Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Super-Resolution Image Restoration from Blurred Low-Resolution Images

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In this paper, we study the problem of reconstructing a high-resolution image from several blurred low-resolution image frames. The image frames consist of decimated, blurred and noisy versions of the high-resolution image. The high-resolution image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, the high-resolution image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore the high-resolution image. Computer simulations are given to illustrate the effectiveness of the proposed method.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. H. Andrew and B. Hunt, Digital Image Restoration, Prentice-Hall, New Jersey, 1977.

    Google Scholar 

  2. B. Bascle, A. Blake, and A. Zissermann, “Motion deblurring and super-resolution from an image sequence,” in Proc. of European Conf. on Computer Vision, Cambridge, UK, Springer-Verlag: Berlin, 1996.

    Google Scholar 

  3. N.K. Bose and K.J. Boo, “High-resolution image reconstruction with multisensors,” International Journal of Imaging Systems and Technology, Vol. 9, pp. 294–304, 1998.

    Article  Google Scholar 

  4. N.K. Bose and K. Boo, “Asymptotic eigenvalue distribution of block-toeplitz matrices,” IEEE Trans. on Information Theory, Vol. 44, No. 2, pp. 858–861, 1998.

    Article  Google Scholar 

  5. N.K. Bose, H. Kim, and H. Valenzuela, “Recursive total least squares algorithm for image reconstruction from noisy undersampled frames,” Multidimensional Systems and Signal Processing, Vol. 4, No. 3, pp. 253–268, 1993.

    Article  Google Scholar 

  6. N.K. Bose, H. Kim and B. Zhou, “performance analysis of the TLS algorithm for image reconstruction from a sequence of undersampled noisy and blurred frames,” International Conference on Image Processing (ICIP ‘94), Austin, Texas, November 13–16, pp. 571–575, 1994.

  7. N.K. Bose and S. Lertrattanapanich, “Advances in wavelet superresolution,” in Proceedings of International Conference on Sampling Theory and Application SAMPTA 2001, May 13–17, 2001, pp. 5–12.

  8. R.H. Chan and M. K. Ng, “Conjugate gradient method for Toeplitz system,” SIAM Review, Vol. 38, pp. 427–482, 1996.

    Article  Google Scholar 

  9. D. Kammler, A First Course in Fourier Analysis, Prentice Hall, 2000.

  10. M. Elad and A. Feuer, “Resolution of single superresolution image from several blurred, noisy and undersampled measured images,” IEEE Trans. on Image Proc., Vol. 6, pp. 1646–1658, 1997.

    Article  Google Scholar 

  11. M. Elad and A. Feuer, “Superresolution restoration of an image sequence: Adaptive filtering approach,” IEEE Trans. on Image Proc., Vol. 8, pp. 387–395, 1999.

    Article  Google Scholar 

  12. M. Elad and Y. Hel-Or, “A fast superresolution reconstruction algorithm for pure translational motion and common space-invariant blur,” IEEE Transaction on Image Processing, Vol. 10, pp. 1187–1193, 2001.

    Article  Google Scholar 

  13. J. Gillete, T. Stadtmiller, and R. Hardie, “Aliasing reduction in staring infrared images using subpixel techniques,” Optical Engineering, Vol. 34, pp. 3130–3137, 1995.

    Google Scholar 

  14. G. Golub and C. Van Loan, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989.

    Google Scholar 

  15. R. Gonzalez and R. Woods, Digital image processing, Addison Wesley, New York, 1992.

    Google Scholar 

  16. R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and Edward A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Optical Engineering, Vo. 37, pp. 247–260, 1998.

    Article  Google Scholar 

  17. M. Irani and S. Peleg, “Improving resolution by image registration,” CVGIP: Graphical Models and Image Processing, Vol. 53, pp. 231–239, 1991.

    Article  Google Scholar 

  18. G. Jacquemod, C. Odet, and R. Goutte, “Image resolution enhancement using subpixel camera displacement,” Signal Processing, Vol. 26, pp. 139–146, 1992.

