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Displaying similar documents to “Enhanced electrical impedance tomography via the Mumford–Shah functional”

Enhanced Electrical Impedance Tomography the Mumford–Shah Functional

Luca Rondi, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach...

Γ -convergence and absolute minimizers for supremal functionals

Thierry Champion, Luigi De Pascale, Francesca Prinari (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we prove that the L p approximants naturally associated to a supremal functional Γ -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer...