A NEW MEDIAN FORMULA WITH APPLICATIONS TO PDE BASED DENOISING

We develop a simple algorithm for finding the minimizer of the function E(x)=Sigma(n)(i)=(1)w(i)vertical bar x-a(i)vertical bar+F(x), when the w(i) are nonnegative and F is strictly convex. If F is also different tiable 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.