In the inverse synthetic aperture radar imaging, the autofocus is a required step for generating high‐quality images. However, due to many factors, the aperture data may be sparse so that the classical motion compensation approaches and imaging algorithms are not proper. On the basis of the compressed sensing technique and two optimisation methods (the gradient projection method and the conjugate gradient method), a novel autofocus algorithm, which can be used in sparse aperture imaging, is proposed in this Letter. The phase errors induced by the translational Doppler frequency are estimated and the focused image is reconstructed simultaneously by dual iterative computation. This approach is verified by real data processing.