Target Localization via Improved Matrix Recovery with $\ell _{0}$-Norm Minimization in Microwave Interferometric Radiometry

With its superior imaging efficiency and outstanding spatial resolution, microwave interferometric radiometry (MIR) demonstrates great potential and value in the field of target localization, including radio frequency interference (RFI) source localization, ship detection, and so on. In this article, we propose a target localization method via improved matrix recovery with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula>-norm minimization. It exploits the low-rank and sparsity properties of visibility samples from target and scene components, respectively. First, we construct the virtual array based on baseline coverage of the primitive sparse array and generate the corresponding augmented covariance matrix (ACM). This augmentation operation improves the degree-of-freedom (DOF) for subsequent array processing. Then, we present the improved matrix recovery (IMR) model with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula>-norm minimization to reconstruct the ACM. In the proposed model, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula>-norm is designed as a penalty term to suppress the scene component, and the Laplacian kernel is used to update the penalty parameter automatically. We adopt block coordinate descent (BCD) to solve the resulting multivariate optimization problem and obtain the scene-suppressed ACM (SSACM). Finally, a subspace-based direction-of-arrival (DOA) estimation method, i.e., MUSIC, is performed on the SSACM to achieve target localization. Experimental analyses using remote sensing synthetic data and airborne measurement data show that the proposed IMR-based method not only exhibits enhanced localization accuracy, angular resolution, and robustness, but also has better detection performance in low to medium signal-to-noise ratio (SNR) scenarios compared to existing commonly used methods.