Nonlinear Inverse Scale Space Methods for Image Restoration

  • Martin Burger
  • Stanley Osher
  • Jinjun Xu
  • Guy Gilboa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)


In this paper we generalize the iterated refinement method, introduced by the authors in [8],to a time-continuous inverse scale-space formulation. The iterated refinement procedure yields a sequence of convex variational problems, evolving toward the noisy image.

The inverse scale space method arises as a limit for a penalization parameter tending to zero, while the number of iteration steps tends to infinity. For the limiting flow, similar properties as for the iterated refinement procedure hold. Specifically, when a discrepancy principle is used as the stopping criterion, the error between the reconstruction and the noise-free image decreases until termination, even if only the noisy image is available and a bound on the variance of the noise is known.

The inverse flow is computed directly for one-dimensional signals, yielding high quality restorations. In higher spatial dimensions, we introduce a relaxation technique using two evolution equations. These equations allow accurate, efficient and straightforward implementation.


Noisy Image Small Scale Feature Iterative Regularization Bregman Distance Quadratic Regularization 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Martin Burger
    • 1
  • Stanley Osher
    • 2
  • Jinjun Xu
    • 2
  • Guy Gilboa
    • 2
  1. 1.Industrial Mathematics InstituteJohannes Kepler UniversityLinzAustria
  2. 2.Department of MathematicsUCLALos AngelesUSA

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