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A MUSIC-ML (MML) processing algorithm for 3-dimensional localization of underwater acoustic sources using a 2-dimensional acoustic vector (AVS) array was proposed recently. The MML processor performs source localization with high accuracy and resolution. But the hardware and computational complexity of the MML processor is very high. In this paper we propose the use of compressive sampling of the AVS array output in the spatial domain for reducing the processor complexity. It is shown that a significant reduction in complexity with negligible performance degradation can be achieved by using compressive sampling. But complexity reduction by reducing the number of sensors without compressive sampling leads to a significant performance degradation.