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Exact minimizer for the couple (L(infinity), BV) and the one-dimensional analogue of the Rudin-Osher-Fatemi model

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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
Uncontrolled Keywords:Exact minimizer; E-functional; K-functional; Rudin-Osher-Fatemi model; L-2; Mathematics
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:14900
Deposited On:19 Apr 2012 09:16
Last Modified:14 Jun 2018 11:05

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