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

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Avishy Carmi, Pini Gurfil, Dimitri Kanevsky
• Keywords: Algorithm, Artificial Intelligence, Augmented Measurement Equation, TSP 2010, Well-known Kf Formulation