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A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution)

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Abstract

Superresolution produces high-quality, high-resolution images from a set of degraded, low-resolution images where relative frame-to-frame motions provide different looks at the scene. Superresolution translates data temporal bandwith into enhanced spatial resolution. If considered together on a reference grid, given low-resolution data are nonuniformly sampled. However, data from each frame are sampled regularly on a rectangular grid. This special type of nonuniform sampling is called interlaced sampling. We propose a new wavelet-based interpolation-restoration algorithm for superresolution. Our efficient wavelet interpolation technique takes advantage of the regularity and structure inherent in interlaced data, thereby significantly reducing the computational burden. We present one- and two-dimensional superresolution experiments to demonstrate the effectiveness of our algorithm.

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References

  1. K. Aizawa, T. Komatsu, and T. Saito, Acquisition of very high resolution images using stereo cameras, inProceedings SPIE Visual Communications and Image Processing ′91, Boston, MA, pp. 318–328, November 1991.

  2. O. Axelsson,Iterative Solution Methods, Cambridge University Press, New York, 1994.

    Google Scholar 

  3. M. Crouse, R. Nowak, and R. Baraniuk, Wavelet-based statiscal signal processing using hidden Markov models,IEEE Trans. Signal Process, 46(4), 886–902, April 1998.

    Google Scholar 

  4. I. Daubechies,Ten Lectures on Waveles, SIMA, New York, 1992.

    Google Scholar 

  5. M. Elad, Super-resolution reconstruction of images. Ph.D. thesis, The Technion-Israel Institute of Technology, December 1996.

  6. C. Ford and D. Etter, Wavelet basis reconstruction of nonuniformly sampled data,IEEE Trans. Circuits and Systems II, 45(8), 1165–1168, August 1998.

    Google Scholar 

  7. R. Hardie, K. Barnard, and E. Amstrong, Joint MAP registration and high-resolution image estimation using a sequence of undersampled images,IEEE Trans. Image Process., 6(12), December 1997.

    Google Scholar 

  8. W. Lukosz, Optical systems with resolving power exceeding the classical limit,J. Opt. Soc. Am., 56(11), 1463–1472, 1966.

    Google Scholar 

  9. W. Lukosz, Optical systems with resolving power exceeding the classical limits II,J. Opt. Soc. Am. 57(7), 932–941, 1967.

    Google Scholar 

  10. S. Mallat, A theory for multiresolution in signal decomposition: The wavelet representation,IEEE Trans. Pattern Anal. Mach. Intellig., 11(7), 674–683, July 1989.

    Google Scholar 

  11. Y. Meyer, Principe d'incertitude, bases Hilbertiennes et algebres d'operateurs, inBourbaki Siminar, vol. 662, Paris, pp. 1985–1986.

  12. N. Nguyen, Numerical techniques for image superresolution, Ph. D. thesis, Stanford University, May 2000.

  13. N. Nguyen, P. Milanfar, and G. Golub, Blind superresolution with generalized cross-validation using Gauss-type quadrature rules, inProceedings of the 33rd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, October 1999.

  14. K. Sauer and J. Allebach, Iterative reconstruction of band-limited images from non-uniformly spaced samples,IEEE Trans. Circuits and systems, CAS-34, 1497–1505, 1987.

    Google Scholar 

  15. H. Shekarforoush and R. Chellappa, Data-driven multi-channel super-resolution with application to video sequences,J. Opt. Soc. Am. A, 16(30), 481–492, March 1999.

    Google Scholar 

  16. E. Simoncelli, Statistical models for images: Compression, restoration and synthesis, inProceedings of the 31st Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 1997.

  17. G. Strang and T. Nguyen,Wavelet and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, 1997.

    Google Scholar 

  18. A. Tekalp, M. Ozkan, and M. Sezan, High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration, inProceedings ICASSP ′92, vol. 3, San Francisco, CA, pp. 169–172, March 1992.

  19. H. Ur and D. Gross, Improved resolution from subpixel shifted pictures,CVGIP: Graphical Models and Image Processing, 54(2), 181–186, March 1992.

    Google Scholar 

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Authors and Affiliations

  1. Scientific Computing and Computational Mathematics Program, Standrod University, 94305-9025, Stanford, California, USA

    Nhat Nguyen

  2. Department of Electrical Engineering, University of California, 95064, Santa Cruz, California, USA

    Peyman Milanfar

Authors
  1. Nhat Nguyen
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  2. Peyman Milanfar
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Additional information

This work was supported in part by the National Science Foundartion Grant CCR-9984246.

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Nguyen, N., Milanfar, P. A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution). Circuits Systems and Signal Process 19, 321–338 (2000). https://doi.org/10.1007/BF01200891

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  • DOI: https://doi.org/10.1007/BF01200891

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