# Structural Properties of Solutions to Total Variation Regularization Problems

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 4, page 799-810
- ISSN: 0764-583X

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topRing, Wolfgang. "Structural Properties of Solutions to Total Variation Regularization Problems." ESAIM: Mathematical Modelling and Numerical Analysis 34.4 (2010): 799-810. <http://eudml.org/doc/197509>.

@article{Ring2010,

abstract = {
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.
},

author = {Ring, Wolfgang},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Total variation regularization; piecewise constant function; convex optimization;
Lebesgue decomposition; singular measures.; optimality system; total variation regularization; Lebesgue decomposition; singular measures; ill-posed problem; least-squares problem},

language = {eng},

month = {3},

number = {4},

pages = {799-810},

publisher = {EDP Sciences},

title = {Structural Properties of Solutions to Total Variation Regularization Problems},

url = {http://eudml.org/doc/197509},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Ring, Wolfgang

TI - Structural Properties of Solutions to Total Variation Regularization Problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 4

SP - 799

EP - 810

AB -
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.

LA - eng

KW - Total variation regularization; piecewise constant function; convex optimization;
Lebesgue decomposition; singular measures.; optimality system; total variation regularization; Lebesgue decomposition; singular measures; ill-posed problem; least-squares problem

UR - http://eudml.org/doc/197509

ER -

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