Joint Sparse Estimation with Cardinality Constraint via Mixed-Integer Semidefinite Programming

The multiple measurement vectors (MMV) problem refers to the joint estimation of multiple signal realizations where the signal samples share a common sparse support over a known dictionary, which is a fundamental challenge in various applications in signal processing, e.g., direction-of-arrival (DOA) estimation. We consider the maximum a posteriori (MAP) estimation of an MMV problem, which is classically formulated as a regularized least-squares (LS) problem with an
$\ell_{2,0}$
-norm constraint and derive an equivalent mixed-integer semidefinite program (MISDP) reformulation, which can be solved by state-of-the-art numerical MISDP solvers at an affordable computation time. Numerical simulations in the context of DOA estimation demonstrate the improved error performance of our proposed method in comparison to several popular DOA estimation methods.