Due to the inaccuracies in radar's measurement, autofocus including range alignment and phase compensation is always essential in inverse synthetic aperture radar (ISAR) imagery. Compressed sensing (CS) based ISAR imagery suggests that the image of target can be reconstructed from much fewer random pulses. Because the number of pulses is inadequate and the pulse intervals are nonuniform, conventional phase compensating algorithms can't work in CS imaging. In this paper, an iterative algorithm is proposed to compensate the phase errors and reconstruct high-resolution focused image from limited pulses. In each iteration, the image of target is reconstructed by CS method, and then the estimation of phase errors is updated based on the reconstructed image. By cycling these steps, well-focused image can be obtained. The smoothed ℓ0 algorithm is used to reconstruct the image, and the idea of minimum entropy optimization is used to estimate the phase errors. Besides, a method of extracting range bins in range profile based on amplitude information is proposed, which can reduce the computational complexity and improve the speed of convergence considerably. Both simulation and experiment results from real radar data demonstrate the effectiveness and feasibility of our method.
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