    Article  Google Scholar 

  19. S. Kim, N. K. Bose, and H. Valenzuela, “Recursive reconstruction of high resolution image from noisy undersampled multiframes,” IEEE Trans. on Acoust., Speech, and Signal Process., Vol. 38, pp. 1013–1027, 1990.

    Google Scholar 

  20. S. Kim and N. K. Bose, “Reconstruction of 2-D bandlimited discrete signals from nonuniform samples,” IEE Proceedings, Vol. 137, No. 3, Part F, pp. 197–203, 1990.

    Google Scholar 

  21. S. Kim and W. Su, “Recursive high-resolution reconstruction of blurred multiframe images,” IEEE Trans. on Image Proc., Vol. 2, pp. 534–539, 1993.

    Article  Google Scholar 

  22. P. Koeck, “Ins and outs of digital electron microscopy,” Microscopy Research and Technique, Vol. 49, pp. 217–223, 2000.

    Article  PubMed  Google Scholar 

  23. T. Komatsu, K. Aizawa, T. Igarashi, and T. Saito, “Signal-processing based method for acquiring very high resolution images with multiple cameras and its theoretical analysis,” IEE Proceedings, Vol. 140, No. 3, Part I, pp. 19–25, 1993.

    Google Scholar 

  24. S. Lertrattanapanich and N.K. Bose, “Latest results on high-resolution reconstruction from video sequences,” Technical Report of IEICE, DSP99-140, The Institution of Electronic, Information and Communication Engineers, Japan, pp. 59–65, 1999.

  25. S. Lertrattanapanich and N.K. Bose, “High resolution image formation from low resolution frames using delaunay triangulation,” IEEE Transactions on Image Processing, Vol. 11, No. 12, 2002.

  26. S. Mann and R. Picard, “Video orbits of the projective group: A simple approach to featureless estimation of parameters,” IEEE Transactions on Image Processing, Vol. 6, pp. 1281–1295, 1997.

    Article  Google Scholar 

  27. M. Ng and N.K. Bose, “Mathematical Analysis of Super-Resolution Methodology,” IEEE Signal Processing Magazine, Vol. 20, pp. 49–61, 2003.

    Article  Google Scholar 

  28. M. Ng, N.K. Bose and J. Koo, “Constrained total least squares computations for high resolution image reconstruction with multisensors,” International Journal of Imaging Systems and Technology, Vol. 12, pp. 35–42, 2002.

    Article  Google Scholar 

  29. M. Ng, R. Chan, and W. Tang, “A fast algorithm for deblurring models with neumann boundary conditions,” SIAM J. Sci. Comput., Vol. 21, pp. 851–866, 1999.

    Article  Google Scholar 

  30. M. Ng, R. Chan, T. Chan, and A. Yip, “Cosine transform preconditioners for high resolution image reconstruction,” Linear Algebra & Its Appls., Vol. 316, pp. 89–104, 2000.

    Google Scholar 

  31. M. Ng and A. Yip, “A fast MAP algorithm for high-resolution image reconstruction with multisensors,” Multidimensional Systems and Signal Processing, Vol. 12, No. 2, pp. 143–164, 2001.

    Article  MathSciNet  Google Scholar 

  32. N. Nguyen and P. Milanfar, “A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution),” Circuits Systems Signal Processing, Vol. 19, No. 4, pp. 321–338, 2000.

    Article  Google Scholar 

  33. N. Nguyen, P. Milanfar, and G. Golub, “Efficient generalized cross-validation with applications to parametric image restoratioin and resolution enhancement,” IEEE Transactions on Image Processing, Vol. 10, pp. 1299–1308, 2001.

    Article  Google Scholar 

  34. S. Park, M. Park and M. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Processing Magazine, Vol. 20, pp. 21–36, 2003.

    Article  Google Scholar 

  35. A. Patti, M. Sezan, and A. Tekalp, “Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time,” IEEE Trans. on Image Proc., Vol. 6, pp. 1064–1076, 1997.

    Article  Google Scholar 

  36. S. Peled and Y. Yeshurun, “Superresolution in MRI: Application to human white matter fiber tract visualization by diffusion tensor imaging,” Magnetic Resonance in Medicine, Vol. 45, pp. 29–35, 2001.

