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This paper presents a novel approach for the reconstruction of super-resolution (SR) synthetic aperture radar (SAR) images in the compressed sensing (CS) theory framework. Recent research has shown that super-resolved data can be reconstructed from an extremely small set of measurements compared to that currently required. Therefore, a CS to produce SAR super-resolution images is introduced in the present work. The proposed approach contributes in three ways. First, enhanced SR results are achieved using a framework that combines CS with a multi-dictionary. Then, the multi-dictionary pairs are trained after classifying the training images through a sparse coding spatial pyramid machine. Each dictionary pair containing low- and high-resolution dictionaries are jointly trained. Finally, the gradient-descent optimization approach is applied to decrease the mutual coherence between the measurement matrix and the representation basis. The CS reconstruction effect is related to incoherence. The effectiveness of this method is demonstrated on TerraSAR-X data.