Linear System Theory and Semidefinite Representations of Atomic Norms

Friday, January 29, 2016 - 9:00am - 9:50am
Keller 3-180
Lieven Vandenberghe (University of California, Los Angeles)
We discuss extensions of recently proposed semidefinite optimization methods for atomic decomposition and 1-norm minimization over infinite dictionaries of complex exponentials. We show that techniques related to the Kalman-Yakubovich-Popov lemma in linear system theory provide simple constructive proofs of these semidefinite formulations. This connection directly leads to extensions to more general dictionaries associated with state-space models and matrix pencils. The results will be illustrated with applications in signal processing.
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