Sparsity-Driven Radar Auto-Focus Imaging Under Over-Wavelength Position Perturbations

We consider a 2D imaging problem where a perturbed mono-static radar is used to detect localized targets situated in a region of interest. In order to deal with position-induced out-of-focus, we proposed a sparsity-driven auto-focus imaging approach in which each radar measurement is modeled as a superposition of weighted and delayed target signatures scattered from the corresponding target phase centers. We iteratively exploit the position-related delays and the target signatures by analyzing data coherence, and consequently form an adaptive projection matrix of the radar measurements. By imposing sparsity on the scattering weights, a sparse image and a dense image, without and with the target signatures respectively, are reconstructed. Compared to existing auto-focus methods, our approach significantly improves radar focus performance in imaging localized targets, even under position perturbations up to 10 wavelengths of the radar central frequency. We validate our algorithm with simulated noisy data.