Subdifferentiation of Nonconvex Sparsity-Promoting Functionals on Lebesgue Spaces

Lipschitzian Properties of Integral Functionals on Lebesgue Spaces

We give a complete characterization of integral functionals which are Lipschitzian on a Lebesgue space Lp with p finite. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces Lp. In every cases, the Lipchitzian properties of the integral functional are described by Lipschitzian properties of the integrand. Mathematics Subje...

Minimax Estimation of Linear Functionals Over Nonconvex Parameter Spaces

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in contrast to the theory for convex parameter spaces rate optimal procedures are often required to be nonlinear. A construction of such nonlinear procedures is g...

On isomorphism of two bases in Morrey-Lebesgue type spaces

Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.

Decomposition of Lebesgue Spaces

Nonlocal Patch-based Image Inpainting through Minimization of a Sparsity Promoting Nonconvex Functional

We propose a convex model for nonlocal image inpainting that fills in missing or damaged areas with different convex combinations of available image patches. The visual quality of inpainted solutions is much better when patches are copied instead of averaged, and we show how this can be achieved by adding a nonconvex sparsity promoting penalty. To promote sparsity of a variable that is constrai...