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 L1 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. © 2013 Springer-Verlag.
CITATION STYLE
Hoeltgen, L., Setzer, S., & Weickert, J. (2013). An optimal control approach to find sparse data for Laplace interpolation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8081 LNCS, pp. 151–164). https://doi.org/10.1007/978-3-642-40395-8_12
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