In a primary research report we have introduced a simple method for recovering sparse signals from a series of noisy observations using a Kalman filter (KF). The new method utilizes a so-called pseudo-measurement technique for optimizing the convex minimization problem following from the theory of compressed sensing (CS). The CS-embedded KF approach has shown promising results when applied for reconstruction of linear Gaussian sparse processes.
This report presents an improved version of the KF algorithm for the recovery of sparse signals. In this work we substitute the l1 norm by an approximate quasi-norm lp, 0 ≤ p < 1. This modification, which better suits the original combinatorial problem, greatly improves the accuracy of the resulting KF algorithm. This, however, involves the implementation of an extended KF (EKF) stage for properly computing the state statistics.
By: Avishy Carmi; Pini Gurfil; Dimitri Kanevsky
Published in: RC24711 in 2008
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