## 4 Cluster-Based Distributed Compressed Sensing for QoS Routing
### Event-Driven Clustering  
#### 4.1.1 Problem Formulation  
Consider a CVSN containing \(N\) homogeneous video sensor nodes denoted by \(S=\{v_{i}|i=1,2,\ldots,N\}\) and some ordinary nodes used for detecting events. Both video sensors and scalar nodes are cognitive radio nodes; they and primary users coexist in CVSN. Video sensors can only observe the object in their FoVs. As shown in Figure 4, the FoVs of video sensor is determined by four parameters: the location of the video sensor (\(L\)), the sensing radius (\(r\)), the sensing direction (\(v\)) and the offset angle (\(\alpha\)). It is assumed that sensing direction \(v\) of all nodes is fixed. Suppose that there are two sensors \(v_{i}\) and \(v_{j}\) with FoVs \(F_{i}\) and \(F_{j}\). Let \(X_{i}\) and \(X_{j}\) denote their observed images, both of which are correlated if \(F_{i}\) and \(F_{j}\) are overlapped with each other. Two metrics which characterize the correlation between adjacent video sensors are introduced to select member nodes. The overlapped ratio of FoVs for \(v_{i}\) and \(v_{j}\), denoted by \(r_{i,j}\), is defined as  
\[r_{i,j}=\frac{S\left(F_{i,j}\right)}{S\left(F_{i}\right)}, \tag{1}\]  
Figure 4: Overlapped FoVs. Figure 3: Cluster-based distributed compressed sensing framework for QoS routing. where \(S\left(F_{i,j}\right)\left(F_{i,j}=F_{i}\cap F_{j}\right)\) is the overlapped area of \(F_{i}\) and \(F_{j}\), and \(S\left(F_{i}\right)\) is the area of \(F_{i}\). If two video sensors have large overlapped ratio of FoVs, large portions of the two observed images are correlated, and they are likely to observe the same event concurrently. Consider two adjacent nodes \(v_{i}\) and \(v_{j}\) with FoVs \(F_{i}\) and \(F_{j}\) that can observe an object of interest. Suppose both nodes capture the image about the object of interest, denoted by \(X_{i}\) and \(X_{j}\). The condition entropy of \(X_{i}\) and \(X_{j}\) is defined as  
\[H\left(X_{i}|X_{j}\right)=H\left(X_{i},X_{j}\right)-H\left(X_{j}\right), \tag{2}\]  
which quantifies correlation between \(v_{i}\) and \(v_{j}\). With the decrease of conditional entropy, the correlation of images captured by \(v_{i}\) and \(v_{j}\) increases. Each video sensor reports its focal length and FoV parameters to the sink. After receiving these parameters, the sink calculates \(r_{i,j}\) between any two video sensors using Equation (1) and distributes corresponding results to each node. Neighbor discovery is provided by the common control channel signaling periodically. By this signaling, all nodes know one-hop and two-hop neighbors and their vacant channels. The clustering process is generated when an event is detected. Event-detecting nodes become member nodes directly. Then, a request message is sent by these member nodes to non-member one-hop neighbors. Upon receiving this request, each non-member node determines whether they join clustering. The condition for becoming member nodes depends on the correlation between nodes. The member nodes newly elected send a message to their non-member one-hop neighbors, and the process continues until the event is not within nodes' FOVs. Assume member node \(v_{i}\) sends request message to its neighbor node, i.e., \(v_{j}\). The weight between \(v_{i}\) and \(v_{j}\), denoted by \(w_{i,j}\), is calculated by  
\[w_{i,j}=\frac{r_{i,j}}{H\left(X_{i}|X_{j}\right)}. \tag{3}\]  
We introduce a correlation threshold, denoted by \(CT\), to represent the correlation degree between two nodes. If weight \(w_{i,j}\) is bigger than \(CT\), node \(v_{j}\) is chosen as a member node. We define set Y that represents member nodes within a cluster. Clusters are formed when an event is detected and maintained until the end of the event. A cluster head is responsible for compressing observed images and then sends compressed data to the sink. Due to the existence of PUs, the channel availability of each node is different, which causes a significant influence on the data transmission of a cluster head.