Alias-Free Interpolation

  • C. V. Jiji
  • Prakash Neethu
  • Subhasis Chaudhuri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3954)


In this paper we study the possibility of removing aliasing in a scene from a single observation by designing an alias-free upsampling scheme. We generate the unknown high frequency components of the given partially aliased (low resolution) image by minimizing the total variation of the interpolant subject to the constraint that part of unaliased spectral components in the low resolution observation are known precisely and under the assumption of sparsity in the data. This provides a mathematical basis for exact reproduction of high frequency components with probability approaching one, from their aliased observation. The primary application of the given approach would be in super-resolution imaging.


Spectral Component High Frequency Component Interpolate Image Interpolate Signal Iterative Back Projection 
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.


  1. 1.
    Chaudhuri, S., Joshi, M.V.: Motion-Free Super-Resolution. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  2. 2.
    Tsai, R.Y., Huang, T.S.: Multiframe Image Restoration and Registration. In: Advances in Computer Vision and Image Processsing, pp. 317–339. JAI Press Inc. (1984)Google Scholar
  3. 3.
    Irani, M., Peleg, S.: Improving Resolution by Image Registration. CVGIP: Graphical Models and Image Processing 53, 231–239 (1991)Google Scholar
  4. 4.
    Schultz, R.R., Stevenson, R.L.: A Bayesian Approach to Image Expansion for Improved Definition. IEEE Trans. on Image Processing 3, 233–242 (1994)CrossRefGoogle Scholar
  5. 5.
    Elad, M., Feuer, A.: Restoration of a Single Superresolution Image from Several Blurred, Noisy and Undersampled Measured Images. IEEE Trans. on Image Processing 6, 1646–1658 (1997)CrossRefGoogle Scholar
  6. 6.
    Nguyen, N., Milanfar, P., Golub, G.: A Computationally Efficient Super-resolution Reconstruction Algorithm. IEEE Trans. Image Processing 10, 573–583 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Lin, Z., Shum, H.Y.: Fundamental Limits of Reconstruction-Based Super-Resolution Algorithms under Local Translation. IEEE Trans. on Pattern Analysis and Machine Intelligence 26, 83–97 (2004)CrossRefGoogle Scholar
  8. 8.
    Shahram, M., Milanfar, P.: Imaging Below the Diffraction Limit: A Statistical Analysis. IEEE Trans. on Image Processing 13, 677–689 (2004)CrossRefGoogle Scholar
  9. 9.
    Rajan, D., Chaudhuri, S.: Generalized Interpolation and its Applications in Super-Resolution imaging. Image and Vision Computing 19, 957–969 (2001)CrossRefGoogle Scholar
  10. 10.
    Candes, E., Romberg, J., Tao, T.: Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information (2004),
  11. 11.
    Donoho, D.L., Elad, M.: Maximal sparsity Representation via l 1 Minimization. The Proc. Nat. Aca. Sci. 100, 2197–2202 (2003)CrossRefzbMATHGoogle Scholar
  12. 12.
    Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C.: Image Inpainting. In: Proc. SIGGRAPH, New Orleans, USA (2000)Google Scholar
  13. 13.
    Chan, T., Kang, S.H.: Error Analysis for Image Inpainting. UCLA CAM report 04-72 (2004)Google Scholar
  14. 14.
    Levy, S., Fullagar, P.K.: Reconstruction of a sparse spike train from a portion of its spectrum and application to high-resolution deconvolution. GEOPHYSICS 46, 1235–1243 (1981)CrossRefGoogle Scholar
  15. 15.
    Santosa, F., Symes, W.W.: Linear inversion of band-limited reflection seismograms. SIAM J. Sci. Statist. Comput. 7, 1307–1330 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Guichard, F., Malgouyres, F.: Total Variation Based Interpolation. In: Proc. European Signal Processing Conference, pp. 1741–1744 (1998)Google Scholar
  17. 17.
    Malgouyres, F., Guichard, F.: Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis. SIAM J. Numerical Analysis 39, 1–37 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. PHYSICA D 60, 259–268 (1992)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • C. V. Jiji
    • 1
  • Prakash Neethu
    • 1
  • Subhasis Chaudhuri
    • 1
  1. 1.Indian Institute of Technology BombayMumbaiIndia

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