%0 Journal Article
%A Cobos Díaz, Fernando
%A Kruglyak, Natan
%T Exact minimizer for the couple (L∞, BV) and the one-dimensional analogue of the Rudin-Osher-Fatemi model
%D 2011
%@ 0021-9045
%U https://hdl.handle.net/20.500.14352/42122
%X 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.
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