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Structural Properties of Solutions to Total Variation Regularization Problems

Wolfgang Ring (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere" , provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.

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