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We present a source localization method based upon a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing an ℓ1-norm penalty; this can also be viewed as an estimation problem with a Laplacian prior. Explicitly enforcing the sparsity of the representation is motivated by a desire to obtain a sharp estimate of the spatial spectrum which exhibits superresolution. To summarize multiple time samples we use the singular value decomposition (SVD) of the data matrix. Our formulation leads to an optimization problem, which we solve efficiently in a second-order cone (SOC) programming framework by an interior point implementation. We demonstrate the effectiveness of the method on simulated data by plots of spatial spectra and by comparing the estimator variance to the Cramer-Rao bound (CRB). We observe that our approach has advantages over other source localization techniques including increased resolution; improved robustness to noise, limitations in data quantity, and correlation of the sources; as well as not requiring an accurate initialization.