Reconstruction of Planar Conductivities in Subdomains from Incomplete Data

Reconstruction of Planar Conductivities in Subdomains from Incomplete Data

We consider the problem of recovering a sufficiently smooth isotropic conductivity from interior knowledge of the magnitude of the current density field |J | generated by an imposed voltage potential f on the boundary. In any dimension n ≥ 2, we show that equipotential sets are global area minimizers in the conformal metric determined by |J |. In two dimensions, assuming the boundary voltage is...

Image Reconstruction from Incomplete Data

Image Reconstruction from Incomplete Data

image reconstruction from incomplete data

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Reconstruction of Smooth Functions from Incomplete Data

In many situations, one is confronted with the problem of trying to reconstruct an unknown continuous function from a finite set of data points or measurements where some of this data is incorrect, missing, or unreliable. If a contiguous set of data points is missing, the problem of reconstruction is highly ill-posed with an infinite dimensional solution set. However, if more information about ...