Newsletter (9 March 2009).

A. Borkowski, Z. Zalevsky, and B. Javidi, J. Opt. Soc. Am. A 26, 589 (2009).
[CrossRef]

Marom, E.

Z. Zalevsky, D. Mendlovic, and E. Marom, Opt. Eng. 39, 1936 (2000).
[CrossRef]

Mendlovic, D.

J. Solomon, Z. Zalevsky, and D. Mendlovic, Appl. Opt. 44, 32, 2005.
[PubMed]

Z. Zalevsky, N. Shamir, and D. Mendlovic, Opt. Eng. 43, 1401 (2004).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and E. Marom, Opt. Eng. 39, 1936 (2000).
[CrossRef]

Z. Zalevsky and D. Mendlovic, Optical Superresolution, 1st ed., Springer Series in Optical Sciences (Springer, 2003).

Mudassar, A. A.

Shamir, N.

Z. Zalevsky, N. Shamir, and D. Mendlovic, Opt. Eng. 43, 1401 (2004).
[CrossRef]

Sohail, M.

Solomon, J.

Weiss, A.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
[CrossRef]

Young, S. S.

S. S. Young and R. G. Driggers, Appl. Opt. 45, 5073 (2006).
[CrossRef] [PubMed]

S. S. Young and R. G. Driggers, Proc. SPIE 5784, 114 (2005).
[CrossRef]

Zalevsky, Z.

Z. Zalevsky and B. Javidi, “A novel approach to attaining high-resolution imaging,” SPIE Electronic Imaging & Signal Processing Newsletter (9 March 2009).

A. Borkowski, Z. Zalevsky, and B. Javidi, J. Opt. Soc. Am. A 26, 589 (2009).
[CrossRef]

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
[CrossRef]

Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, Opt. Express 14, 5178 (2006).
[CrossRef] [PubMed]

J. Solomon, Z. Zalevsky, and D. Mendlovic, Appl. Opt. 44, 32, 2005.
[PubMed]

Z. Zalevsky, N. Shamir, and D. Mendlovic, Opt. Eng. 43, 1401 (2004).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and E. Marom, Opt. Eng. 39, 1936 (2000).
[CrossRef]

Z. Zalevsky and D. Mendlovic, Optical Superresolution, 1st ed., Springer Series in Optical Sciences (Springer, 2003).

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Micron (1)

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, Micron 38, 115 (2007).
[CrossRef]

Opt. Eng. (2)

Z. Zalevsky, D. Mendlovic, and E. Marom, Opt. Eng. 39, 1936 (2000).
[CrossRef]

Z. Zalevsky, N. Shamir, and D. Mendlovic, Opt. Eng. 43, 1401 (2004).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

S. S. Young and R. G. Driggers, Proc. SPIE 5784, 114 (2005).
[CrossRef]

SPIE Electronic Imaging & Signal Processing Newsletter (1)

Z. Zalevsky and B. Javidi, “A novel approach to attaining high-resolution imaging,” SPIE Electronic Imaging & Signal Processing Newsletter (9 March 2009).

Other (1)

Z. Zalevsky and D. Mendlovic, Optical Superresolution, 1st ed., Springer Series in Optical Sciences (Springer, 2003).

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Figures (5)

Fig. 1
Fig. 1

Subpixel (image-energy) values at subpixel locations in an image profile over a pixel.

Fig. 2
Fig. 2

Retrieved subpixel values over a pixel.

Fig. 3
Fig. 3

Left, original Lena part over a pixel, before adaptation to one dimension for processing through the 1D geometric superresolution technique; right, recovered Lena part over a pixel, after applying the geometric superresolution technique and converting back to two dimensions.

Fig. 4
Fig. 4

Standard deviation of the error in reconstruction (in dynamic range of 255) versus noise level (having a variance of normalized-dynamic range 0–1) of our suggested technique (upper curve) and of a simple deconvolution tech nique (lower curve).

Fig. 5
Fig. 5

Tolerance of the technique to random fluctuation/error in subpixel shift is shown by the standard deviation (in the dynamic range of 255) caused by the random fluctuation during subpixel shift. The fluctuation is described in terms of error percentage from the planned position.

Equations (9)

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G = { g 1 , g 2 , g 3 , , g N } = { g i | i : 1 to N } .
x i = Round ( 1 + Cos ( π N 1 ( n 1 ) ) ) | n : 1 to ( 2 N 1 ) ,
X j = { x j , 1 , x j , 2 , , x j , 3 , , , x j , N } = { x j , i = Round ( 1 + Cos ( π N 1 ( j + i 2 ) ) ) | i : 1 to N } .
X j | j : 1 to N = { x j , 1 , x j , 2 , , x j , 3 , , , x j , N } | j : 1 to N = { x j , i = Round ( 1 + Cos ( π N 1 ( j + i 2 ) ) ) | i : 1 to N } | j : 1 to N .
p j = i = 1 N x j , i g i
p j | j : 1 to N = i = 1 N x j , i g i | j : 1 to N set of N equations .
P = M · G ,
G = M 1 P .
P = { 1481 , 1145 , 1041 , 664 , 656 , 787 , 772 , 680 , 1001 , 1310 , 1547 , 1697 }

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