Abstract
We consider a variational approach to the problem of recovering missing parts in a panchromatic digital image. Representing the image by a scalar function u, we propose a model based on the relaxation of the energy
which takes into account the perimeter of the level sets of u as well as the LP norm of the mean curvature along their boundaries. We investigate the properties of this variational model and the existence of minimizing functions in BV. We also address related issues for integral varifolds with generalized mean curvature in LP.
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Ambrosio, L., Masnou, S. (2003). On a Variational Problem Arising in Image Reconstruction. In: Colli, P., Verdi, C., Visintin, A. (eds) Free Boundary Problems. ISNM International Series of Numerical Mathematics, vol 147. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7893-7_2
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DOI: https://doi.org/10.1007/978-3-0348-7893-7_2
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