MSE Analysis of the Projected Gradient Algorithm on Unions of Subspaces

Conference: WSA 2018 - 22nd International ITG Workshop on Smart Antennas
03/14/2018 - 03/16/2018 at Bochum, Deutschland

Proceedings: ITG-Fb. 276: WSA 2018

Pages: 5Language: englishTyp: PDF

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Wiese, Thomas; Shibli, Kamel; Utschick, Wolfgang (Professur für Methoden der Signalverarbeitung, Technische Universität München, 80290 Munich, Germany)

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.