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piecewise constant function

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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StructuralProperties of Solutions to Total Variation Regularization Problems
Wolfgang Ring
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 4 / July 2000

Published online by Cambridge University Press:

15 April 2002, pp. 799-810

Print publication:

July 2000
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In dimension one it is proved that the solution to a total variation-regularizedleast-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 operatorto be inverted. A similar, but weaker result is derived in dimension two.