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We develop an efficient structured sparse antenna array architecture for coherent imaging of sparse but otherwise unknown scenes. In this architecture, the array elements are configured in a periodic nonuniform pattern that can be viewed as the superposition of multiple sparse uniform subarrays. For such structure, we develop an efficient pattern design procedure using co-array analysis, and we describe robust and efficient algorithms implementing the required associated array processing, which comprise scene support recovery, followed by image reconstruction. In addition, we develop a practical method for detecting reconstruction failures when the scene density exceeds the level for which the array was designed, so that false images are not produced. As a demonstration of its viability, the architecture is used to reconstruct a simulated natural scene.