Polar format algorithm is an imaging approach for spotlight mode synthetic aperture radar (SAR). It increases the load of data transmission and storage severely because of the greater synthetic aperture length. Synthetic aperture radar imaging by compressive sensing can reduce the sampling rate. Previous studies result in a decrease in image quality because they assume that the two dimensions of images are separable and ignore the range migration. An imaging approach based on range-cross compressive sensing is presented. It can correct the range migration and ensure the range and range-cross resolution of the image. The method introduces the Fourier basis varying with the range spatial frequency

reconstructing the image based on compressive sensing. It ensures the range and range-cross resolution because it may be an efficient substitute for Polar format algorithm range-cross interpolation and eliminates the range migration. The simulations and live data processing results show the validity of the proposed approach.