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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Variational Methods for Denoising Matrix Fields
verfasst von : S. Setzer, G. Steidl, B. Popilka, B. Burgeth
Erschienen in: Visualization and Processing of Tensor Fields
Verlag: Springer Berlin Heidelberg
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The restoration of scalar-valued images via minimization of an energy functional is a well-established technique in image processing. Recently, higher-order methods have proved their advantages in edge preserving image denoising. In this chapter, we transfer successful techniques like the minimization of the Rudin-Osher-Fatemi functional and the infimal convolution to matrix fields, where our functionals couple with different matrix channels. For the numerical computation, we use second-order cone programming. Moreover, taking the operator structure of matrices into account, we consider a new operator-based regularization term. This is the first variational approach for denoising tensor-valued data that takes the operator structure of matrices, in particular the operation of matrix multiplication into account. Using matrix differential calculus, we deduce the corresponding Euler-Lagrange equation and apply it for the numerical solution by a steepest descent method.