We consider the application of compressive imaging theory to the problem of wide-area persistent surveillance. While the compressive sensing theory enjoys significant research attention, mainly because of the possibilities for orders-of-magnitude increases in signal/image processing applications, the application areas for compressive imaging have not kept pace due to the lack of an optical architecture which could directly improve current sensing capabilities. There are now cases in the literature and under study where optical architectures have been developed which require the incorporation of compressive imaging in order to perform the indicated exploitation application. This paper utilizes one such architecture to show a dramatic (two orders of magnitude) increase in performance for the application of wide-area persistent surveillance. This application together with its architecture is described as a field-of-view (FOV) multiplexing imager, and its relation to compressive imaging is discussed and exploited for increased field-of-regard (FOR) imaging. A simulated example is given in the last section with qualitatively impressive results. The optical architecture of FOV multiplexing, while showing a significant performance increase over current capabilities, also opens some interesting research questions.