Rotating Synthetic Aperture Radar (ROSAR) can generate a 360$^\circ$ image of
its surrounding environment using the collected data from a single moving
track. Due to its non-linear track, the Back-Projection Algorithm (BPA) is
commonly used to generate SAR images in ROSAR. Despite its superior imaging
performance, BPA suffers from high computation complexity, restricting its
application in real-time systems. In this paper, we propose an efficient
imaging method based on robust sparse array synthesis. It first conducts
range-dimension matched filtering, followed by azimuth-dimension matched
filtering using a selected sparse aperture and filtering weights. The aperture
and weights are computed offline in advance to ensure robustness to array
manifold errors induced by the imperfect radar rotation. We introduce robust
constraints on the main-lobe and sidelobe levels of filter design. The
resultant robust sparse array synthesis problem is a non-convex optimization
problem with quadratic constraints. An algorithm based on feasible point
pursuit and successive convex approximation is devised to solve the
optimization problem. Extensive simulation study and experimental evaluations
using a real-world hardware platform demonstrate that the proposed algorithm
can achieve image quality comparable to that of BPA, but with a substantial
reduction in computational time up to 90%.