A radar apparatus for obtaining a higher resolution than conventional SAR apparatus without increasing the bandwidth comprises a transmitter antenna and a receiver antenna. A mixer mixes said receive signal with said transmit signal to obtain a mixed receive signal, and a sampling unit samples said mixed receive signal to obtain receive signal samples from a period of said receive signal. A processor processes said receive signal samples by defining a spatial grid in the scene with a finer grid resolution than obtainable by application of a synthetic aperture radar algorithm on the receive signal samples and determining reflectivity values at grid points of said spatial grid by defining a signal model including the relative geometry of said transmitter antenna and said receiver antenna with respect to the scene, said transmit signal and said spatial grid and applying compressive sensing on said receive signal using said signal model.