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Based on compressive sensing theory, a new method for high resolution inverse aperture radar (ISAR) imaging of maneuvering target is proposed. In this method, only a few measurements in ambiguity function plane are sampled to reconstruct the time-frequency distribution by solving the inverse problem using basis pursuit method. With a Gaussian window as a sampling function, the trade-off between the cross-term suppression and resolution is properly dealt with, and the proposed method obtains clear ISAR image of maneuvering target with a high resolution. The effectiveness of the proposed method is studied with testing data.