## 4 The Structure Fidelity Data Collection Framework
### Nodes Scheduling Scheme Based on the Structural Similarity Index  
After the cluster construction, the member nodes send all readings to the single cluster head node. In this case, the cluster head creates continuous images over time, where each image is composed of the readings sensed by all nodes at an instant. For a nodes scheduling scheme, only a subset of nodes is selected to work and sample, while the rest of sensor nodes go to sleep to save energy. Based on our data transmission model, the readings of unselected sensor nodes are replaced by the cluster head readings from the same time. The replaced dataset denoted \(Y_{M\times N}\) can provide a good structural similarity index over the monitored area during the subsequent data collection phase. The main goal of our scheduling scheme is to enable the nodes with greater contribution to the SSIM index to enter active mode. Since the SSIM index is a way to measure the image structure quality from three different aspects: mean distortion, variance distortion and loss correlation, it is hard to calculate each individual node's contribution to overall structure of collected data. From the property (3) of the SSIM index, however, we know that the maximal value 1 is achieved only when the image signals being compared are identical. In other words, the closer they are to each other, the closer SSIM is to 1. The increase in the deviation between the distorted image and the reference image inevitably leads to a decrease in the SSIM index. Based on the replacement principle as described above, our nodes scheduling scheme tries to sort the member nodes in decreasing order of the deviation between the readings of them and the cluster head, and add the sensor node one by one into the active node set until the predefined structure fidelity is met, such that the SSIM index will undergo the largest increase as the addition of the candidate node. We present a heuristic algorithm to tackle the problem of active nodes selection. Initially, the active node subset \(A\) only includes the cluster head node while all elements in the member node set \(Q\) are unselected. At this point, the cluster head generates a data sequence viewed as the first image with the largest distortion \(Y_{i}^{1}=[x_{iC},x_{iC},\cdots,x_{iC}]\), where \(x_{iC}\) denote the reading from the cluster head at the time \(i\) and all readings of member nodes are replaced by \(x_{iC}\). Let \(x_{ij}\) be the reading of the \(j\)-th member node at the time \(i\), and the reference image is represented by \(X_{i}=[x_{i1},x_{i2},\cdots,x_{ij},\cdots,x_{i(N-1)},x_{iC}]\). The node \(j\) among the set \(Q\) is selected into the active set \(A\) if and only if \(x_{ij}\) is with the biggest difference with \(x_{iC}\). Then, the node \(j\) is removed from the set \(Q\) and the second distorted image is given by \(Y_{i}^{2}=[x_{iC},x_{iC},\cdots,x_{ij},\cdots,x_{iC},x_{iC}]\). The value of \(SSIM(X_{i},Y_{i}^{2})\) can be calculated through Equation (6). So repeatedly until a minimal subset is built while meeting the predefined threshold. \(Y_{i}^{N}\) is equal to \(X_{i}\), where all nodes will be incorporated into the active node set \(A\) when the threshold is set to 1. Here we define the contribution rate of node to the structural similarity. **Definition 1**.