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2010

Methods for sparse signal recovery using Kalman filtering with embedded pseudo-measurement norms and quasi-norms

9 years 11 months ago
Methods for sparse signal recovery using Kalman filtering with embedded pseudo-measurement norms and quasi-norms
We present two simple methods for recovering sparse signals from a series of noisy observations. The theory of compressed sensing (CS) requires solving a convex constrained minimization problem. We propose solving this optimization problem by two algorithms that rely on a Kalman filter (KF) endowed with a pseudo-measurement (PM) equation. Compared to a recently-introduced KF-CS method, which involves the implementation of an auxiliary CS optimization algorithm (e.g., the Dantzig selector), our method can be straightforwardly implemented in a stand-alone manner, as it is exclusively based on the well-known KF formulation. In our first algorithm, the PM equation constrains the norm of the estimated state. In this case, the augmented measurement equation becomes linear, so a regular KF can be used. In our second
Avishy Carmi, Pini Gurfil, Dimitri Kanevsky
Added 22 May 2011
Updated 22 May 2011
Type Journal
Year 2010
Where TSP
Authors Avishy Carmi, Pini Gurfil, Dimitri Kanevsky
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