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) = {f L(R2 Suppose s F(R2
 

Summary: 1
Abstract
Let
F(R2
) = {f L(R2
) L1(R2
) : f 0}.
Suppose s F(R2
) and : R [0, ). Suppose is zero at zero, positive
away from zero and convex. For f F() let
F(f) =
Z

(f(x) - s(x)) dL2
x;
L2
here is Lebesgue measure on R2
. In the denoising literature F would
be called a fidelity in that it measures how much f differs from s which
could be a noisy grayscale image. Suppose 0 < < and let

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics