@inproceedings{HSW2013,
 pages         = {151--164},
 booktitle     = {Energy Minimization Methods in Computer Vision and Pattern Recognition},
 author        = {Hoeltgen, Laurent and Setzer, Simon and Weickert, Joachim},
 editor        = {Heyden, Anders and Kahl, Frederik and Olsson, Carl and Oskarsson, Magnus and Tay, Xue-Cheng},
 title         = {An Optimal Control Approach to Find Sparse Data for {L}aplace Interpolation},
 publisher     = {Springer Berlin Heidelberg},
 doi           = {10.1007/978-3-642-40395-8_12},
 keywords      = {reviewed},
 series        = {Lecture Notes in Computer Science},
 year          = {2013},
 date          = {2013},
 abstract      = {Finding optimal data for inpainting is a key problem in the
context of partial differential equation-based image compression. We
present a new model for optimising the data used for the reconstruction
by the underlying homogeneous diffusion process. Our approach is based
on an optimal control framework with a strictly convex cost functional
containing an $L_1$ term to enforce sparsity of the data and non-convex
constraints. We propose a numerical approach that solves a series of
convex optimisation problems with linear constraints. Our numerical
examples show that it outperforms existing methods with respect to
quality and computation time},
 timestamp     = {2016-03-05},
 crossref      = {HKOO2013}
}