A Generalized and Accelerated Approach of Ambiguity-Free Imaging for Sub-Nyquist SAR

Despite the success of compressive sensing (CS) algorithms in sub-Nyquist synthetic aperture radar (SAR) imaging, they lack a generalized ambiguity-depression capability and suffer from high computational complexity. To address these weaknesses, we propose a novel imaging approach that simultaneously suppresses ambiguity introduced by nonuniform sampling and nonideal azimuth antenna patterns while enhancing resolution performance for wide-swath sub-Nyquist SAR imaging. To improve efficiency, we employ the randomized block coordinate descent based on the accelerated fast iterative shrinkage threshold algorithm (FISTA) to obtain the desired ambiguity-free image. In the accelerated FISTA, we incorporate two measures to reduce computational complexity. First, we analytically formulate the update stepsize using the singular-value perturbation theory, Kronecker product technique, and orthogonality of the uniformly discrete Fourier matrix. This enables efficient computation of the Lipschitz constant. Second, we expedite the computation of the gradient matrix through efficient frequency domain techniques. Numerical results using both simulated data and realistic SAR echo validate the effectiveness of our proposed method and demonstrate its advantages over existing algorithms.