Journal of Mathematical Imaging and Vision

, Volume 39, Issue 1, pp 1–12 | Cite as

Direct Sparse Deblurring

  • Yifei LouEmail author
  • Andrea L. Bertozzi
  • Stefano Soatto
Open Access


We propose a deblurring algorithm that explicitly takes into account the sparse characteristics of natural images and does not entail solving a numerically ill-conditioned backward-diffusion. The key observation is that the sparse coefficients that encode a given image with respect to an over-complete basis are the same that encode a blurred version of the image with respect to a modified basis. Following an “analysis-by-synthesis” approach, an explicit generative model is used to compute a sparse representation of the blurred image, and its coefficients are used to combine elements of the original basis to yield a restored image.


Deblurring Sparse coding Over-complete dictionary 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Yifei Lou
    • 1
    Email author
  • Andrea L. Bertozzi
    • 1
  • Stefano Soatto
    • 2
  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Computer Science DepartmentUCLALos AngelesUSA

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