Skip to main content
SpringerLink
Log in

A wavelet transform based POCS Superresolution algorithm

  • Published:
Journal of Electronics (China)

Abstract

Research interest in multi-frame Superresolution has risen substantially in recent years. This paper presents a modified Projection Onto Convex Set (POCS) superresolution method based on wavelet transform. The method analyzes the image formation model from wavelet multiresolution analysis point of view and defines an closed convex set and its corresponding projection based on wavelet transform. An iterative procedure is utilized to reduce the estimated errors of the result image, and this guarantees the estimated image to lay in the intersection of different convex sets, thus produces a high resolution image with a reduced error. The effectiveness of the algorithm is demonstrated by experimental results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. G. Gleed, A. H. Lettington. Application of superresolution techniques to passive millimetre-wave images. Proceedings of SPIE, Bellingham, WA, 1991, SPIE 1567, 65–72.

    Article  Google Scholar 

  2. D. G. Gleed, A. H. Lettington. High speed superresolution technique for passive millimetre-wave imaging systems. Proceedings of SPIE, Bellingham, WA, 1994, SPIE 2182, 255–265.

    Article  Google Scholar 

  3. H. Greenspan, S. Peled, G. Oz, et al. MRI inter-slice reconstruction using super-resolution. Magnetic Resonance Imaging, 20(2002)5, 437–446.

    Article  Google Scholar 

  4. R. W. Gerchberg. Super-resolution through error energy reduction. Optica Acta, 21(1974)9, 709–720.

    Google Scholar 

  5. A. Papoulis. A new algorithm in spectral analysis and bandlimited extrapolation. IEEE Trans. on Circuits and Systems, CAS-22(1975)9, 735–742.

    Article  MathSciNet  Google Scholar 

  6. P. J. Sementilli, B. R. Hunt, M. S. Nadar. Analysis of the limit to superresolution in incoherent imaging. Journal of Optical Society of America A: Optics, Image Science, and Vision, 10(1993)11, 2265–2276.

    Article  Google Scholar 

  7. M. Elad, A. Feuer. Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images. IEEE Trans. on Image processing, 6(1997)12, 1646–1658.

    Article  Google Scholar 

  8. D. C. Youla. Generalized image restoration by the method of alternating orthogonal projections. IEEE Trans. on Circuits and Systems, CAS-25(1978)9, 694–702.

    Article  MathSciNet  Google Scholar 

  9. A. J. Patti, M. I. Sezan, A. M. Tekalp. Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time. IEEE Trans. on Image Processing, 6(1997)8, 646–1658.

    Article  Google Scholar 

  10. M. K. Ozkan, A. M. Tekalp, M. I. Sezan. POCS-based restoration of space-varying blurred images. IEEE Trans. on Image Processing, 3(1994)4, 450–454.

    Article  Google Scholar 

  11. M. I. Sezan. An overview of convex projections theory and its applications to image recovery problems. Ultramicroscopy, 40(1992)1, 55–67.

    Article  Google Scholar 

  12. S. Mallat. A Wavelet Tour of Signal Processing. San Diego, Acedemic Press, 1999, 265–272.

    MATH  Google Scholar 

  13. T. Frajka, K. Zeger. Downsampling dependent upsampling of images. Signal Processing: Image Communication, 19(2004)3, 257–265.

    Article  Google Scholar 

  14. R. Chan, T. Chan, L. Shen, et al. Wavelet algorithms for high-resolution image reconstruction. SIAM Journal on Scientific Computing, 24(2003)4, 1408–1432.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, 710071, China

    Bin Tian

  2. Laboratory for Computational Neuroscience, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Bin Tian, Robert J. Sclabassi, Jennting T. Hsu, Qiang Liu & Mingui Sun

  3. Departments of Neurological Surgery, Biomedical Engineering and Electrical Engineering University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Robert J. Sclabassi, Jennting T. Hsu, Qiang Liu, Ching Chung Li & Mingui Sun

Authors
  1. Bin Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert J. Sclabassi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jennting T. Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qiang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ching Chung Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mingui Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Tian.

Additional information

Communication author: Tian Bin, born in 1970, male, Ph.D., associate professor. State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China.

About this article

Cite this article

Tian, B., Sclabassi, R.J., Hsu, J.T. et al. A wavelet transform based POCS Superresolution algorithm. J. of Electron.(China) 24, 642–648 (2007). https://doi.org/10.1007/s11767-006-0023-7

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11767-006-0023-7

Key words

CLC index

Search

Navigation