In this paper we apply Meyer’s G-norm for image processing problems. We use a definition of the G-norm as norm of linear functionals on BV, which seems to be more feasible for numerical computation. We establish the equivalence between Meyer’s original definition and ours and show that computing the norm can be expressed as an interface problem. This allows us to define an algorithm based on the level set method for its solution. Alternatively we propose a fixed point method based on mean curvature type equations. A computation of the G-norm according to our definition additionally gives functions which can be used for denoising of simple structures in images under a high level of noise. We present some numerical computations of this denoising method which support this claim.
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Dedicated to David Gottlieb on his 60th birthday.
Stefan Kindermann on leave from University Linz, Austria.
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Kindermann, S., Osher, S. & Xu, J. Denoising by BV-duality. J Sci Comput 28, 411–444 (2006). https://doi.org/10.1007/s10915-006-9074-z
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DOI: https://doi.org/10.1007/s10915-006-9074-z