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Waves from a sparse set of source hidden in additive noise are observed by asensor array. We treat the estimation of the sparse set of sources as ageneralized complex-valued LASSO problem. The corresponding dual problem isformulated and it is shown that the dual solution is useful for selecting theregularization parameter of the LASSO when the number of sources is given. Thesolution path of the complex-valued LASSO is analyzed. For a given number ofsources, the corresponding regularization parameter is determined by anorder-recursive algorithm and two iterative algorithms that are based on afurther approximation. Using this regularization parameter, the DOAs of allsources are estimated.

Using the LASSO's Dual for Regularization in Sparse Signal Reconstruction from Array Data