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One of the fundamental problems in Synthetic Aperture Radar (SAR) imaging is phase errors. Phase errors occur when the time required for the transmitted signal from SAR to the target and back cannot be obtained properly either because the distance between the SAR platform and the target cannot be measured exactly or in the case of random delays in the signal due to propagation in atmospheric turbulence. Phase errors cause blurring of the reconstructed image in the cross range direction. In this study, a nonquadratic regularization-based framework is proposed for joint image formation and phase error removal. The method involves the optimization of a cost function with respect to the image as well as the phase errors. Experimental results show the effectiveness of the proposed method.