A Preconditioned Hessian-Like Proximal Gradient Algorithm for Sparse ML-DOA Estimation

Maximum Likelihood (ML) Direction-of-Arrival (DoA) estimation under the Vectorized Covariance Matrix Model (VCMM) offers improved performance but remains computationally intensive. To alleviate this issue, sparse formulations have been adopted and shown to be asymptotically equivalent to the ML using a proper regularization parameter choice. Yet, the resulting sparse criterion remains intricate and is typically minimized using slow first-order methods such as the Proximal Gradient Algorithm (PGA). To improve convergence speed, an Hessian-like preconditioned PGA is introduced. As the associated proximal operator lacks a closed-form expression, an IRL1 scheme, known to converge to a critical point of the $\ell_{0}$-regularized criterion is employed, enabling its numerical evaluation via the Chambolle-Pock (CP) algorithm. This approach yields faster convergence and enhanced performance in low-SNR scenarios by exploiting the local geometry encoded in the Hessian.