Summary: 1
TOTAL VARIATION REGULARIZATION FOR IMAGE
DENOISING; III. EXAMPLES.
WILLIAM K. ALLARD
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
nloc(F)