On Tensor-Based PDEs and Their Corresponding Variational Formulations with Application to Color Image Denoising

Freddie Åström^{1, 2}, George Baravdish³, and Michael Felsberg^{1, 2}

¹Computer Vision Laboratory, Department of E.E., Linköping University, Sweden
Freddie.Astrom@liu.se
Michael.Felsberg@liu.se

²Center for Medical Image Science and Visualization (CMIV), Linköping University, Sweden

³Department of Science and Technology, Linköping University, Sweden
George.Baravdish@liu.se

Abstract. 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.

LNCS 7574, p. 215 ff.

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