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We propose a sparse signal representation-based method for complex-valued imaging. Many coherent imaging systems such as synthetic aperture radar (SAR) have an inherent random phase, complex-valued nature. On the other hand sparse signal representation, which has mostly been exploited in real-valued problems, has many capabilities such as superresolution and feature enhancement for various reconstruction and recognition tasks. For complex-valued problems, the key challenge is how to choose the dictionary and the representation scheme for effective sparse representation. We propose a mathematical framework and an associated optimization algorithm for a sparse signal representation-based imaging method that can deal with these issues. Simulation results show that this method offers improved results compared to existing powerful imaging techniques.