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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.

49K40Sensitivity, stability, well-posedness of optimal solutions
65J20Improperly posed problems; regularization (numerical methods in abstract spaces)
47A52Ill-posed problems, regularization
49M30Other numerical methods in calculus of variations
Full Text: DOI EuDML
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