Abstract
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.
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References
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)
Bracewell, R.: The Fourier Transform and its Applications, 2nd edn. McGraw-Hill, New York (1978)
Chaudhuri, S. (ed.): Super-Resolution Imaging. Kluwer Academic Publishers, Dordrecht (2001)
Gerchberg, R.W.: Super-resolution through Error Energy Reduction. Optica Acta 21(9), 709–720 (1974)
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)
Greenspan, H., Oz, G., Kiryati, N., Peled, S.: MRI inter-slice reconstruction using super-resolution. Magnetic Resonance Imaging 20, 437–446 (2002)
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)
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)
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)
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)
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)
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)
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)
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)
Liang, Z., Lauterbur, P.C.: Principles of Magnetic Resonance Imaging, A Signal Processing Perspective. IEEE Press, New York (2000)
Margosian, P., Schmitt, F.: Faster MR Imaging: Imaging with Half the Data. Heath Care Instrumentation 1, 195–197 (1986)
Mayer, G.S.: Synthetic Aperture MRI. M.Sc. Thesis, The University of Calgary (2003)
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)
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)
Papoulis, A.: A New Algorithm in Spectral Analysis and Band-Limited Extrapolation. IEEE Transactions on Circuits and Systems CAS-22(9), 735–742 (1975)
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)
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)
Peled, S., Yeshurun, Y.: Superresolution in MRI - Perhaps Sometimes. Magnetic Resonance in Medicine 48, 409 (2002)
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)
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)
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)
Scheffler, K.: Superresolution in MRI? Magnetic Resonance in Medicine 48, 408 (2002)
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)
Youla, D.: Generalized Image Restoration by the Method of Alternating Orthogonal Projections. IEEE Transactions on Circuits and Systems CAS-25(9) (1978)
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Mayer, G.S., Vrscay, E.R. (2006). Mathematical Analysis of “Phase Ramping” for Super-Resolution Magnetic Resonance Imaging. In: Campilho, A., Kamel, M.S. (eds) Image Analysis and Recognition. ICIAR 2006. Lecture Notes in Computer Science, vol 4141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11867586_8
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DOI: https://doi.org/10.1007/11867586_8
Publisher Name: Springer, Berlin, Heidelberg
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