High-resolution, quantitative signal subspace imaging for synthetic aperture radar (2112.12270v1)

Abstract: We consider synthetic aperture radar imaging of a region containing point-like targets. Measurements are the set of frequency responses to scattering by the targets taken over a collection of individual spatial locations along the flight path making up the synthetic aperture. Because signal subspace imaging methods do not work on these measurements directly, we rearrange the frequency response at each spatial location using the Prony method and obtain a matrix that is suitable for these methods. We arrange the set of these Prony matrices as one block-diagonal matrix and introduce a signal subspace imaging method for it. We show that this signal subspace method yields high-resolution and quantitative images provided that the signal-to-noise ratio is sufficiently high. We give a resolution analysis for this imaging method and validate this theory using numerical simulations. Additionally, we show that this imaging method is stable to random perturbations to the travel times and validate this theory with numerical simulations using the random travel time model for random media.