Dictionary identification: sparse matrix-factorization via l1-minimization
IEEE Transactions on Information Theory
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When applied to array processing, the Pisarenko harmonic decomposition (PHD) method is limited to linear equispaced arrays. We present an approach that allows us to extend it to general arrays, although for the ease of exposition, we consider only sparse linear arrays. We exploit the fact that the PHD can be seen as a deconvolution or model-fitting approach that minimizes an t1 norm and can thus be implemented as a standard linear program. Looking at the PHD from this point of view has two advantages: it allows us to extend its applicability to arbitrary arrays, and by diverging slightly from the basic philosophy, it allows us to improve its performance, which is often quite poor in its original version