Multidimensional Systems and Signal Processing

, Volume 18, Issue 2–3, pp 173–188 | Cite as

An efficient algorithm for superresolution in medium field imaging

Original Article


In this paper, we study the problem of reconstruction of a high-resolution (HR) image from several blurred low-resolution (LR) image frames in medium field. The image frames consist of blurred, decimated, and noisy versions of a HR image. The HR 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, a HR image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore HR images in the aperiodic boundary condition. Computer simulations are given to illustrate the effectiveness of the proposed approach.


Superresolution Medium field Preconditioned conjugate gradient method Fast Fourier transforms Toeplitz matrix Deblussing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Biggs, D., & Andrews, M. (1998). Asymmetric iterative blind deconvolution of multiframe images. In: Proceedings of the SPIE Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, 3461, 328–338.Google Scholar
  2. Bose N.K., Boo K.J. (1998). High-resolution image reconstruction with multisensors. International Journal of Imaging Systems and Technology 9: 294–304CrossRefGoogle Scholar
  3. Bose N.K., Lertrattanapanich S. (2004). Polynomial matrix factorization, multidimensional filter banks, and wavelets. In: Benedetto J.J., Zayed A.I. (eds) Sampling, wavelets and tomography. BostonL, Birkhaeuser, pp 138–156Google Scholar
  4. Bose, N. K., Ng, M. K., & Yau, A. C. (2005). Super-resolution image restoration from blurred observations. In: Proceedings of the International symposium of circuits and systems, Kobe, Japan, pp. 6296-6299.Google Scholar
  5. Bose, N. K., Ng, M. K., & Yau, A. C. (2006). A fast algorithm for image superresolution from blurred observations. EURASIP Journal on Applied Signal Processing, doi: 10.1155/ASP/2006/35726Google Scholar
  6. Elad M., Feuer A. (1997). Resolution of single superresolution image from several blurred, noisy and undersampled measured images. IEEE Transactions on Image Processing 6: 1646–1658CrossRefGoogle Scholar
  7. Elad M., Feuer A. (1999). Superresolution restoration of an image sequence: Adaptive filtering approach. IEEE Transactions on Image Processing 8: 387–395CrossRefGoogle Scholar
  8. Granrath D., Lersch J. (1998). Fusion of images on affine sampling grids. Journal of Optical Society of America 15(4): 791–801Google Scholar
  9. Hanisch R.J., White R.L., Gilliland R.L. (1997). Deconvolution of Hubble space telescope images and spectra Deconvolution of Images and Spectra (2nd ed). San Diego, CA, Academic Press, pp. 311–360Google Scholar
  10. Kim S., Bose N.K., Valenzuela H. (1990). Recursive reconstruction of high resolution image from noisy undersampled multiframes. IEEE Transactions on Acoustics, Speech, and Signal Processing 38: 1013–1027CrossRefGoogle Scholar
  11. Kim S., Bose N.K. (1990). Reconstruction of 2-D bandlimited discrete signals from nonuniform samples. IEEE Proceedings 137(3): 197–204Google Scholar
  12. Lertrattanapanich, S. (1999). Image Registration for Video Mosaic. University Park, PA: M.S., The Pensylvania State University.Google Scholar
  13. Lertrattanapanich S., Bose N.K. (2002). High resolution image formation from low resolution frames using Delaunay Triangulation. IEEE Transactions on Image Processing 17(2): 1427–1441CrossRefMathSciNetGoogle Scholar
  14. Lertrattanapanich, S. (2003). Superresolution from degraded image sequence using spatial tessellations and wavelets. Ph. D. Dissertation, Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, USA. Superresolution/PhDThesis.pdf.Google Scholar
  15. Lipson S., Lipson H., Tannhauser D. (1995). Optical Physics. UK, Cambridge University PressGoogle Scholar
  16. Mann S., Picard R. (1997). Video orbits of the projective group: A simple approach to featureless estimation of parameters. IEEE Transactions on Image Processing 6: 1281–1295CrossRefGoogle Scholar
  17. Ng M., Bose N.K., Koo J. (2002). Constrained total least squares computations for high resolution image reconstruction with multisensors. International Journal of Imaging Systems and Technology 12: 35–42CrossRefGoogle Scholar
  18. Nguyen N., Milanfar P. (2000). A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution). Circuits Systems Signal Processing 19(4): 321–338MATHCrossRefGoogle Scholar
  19. Paesler M., Moyer P. (1996). Near field optics theory, instrumentation and applications. New York, WileyGoogle Scholar
  20. Patti A., Sezan M., Tekalp A. (1997). Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time. IEEE Transactions on Image Processing 6(8): 1064–1076CrossRefGoogle Scholar
  21. Rhee S., Kang M. (1999). Discrete cosine transform based regularized high-resolution image reconstruction algorithm. Optical Engineering 38(8): 1348–1356Google Scholar
  22. Sauer K., Allebach J. (1987). Iterative reconstruction of band-limited images from nonuniformly spaced samples. IEEE Transactions on Circuits & Systems 34(12): 1497–1506CrossRefGoogle Scholar
  23. Tsai R., Huang T. (1984). Multiframe image restoration and registration. Advances in computer vision and image processing: image reconstruction from incomplete observations (Vol.1). London, JAI Press, pp. 317–339Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsThe University of Hong KongHong KongHong Kong
  2. 2.Department of Electrical Engineering, The Spatial and Temporal Signal Processing CenterThe Pennsylvania State UniversityUniversity ParkU.S.A
  3. 3.Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong

Personalised recommendations