TY - GEN
T1 - Low complexity projection-based adaptive algorithm for sparse system identification and signal reconstruction
AU - Slavakis, Konstantinos
AU - Theodoridis, Sergios
AU - Yamada, Isao
PY - 2010/12/1
Y1 - 2010/12/1
N2 - 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.
AB - 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.
KW - Adaptive filtering
KW - convex sets
KW - projection
KW - sparsity
KW - subgradient projection
UR - http://www.scopus.com/inward/record.url?scp=79958017037&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79958017037&partnerID=8YFLogxK
U2 - 10.1109/ACSSC.2010.5757653
DO - 10.1109/ACSSC.2010.5757653
M3 - Conference contribution
AN - SCOPUS:79958017037
SN - 9781424497218
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 703
EP - 707
BT - Conference Record of the 44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010
T2 - 44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010
Y2 - 7 November 2010 through 10 November 2010
ER -