Resolution enhancement of two-dimensional grid-free compressive beamforming

Reconstructing the acoustic source distribution via imposing a sparsity constraint on a continuum, the atomic norm minimization (ANM) based grid-free compressive beamforming can eliminate the basis mismatch of conventional grid-based compressive beamforming. However, it works well only for sufficiently separated sources, which prohibits high resolution. The drawback arises because it uses an atomic norm to measure the source sparsity, while the atomic norm is not a direct sparse metric and its minimization is equivalent to the sparsity constraint only when the sources are sufficiently separated. This paper devotes itself to overcoming the drawback for the two-dimensional ANM based grid-free compressive beamforming. First, a sparse metric that can promote sparsity to a greater extent than the atomic norm is proposed. Then, using this metric a minimization problem is formulated and the majorization-minimization (MM) solving algorithm is introduced. MM iteratively conducts atomic norm minimization with a sound reweighting strategy, and therefore the developed method can be termed as iterative reweighted atomic norm minimization (IRANM). Both simulations and experiments demonstrate that whether a standard uniform rectangular array or a non-uniform array constituted by a small number of microphones is utilized, IRANM can overcome the drawback and thus enhance the resolution.