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Compressed sensing (CS) has emerged as a promising technique to jointly sense and compress sparse signals. One of the most promising applications of CS is compressive imaging. Leveraging the fact that images can be represented as approximately sparse signals in a transformed domain, images can be compressed and sampled simultaneously using low-complexity linear operations. Recently, these techniques have been extended beyond imaging to encode video. Much of the compression in traditional video encoding comes from using motion vectors to take advantage of the temporal correlation between adjacent frames. However, calculating motion vectors is a processing-intensive operation that causes significant power consumption. Therefore, any technique appropriate for resource constrained video sensors must exploit temporal correlation through low-complexity operations. In this tutorial, we first briefly discuss challenges involved in the transmission of video over a wireless multimedia sensor network (WMSN). We then discuss the different techniques available for applying CS encoding first to images, and then to videos for error-resilient transmission in lossy channels. Existing solutions are examined, and compared in terms of applicability to wireless multimedia sensor networks (WMSNs). Finally, open issues are discussed and future research trends are outlined.