Cobos, Fernando and Kruglyak, Natan
(2011)
*Exact minimizer for the couple (L(infinity), BV) and the one-dimensional analogue of the Rudin-Osher-Fatemi model.*
Journal of Approximation Theory, 163
(4).
pp. 481-490.
ISSN 0021-9045

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021904510002030

## Abstract

We provide a simple algorithm that constructs an exact minimizer for the E-functional

E(t, f ; L∞, BV) = inf

‖g‖L∞≤t

‖ f − g‖BV .

Here L∞, BV stand for the space of bounded functions and the space of functions with bounded variation

on the interval [a, b], respectively. As a corollary we obtain the following formula for the K-functional

K(N, f ; BV, L∞) v sup

a≤x0≤···≤xN≤b

−N

i=1

| f (xi ) − f (xi+1)|.

We also discussed the connection between the results and the Rudin–Osher–Fatemi denoising model.

Item Type: | Article |
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Uncontrolled Keywords: | Exact minimizer; E-functional; K-functional; Rudin-Osher-Fatemi model; L-2; Mathematics |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 14900 |

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Deposited On: | 19 Apr 2012 09:16 |

Last Modified: | 22 Oct 2013 14:48 |

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