## 1 Introduction  
Wireless sensor network (WSN) has been well-suited for use with a variety of applications including environmental monitoring, biological detection, smart spaces, and battlefield surveillance. These applications can be divided into two broad categories in terms of the way of data collection based on the observer interest: event-based detection and continuous data sampling. In event-based detection, the sensors report the data expected to collect to the sink only when an event of interest occurs. It means that the significant characteristic of the event-based detection in WSNs is delay intolerant and error sensitive. In other words, the data delivered to the sink need to be reliable once an emergency occurred within the sensing range of sensors is detected in real time. In this context, the detection success rate of interested events is crucial to the efficiency of the application. Coverage-based scheduling methods can achieve full coverage of the target area by finding the disjoint cover sets of sensor nodes, and thus greatly improve the event detection rate. The network lifetime can be increased due to only one cover set is active and send their readings, while the remainder of the nodes goes to sleep and waits for the next time to be reused. To avoid the area uncovered, it is necessary to guarantee that the number of sensor nodes in each set is enough to cover the whole network. In the continuous data sampling applications, the local measures in the sensor node's sensing area are regularly sampled and reported, such as the ambient temperature and humidity. After receiving all samples, the sink generates a data snapshot of the area at one point in time. Some applications may be more tolerant to discrepancies in the sensed values, not demanding the receiving data without any error. In a general case, the observers are more focused on the evolving process or spatial structure evolution of certain physical phenomenon in the monitored area. Such frequent sampling behavior expends more energy than the event detection. Thus reducing energy waste is even more important to the continuous data sampling applications. Unlike the event-based detection, the continuous data sampling applications are delay and error tolerant. Differences between them lead to that the coverage-based scheduling methods are unusable for the applications characterized by continuous sampling. WSNs have great potential that are exploited for many applications in real world scenarios. However, it has been concluded that the problems of energy constraint and data redundancy emerge inevitably in the course of designing an application of WSNs, especially for high-density large scale network. First, due to the relative less energy consumption on computation and sensing, wireless communications resulting from data delivery consume significant amount of power of sensor nodes only equipped with limited battery. In order to achieve longer lifetime, one of design challenges for WSNs is to reduce the amount of communication as much as possible without sacrificing measurement integrity. Second, to satisfy full network coverage requirements [1] and compensate for the impact of nodes failure [2,3], sensor nodes are deployed with much greater density than is needed. Therefore, for the general case in which sensor nodes is highly over-deployed, it is common that nodes redundancy results in data redundancy, whereas we can infer the degree of node redundancy through analyzing the sensed data set. Further, the redundant sensor nodes can be scheduled to the sleep mode to save energy when the predefined observation fidelity is satisfied. The problem behind this approach is how to determine the observation fidelity. Much of existing work in this area is still based on the error sensitivity approach, where the mean square error (MSE) is considered as the sole type of distortion. The inherentdisadvantage of this method, however, is that MSE dose not provide a good approximation of perceived structural information in the continuous data sampling applications.