Skip to main content
SpringerLink
Log in

A Fast MAP Algorithm for High-Resolution Image Reconstruction with Multisensors

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

In many applications, it is required to reconstruct a high-resolution image from multiple, undersampled and shifted noisy images. Using the regularization techniques such as the classical Tikhonov regularization and maximum a posteriori (MAP) procedure, a high-resolution image reconstruction algorithm is developed. Because of the blurring process, the boundary values of the low-resolution image are not completely determined by the original image inside the scene. This paper addresses how to use (i) the Neumann boundary condition on the image, i.e., we assume that the scene immediately outside is a reflection of the original scene at the boundary, and (ii) the preconditioned conjugate gradient method with cosine transform preconditioners to solve linear systems arising from the high-resolution image reconstruction with multisensors. The usefulness of the algorithm is demonstrated through simulated examples.

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. K. Aizawa, T. Komatsu and T. Saito, Acquisition of Very High Resolution Images Using Stereo Camera, Proc. SPIE Visual Communications and Image Processing, V1605 (1991), p. 318–328.

    Google Scholar 

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

    Google Scholar 

  3. M. Banham and A. Katsaggelos, Digital Image Restoration, IEEE Signal Processing Magazine, March 1997, pp. 24–41.

  4. E. Boman and I. Koltracht, Fast Transform Based Preconditioners for Toeplitz Equations, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 628–645.

    Google Scholar 

  5. N. Bose and K. Boo, High-resolution Image Reconstruction with Multisensors, International Journal of Imaging Systems and Technology, 9 (1998), pp. 294–304.

    Google Scholar 

  6. N. Bose and K. Boo, Two-dimensional Model-based Power Spectrum Estimation for Nonextendible Correlation Bisequences, Circuits Systems Signal Processing, 16 (1997), pp. 141–163.

    Google Scholar 

  7. R. Chan, T. Chan, M. Ng, W. Tang, and C. Wong, Preconditioned Iterative Methods for High-resolution Image Reconstruction with Multisensors, Proceedings to the SPIE Symposium on Advanced Signal Processing: Algorithms, Architectures, and Implementations, Vol. 3461, San Diego CA, July, 1998, Ed: F. Luk.

  8. R. Chan, T. Chan, and C. Wong, Cosine Transform Based Preconditioners for Total Variation Minimization Problems in Image Processing, Iterative Methods in Linear Algebra, II, V3, IMACS Series in Computational and Applied Mathematics, Proceedings of the Second IMACS International Symposium on Iterative Methods in Linear Algebra, Bulgaria, June, 1995, pp. 311–329, Ed: S. Margenov and P. Vassilevski.

  9. R. Chan and M. Ng, Conjugate Gradient Methods for Toeplitz Systems, SIAM Review, 38 (1996), pp. 427–482.

    Google Scholar 

  10. G. Golub and C. Van Loan, Matrix Computations, 3rd ed., The Johns Hopkins University Press, 1996.

  11. R. Gonzalez and R. Woods, Digital Image Processing, Addison Wesley, New York, 1992.

    Google Scholar 

  12. G. Jacquemod, C. Odet and R. Goutte, Image Resolution Enhancement Using Subpixel Camera Displacement, Signal Processing, 26 (1992), pp. 139–146.

    Google Scholar 

  13. S. Kim, N. Bose and H. Valenzuela, Recursive Reconstruction of High Resolution Image from Noisy Undersampled Multiframes, IEEE Trans. on Acoust., Speech, and Signal Process., 38 (1990), pp. 1013–1027.

    Google Scholar 

  14. S. Kim and W. Su, Recursive High-resolution Reconstruction of Blurred Multiframe Images, IEEE Trans. on Image Proc., 2 (1993), pp. 534–539.

    Google Scholar 

  15. R. Lagendijk and J. Biemond, Iterative Identification and Restoration of Images, Kluwer Academic Publishers, 1991.

  16. F. Luk and D. Vandevoorde, Reducing Boundary Distortion in Image Restoration, Proc. SPIE 2296, Advanced Signal Processing Algorithms, Architectures and Implementations VI, 1994.

  17. M. Ng, R. Chan and W. Tang, A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions, SIAM J. Sci. Comput., 21 (1999), pp. 851–866.

    Google Scholar 

  18. M. Ng. R. Chan, T. Chan and A. Yip, Cosine Transform Preconditioners for High Resolution Image Reconstruction, Linear Algebra Appls., 316 (2000), pp. 89–104.

    Google Scholar 

  19. M. Ng and R. Plemmons, Fast Recursive Least Squares Adaptive Filtering by using FFT-based Conjugate Gradient Iterations, SIAM J. Sci. Comput., 17 (1996), pp. 920-941.

    Google Scholar 

  20. R. Schultz and R. Stevenson, Extraction of High-resolution Frames from Video Sequences, IEEE T. Image Proces., 5 (1996), pp. 996–1011.

    Google Scholar 

  21. H. Stark and P. Oskoui, High-resolution Image Recovery from Image-plane Arrays Using Convex-projections, J. Opt. Soc. amer. A, 6 (1989), pp. 1715–1726.

    Google Scholar 

  22. A. Tekalp, M. Ozkan and M. Sezan, High-resolution Image Reconstruction from Lower-resolution Image Sequences and Space-varying Image Restoration, In Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process., III, pp. 169–172, San Francisco, CA, March 1992.

    Google Scholar 

  23. R. Tsai and T. Huang, Multiframe Image Restoration and Registration, Advances in Computer Vision and Image Processing, 1 (1984), pp. 317–339.

    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

  2. Department of Mathematics, The University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA, 90095-1555

    Andy M. Yip

Authors
  1. Michael K. Ng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andy M. Yip
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ng, M.K., Yip, A.M. A Fast MAP Algorithm for High-Resolution Image Reconstruction with Multisensors. Multidimensional Systems and Signal Processing 12, 143–164 (2001). https://doi.org/10.1023/A:1011136812633

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011136812633

Search

Navigation