    Article  PubMed  Google Scholar 

  37. L. Poletto and P. Nicolosi, “Enhancing the spatial resolution of a two-dimensional discrete array detector,” Engineering, Vol. 38, pp. 1748–1757, 1999.

    Google Scholar 

  38. S. Rhee and M. Kang, “Discrete cosine transform based regularized high-resolution image reconstruction algorithm,” Optical Engineering, Vol. 38, No. 8, pp. 1348–1356, 1999.

    Article  Google Scholar 

  39. D. Rajan and S. Chaudhuri, “An MRF-based Approach to Generation of Super-Resoltuion Images from Blurred Observations,” Journal of Mathematical Imaging and Vision, Vol. 16, pp. 5–15, 2002.

    Article  MathSciNet  Google Scholar 

  40. K. Sauer and J. Allebach, “Iterative Reconstruction of Band-limited Images from Nonuniformly Spaced Samples,” IEEE Trans. on Circuits & Systems, Vol. 34, No. 12, pp. 1497–1506, 1987.

    Google Scholar 

  41. R. Schultz and R. Stevenson, “Extraction of high-resolution frames from video sequences,” IEEE Trans. Image Proces., Vol. 5, pp. 996–1011, 1996.

    Article  Google Scholar 

  42. H. Stark and P. Oskoui, “High-resolution image recovery from image-plane arrays using convex-projections,” J. Opt. Soc. Amer. A, Vol. 6, pp. 1715–1726, 1989.

    Google Scholar 

  43. A. Tekalp, M. Ozkan, and M. Sezan, “Superresolution video reconstruction with arbitrary sampling lattices and non-zero aperture time,” IEEE Trans. Image Proc., Vol. 6, pp. 1064–1076, 1997.

    Article  Google Scholar 

  44. R. Tsai and T. Huang, “Multiframe image restoration and registration,” Advances in Computer Vision and Image Processing: Image Reconstruction from Incomplete Observations, Thomas S. Huang (Ed.), London, 1984, Vol. 1, pp. 317–339, JAI Press.

    Google Scholar 

  45. H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP: Graphical Models and Image Processing, Vol. 54, No. 2, pp. 181–186, 1992.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

    Michael K. Ng & Andy C. Yau

Authors
  1. Michael K. Ng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andy C. Yau
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by Hong Kong Research Grants Council Grant Nos. HKU 7130/02P, 7046/03P, 7035/04P and HKU CRCG Grant No. 10205775.

Michael K. Ng is a Professor of the Mathematics Department, Hong Kong Baptist University, and is Adjunct Research Fellow in the E-Business Technology Institute at the University of Hong Kong. Michael was a Research Fellow (1995–1997) of Computer Sciences Laboratory, Australian National University, and an Assistant/Associate Professor (1997–2005) of the Mathematics Department, the University of Hong Kong before joining Hong Kong Baptist University in 2005. Michael was one of the finalists and honourable mention of Householder Award IX, in 1996 at Switzerland, and he obtained an excellent young researcher’s presentation at Nanjing International Conference on Optimization and Numerical Algebra, 1999. In 2001, he has been selected as one of the recipients of the Outstanding Young Researcher Award of the University of Hong Kong. Michael has published and edited several books, and published extensively in international journals and conferences, and has organized and served in many international conferences. Now he serves on the editorial boards of SIAM Journal on Scientific Computing, Numerical Linear Algebra with Applications, Multidimensional Systems and Signal Processing, International Journal of Computational Science and Engineering, Numerical Mathematics, A journal of Chinese Universities (English Series), and several special issues of the international journals.

Andy C. Yau received the undergraduate (1998–2001) from the Chinese University of Hong Kong, and the M.Phil degree (2002–2004) from the University of Hong Kong. He is a PhD student of the University of Hong Kong. His research area is image processing and scientific computing.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ng, M.K., Yau, A.C. Super-Resolution Image Restoration from Blurred Low-Resolution Images. J Math Imaging Vis 23, 367–378 (2005). https://doi.org/10.1007/s10851-005-2028-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-005-2028-5

Keywords

Search

Navigation