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Low complexity projection-based adaptive algorithm for sparse system identification and signal reconstruction

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3 Author(s)
Slavakis, K. ; Dept. Telecommun. Sci. & Technol., Univ. of Peloponnese, Tripolis, Greece ; Theodoridis, S. ; Yamada, I.

The present paper introduces a low complexity online convex analytic tool for time-varying sparse system identification and signal reconstruction tasks. The available information enters the design in two ways; (i) the sequentially arriving training data generate a sequence of simple closed convex sets, namely hyperslabs, and (ii) the information regarding the cardinality of the support of the unknown system/signal is used to create another sequence of closed convex sets, namely weighted ℓ1-balls. In such a way, searching for the unknown system/signal becomes the task of solving a convex feasibility problem with an infinite number of constraints. The basic tool to solve such a problem, with computational load that scales linearly to the number of unknowns, is the projection onto a closed convex set, and more importantly the subgradient projection mapping associated to a convex function. A convergence analysis of the proposed algorithm is given based on very recent advances of projection-based adaptive algorithms, and numerical results are presented to support the introduced theory.

Published in:

Signals, Systems and Computers (ASILOMAR), 2010 Conference Record of the Forty Fourth Asilomar Conference on

Date of Conference:

7-10 Nov. 2010