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Recently the rapid imaging based on the compressive sensing (CS) theory have attracted increasing interests, which simultaneously sampling and compressing signals or images. Radar imaging based CS is a potential way to obtain the high-resolution radar images without the constraint of Nyquist sampling rate. In this paper, we proposed a radar remote-sensing imaging approach based on compressive sensing and fast Bayesian matching pursuit (FBMP) recovery algorithm. Some experiments are taken and the results indicate that an accurate reconstruction of high-resolution radar images are obtained, with fewer measurements than most its counterparts(e.g., MP, OMP, StOMP, GPSR),but resulting in lower normalized MSE(NMSE). Although BCS obtains lower NMSE than FBMP,simultaneously with higher time complexity and sparsity.