Nonlinear inverse scale space methods for image restoration

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Nonlinear inverse scale space methods for image restoration (2005)

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by Martin Burger , Stanley Osher , Jinjun Xu , Guy Gilboa

Venue:	Communications in Mathematical Sciences
Citations:	65 - 18 self

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@INPROCEEDINGS{Burger05nonlinearinverse,
    author = {Martin Burger and Stanley Osher and Jinjun Xu and Guy Gilboa},
    title = {Nonlinear inverse scale space methods for image restoration},
    booktitle = {Communications in Mathematical Sciences},
    year = {2005},
    pages = {2006}
}

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Abstract

Abstract. 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. 1

Keyphrases

nonlinear inverse scale space method image restoration noisy image discrepancy principle iterated refinement procedure hold straightforward implementation iterated refinement procedure convex variational problem high quality restoration inverse scale space method penalization parameter iteration step spatial dimension relaxation technique evolution equation iterated refinement method one-dimensional signal inverse flow noise-free image time-continuous inverse scale-space formulation limiting flow similar property

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