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We propose a vision for combining well-known array processing techniques with recent developments in the compressive sensing community to address a broad range of signal processing problems related to oceanography. Our goal is to set up a general mathematical framework to address and solve sensor array problems that involve time-varying sparse processes. Specifically we propose a compressive sensor array system that potentially reduces the need for high intensity signals by exploiting the spatial redundancy of the sensor array and the sparsity of data in the volume of interest. Simulations are presented to illustrate the high performance of sparse reconstruction techniques that are key to proposed sensor array.