A new median formula with applications to PDE based denoising
Yingying Li, Yingying Li, Stanley Osher, Stanley Osher · Communications in Mathematical Sciences · 2009
We develop a simple algorithm for finding the minimizer of the function E(x) = P n i=1 w i |xa i | + F (x), when the w i are nonnegative and F is strictly convex.If F is also differentiable and F ′ is bijective, we obtain an explicit formula in terms of a median.This enables us to obtain approximate solutions to certain important variational problems arising in image denoising.We also present a generalization with E(x) = J(x) + F (x) for J(x) a convex piecewise differentiable function with a finite number of nondifferentiable points.