Mathematical Analysis of “Phase Ramping” for Super-Resolution Magnetic Resonance Imaging

  • Gregory S. Mayer
  • Edward R. Vrscay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4141)


Super-resolution image processing algorithms are based on the principle that repeated imaging together with information about the acquisition process may be used to enhance spatial resolution. In the usual implementation, a series of low-resolution images shifted by typically subpixel distances are acquired. The pixels of these low-resolution images are then interleaved and modeled as a blurred image of higher resolution and the same field-of-view. A high-resolution image is then obtained using a standard deconvolution algorithm. Although this approach has been applied in magnetic resonance imaging (MRI), some controversy has surfaced regarding the validity and circumstances under which super-resolution may be applicable. We investigate the factors that limit the applicability of super-resolution MRI.


Magnetic Resonance Imaging Magnetic Resonance Imaging Data Discrete Series Spatial Shift Magnetic Resonance Spec 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Borman, S., Stevenson, R.: Spatial resolution enhancement of low-resolution image sequences - a review. In: Proceedings of the 1998 Midwest Symposium on Circuits and Systems, Notre Dame IN (1998)Google Scholar
  2. 2.
    Bracewell, R.: The Fourier Transform and its Applications, 2nd edn. McGraw-Hill, New York (1978)MATHGoogle Scholar
  3. 3.
    Chaudhuri, S. (ed.): Super-Resolution Imaging. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
  4. 4.
    Gerchberg, R.W.: Super-resolution through Error Energy Reduction. Optica Acta 21(9), 709–720 (1974)Google Scholar
  5. 5.
    Greenspan, H., Peled, S., Oz, G., Kiryati, N.: MRI inter-slice reconstruction using super-resolution. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, p. 1204. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Greenspan, H., Oz, G., Kiryati, N., Peled, S.: MRI inter-slice reconstruction using super-resolution. Magnetic Resonance Imaging 20, 437–446 (2002)CrossRefGoogle Scholar
  7. 7.
    Haacke, M.E., Mitchell, J., Doohi, L.: Improved Contrast at 1.5 Tesla Using Half-Fourier Imaging: Application to Spin-Echo and Angiographic Imaging. Magnetic Resonance Imaging 8, 79–90 (1990)CrossRefGoogle Scholar
  8. 8.
    Haacke, M.E., Lindskog, E.D., Lin, W.: A Fast, Iterative, Partial-Fourier Technique Capable of Local Phase Recovery. Journal of Magnetic Resonance 92, 126–145 (1991)Google Scholar
  9. 9.
    Haacke, M.E., Brown, R.W., Thompson, M.R., Venkatesan, R.: Magnetic Resonance Imaging: Physical Principles and Sequence Design. John Wiley & Sons, Inc., USA (1999)Google Scholar
  10. 10.
    Hinshaw, W., Lent, A.: An Introduction to NMR Imaging: From the Bloch Equation to the Imaging Equation. Proceedings of the IEEE 71(3), 338–350 (1983)CrossRefGoogle Scholar
  11. 11.
    Irani, M., Peleg, S.: Motion analysis for image enhancement: resolution, occlusion, and transparency. Journal of Visual Communication and Image Representation 4(4), 324–335 (1993)CrossRefGoogle Scholar
  12. 12.
    Jain, A., Ranganath, S.: Extrapolation Algorithms for Discrete Signals with Application in Spectral Estimation. IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP-29(4), 830–845 (1981)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Kornprobst, P., Peeters, R., Nikolova, M., Deriche, R., Ng, M., Hecke, P.V.: A superresolution framework for fMRI sequences and its impact on resulting activation maps. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003. LNCS, vol. 2879, pp. 117–125. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Liang, Z., Boada, F.E., Constable, R.T., Haacke, M.E., Lauterbur, P.C., Smith, M.R.: Constrained Reconstruction Methods in MR Imaging. Reviews of Magnetic Resonance in Medicine 4, 67–185 (1992)Google Scholar
  15. 15.
    Liang, Z., Lauterbur, P.C.: Principles of Magnetic Resonance Imaging, A Signal Processing Perspective. IEEE Press, New York (2000)Google Scholar
  16. 16.
    Margosian, P., Schmitt, F.: Faster MR Imaging: Imaging with Half the Data. Heath Care Instrumentation 1, 195–197 (1986)Google Scholar
  17. 17.
    Mayer, G.S.: Synthetic Aperture MRI. M.Sc. Thesis, The University of Calgary (2003)Google Scholar
  18. 18.
    McGibney, G., Smith, M.R., Nichols, S.T., Crawley, A.: Quantitative Evaluation of Several Partial Fourier Reconstruction Algorithms Used in MRI. Magnetic Resonance in Medicine 30, 51–59 (1993)CrossRefGoogle Scholar
  19. 19.
    Ng, K.P., Deriche, R., Kornprobst, P., Nikolova, M.: Half-Quadratic Regularization for MRI Image Restoration. In: IEEE Signal Processing Conference, pp. 585–588 (2003) (Publication No. : 76681)Google Scholar
  20. 20.
    Papoulis, A.: A New Algorithm in Spectral Analysis and Band-Limited Extrapolation. IEEE Transactions on Circuits and Systems CAS-22(9), 735–742 (1975)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Peeters, R., et al.: The Use of Super-Resolution Techniques to Reduce Slice Thickness in Functional MRI. International Journal of Imaging Systems and Technology 14, 131–138 (2004)CrossRefGoogle Scholar
  22. 22.
    Peled, S., Yeshurun, Y.: Superresolution in MRI: Application to Human White Matter Fiber Tract Visualization by Diffusion Tensor Imaging. Magnetic Resonance in Medicine 45, 29–35 (2001)CrossRefGoogle Scholar
  23. 23.
    Peled, S., Yeshurun, Y.: Superresolution in MRI - Perhaps Sometimes. Magnetic Resonance in Medicine 48, 409 (2002)CrossRefGoogle Scholar
  24. 24.
    Sanz, J., Huang, T.: Discrete and Continuous Band-Limited Signal Extrapolation. IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP-31(5), 1276–1285 (1983)CrossRefGoogle Scholar
  25. 25.
    Sanz, J., Huang, T.: Some Aspects of Band-Limited Signal Extrapolation: Models, Discrete Approximations, and Noise. IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP-31(6), 1492–1501 (1983)CrossRefGoogle Scholar
  26. 26.
    Sabri, M.S., Steenaart, W.: An Approach to Band-Limited Signal Extrapolation: The Extrapolation Matrix. IEEE Transactions on Circuits and Systems CAS-25(2) (1978)Google Scholar
  27. 27.
    Scheffler, K.: Superresolution in MRI? Magnetic Resonance in Medicine 48, 408 (2002)CrossRefGoogle Scholar
  28. 28.
    Tsai, R., Huang, T.: Multiframe image restoration and registration. In: Advances in Computer Vision and Image Processing, vol. 1, pp. 317–339. JAI Press Inc., Greenwich (1984)Google Scholar
  29. 29.
    Youla, D.: Generalized Image Restoration by the Method of Alternating Orthogonal Projections. IEEE Transactions on Circuits and Systems CAS-25(9) (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gregory S. Mayer
    • 1
  • Edward R. Vrscay
    • 1
  1. 1.Department of Applied Mathematics, Faculty of MathematicsUniversity of WaterlooWaterloo, OntarioCanada

Personalised recommendations