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Structural properties of solutions to total variation regularization problems. (English) Zbl 1018.49021
Summary: 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.

MSC:
49K40 Sensitivity, stability, well-posedness
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47A52 Linear operators and ill-posed problems, regularization
49M30 Other numerical methods in calculus of variations (MSC2010)
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