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This paper investigates the potential of the compressed sensing (CS) paradigm for video streaming in Wireless Multimedia Sensor Networks. The objective is to co-design a low-complexity video encoder based on compressed sensing and a rate-adaptive streaming protocol for wireless video transmission. The proposed rate control scheme is designed with the objectives to maximize the received video quality at the receiver and to prevent network congestion while maintaining fairness between multiple video transmissions. Video distortion is represented through analytical and empirical models and minimized based on a new cross-layer control algorithm that jointly regulates the video encoding rate and the channel coding rate at the physical layer based on the estimated channel quality. The end-to-end data rate is regulated to avoid congestion while maintaining fairness in the domain of video quality rather than data rate. The proposed scheme is shown to outperform TCP-Friendly Rate Control (TFRC).