Constrained nonlinear minimum mse estimation

TL;DR: A simple closed form formula is derived that reveals the structure of the restricted estimator for a wide class of constraints in the problem of minimum mean-squared error estimation.

Abstract: We address the problem of minimum mean-squared error (MMSE) estimation where the estimator is constrained to belong to a predefined set of functions. We derive a simple closed form formula that reveals the structure of the restricted estimator for a wide class of constraints. Using this formula we study various types of constrained estimation problems that arise commonly in the fields of signal processing and communication.