MSE Analysis of the Projected Gradient Algorithm on Unions of Subspaces

Abstract

We present a mean-squared-error (MSE) analysis of
the projected gradient algorithm when applied to linear inverse
problems with constraint sets that are unions of subspaces. This
algorithm has been recently presented as a generalization of
the iterative hard thresholding algorithm. The main difficulty
with the MSE analysis is to calculate the expected value of the
supremum of a continuous random process. We present a simple
approach to calculate the expected supremum, which builds upon
the concept of Lipschitz random processes.