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Internet of Things (IoT) interconnects resource constrained devices for providing smart applications to citizens. These devices have to be able to ensure both a minimum Quality of Service (QoS) and a minimum level of security when gathering and transmitting data. Compressive Sensing (CS) is a relatively new theory that performs simultaneous lightweight compression and encryption and can be used to prolong the battery lifetime of devices. In this paper, we stress the fact that on the contrary with most previous approaches, the sparsity of the signals can change significantly due to their time-varying nature. We propose a rate-adaptive scheme for maintaining a maximum level of reconstruction error at the receiver, and ensure the QoS requirements. This scheme uses a change point detection method, detecting the change in the sparsity, and estimating the optimum compression rate for maintaining a minimum reconstruction error. Performance is evaluated using real experimental data.