The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data term and a smoothness term is investigated. We show the necessary conditions for a PDE to be the E-L equation for a corresponding functional. This energy functional is applied to a color image denoising problem and it is shown that the method compares favorably to current state-of-the-art color image denoising techniques. © 2012 Springer-Verlag.
CITATION STYLE
Åström, F., Baravdish, G., & Felsberg, M. (2012). On tensor-based PDEs and their corresponding variational formulations with application to color image denoising. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7574 LNCS, pp. 215–228). https://doi.org/10.1007/978-3-642-33712-3_16
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