On the K functional between L1 and L2 and some other K functionals
Journal of Approximation Theory
An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
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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@?"B"V. 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^~)@?supa@?x"0@?...@?x"N@?b@?i=1N|f(x"i)-f(x"i"+"1)|. We also discussed the connection between the results and the Rudin-Osher-Fatemi denoising model.