We present a simple method for recovering sparse signals from a series of noisy observations. Our algorithm is a Kalman filter (KF) that utilize a so-called pseudo-measurement technique for optimizing the convex minimization problem following from the theory of compressed sensing (CS). Compared to the recently introduced CS-KF in [1] which involves the implementation of an additional CS optimization algorithm (e.g., the Dantzig selector), our method is remarkebly easy to implement as it is exclusively based on the KF formulation. The results of an extensive numerical study are provided demonstrating the performance and viability of the new method. Sparse Signal Recovery Consider an R-valued random discrete-time process {xk}k=1 that is sparse in some known orthonormal sparsity basis ψ ∈ R, that is zk = ψ xk, |supp(zk)| << n (1) where supp(zk) denotes the support of zk. Assume that zk evolves according to zk+1 = Azk + wk (2) where A ∈ R and {wk}k=1 is a zero-mean white Gaussian sequence with covariance Qk. The process xk is measured using a sequence of noisy observations given by yk = Hxk + ζk = H zk + ζk (3) where {ζk} ∞ k=1 is a zero-mean white Gaussian sequence with covariance Rk, and H := H ψ ∈ R with m < n. Letting y := [y1, . . . , yk], our problem is defined as follows. We are interested in a y -measurable estimator x̂k such that the minimum mean square error (MMSE) E [
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