For the problem of first-order and second-order range migration in ISAR imaging under the condition of wide angle and wide bandwidth, a method for sparse azimuth data is proposed to obtain high-resolution ISAR images. After stretch processing, envelope alignment and residual video phase removal, the sparse recovery algorithm that sparse base is constructed by the Keystone transform is used to achieve range migration correction and the missing range profile reconstruction, and then the second-order phase estimation method based on fractional Fourier transform is used to estimate and compensate the second-order rotational phase. Simulation results show the method can effectively improve the imaging quality.