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.
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Burger, M., Osher, S., Xu, J., Gilboa, G. (2005). Nonlinear Inverse Scale Space Methods for Image Restoration. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_3
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DOI: https://doi.org/10.1007/11567646_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29348-4
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