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Stepped-frequency waveforms can achieve an ultrawide bandwidth by using a sequence of single-frequency pulses. The advantages of stepped-frequency waveforms are low hardware requirements and high resolution. However, the stepped-frequency waveform requires a long time period to transmit the signals, which limits its application in synthetic aperture radar (SAR). The available imaging range width is usually very narrow, unless the range and azimuth resolutions are both decreased. In this paper, a random-frequency SAR imaging scheme based on compressed sensing is proposed. If the targets are sparse or compressible, it is sufficient to transmit only a small number of random frequencies to reconstruct the image of the targets. This means that the limitations of the stepped-frequency technique for SAR can be overcome. The available imaging range width can be enlarged significantly, while the range and azimuth resolutions are both maintained. Random undersampling is very easy to implement for both range and azimuth dimensions, and no new hardware components are needed. Simulation and experimental results are presented to demonstrate the validity of the proposed method.