A minimax approach for mean square denoising

Minimax estimation aims at finding optimal estimators in the worst case situation compatible with the available information. In the present work, we consider the minimax mean square denoising of a random vector using a nonlinear estimator. The data set over which the minimax estimator is looked for takes the general form of a convex set where the correlation matrix of the data is constrained to lie. Also, additional convex constraints on the weights defining the estimator can be taken into account in the proposed approach