# Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial
## 20 Energy Optimization in Wireless Visual Sensor Networks While Maintaining Image Quality
### System Model  
[PERSON] et al. consider a network of camera sensors in [15] that do not involve any routing, but rather transmit directly to a fusion center. Each camera node consists of four modules that consume energy, these are the transmitter module, the compression module, the imaging module and the power module. Each sensor has \(W_{s}^{i}\) pixels in horizontal direction and \(H_{s}^{i}\) pixels in vertical direction. The average number of bits required to quantize each pixel value, after compression, is \(N_{b}^{i}\) and the frame rate of imaging is assumed to be \(f_{frame}\) fps (frame per second). The required bit rates for transmitting video from each camera node to the fusion center (the sink node) is then equal to \(f_{frame}W_{s}H_{s}N_{b}\) bps (bits per second). To achieve a threshold SNR at the fusion center, a camera sensor node is required to transmit with the following power level:  
\[p_{i}^{t}=\frac{(4\pi)^{2}\,N\gamma_{th}B}{\lambda_{c}^{2}G_{r}G_{t}}\left(d_{i }^{fc}\right)^{2} \tag{37}\]  
where \(N\) is the power spectral density of additive white Gaussian noise (AWGN), \(\gamma_{th}\) is the SNR threshold, \(\lambda_{c}\) is the carrier wavelength \(G_{r}\) and \(G_{t}\) are the receive and transmit antenna gains respectively, \(B\) is the transmission bandwidth and \(d_{i}^{fc}\) is the distance between the wireless camera node \(i\) and the fusion center. The total amount of energy consumed by a camera sensor node is:  
\[E_{i}^{total}=p_{i}^{t}f_{frame}W_{s}^{i}H_{s}^{i}N_{b}^{i}+\alpha\Delta f_{i} +p_{i}^{cvid}T+\tau\Delta\theta_{i} \tag{38}\]  
where \(\alpha\Delta f_{i}\) is the amount of consumed energy by a miniature motor to change the focal length \(f_{i}\) of the camera lens by \(\Delta f_{i}\) using a force of \(\alpha\), and \(p_{i}^{cvid}\) the power consumed by the imaging module for time \(T\).  
The _field of vision_ (FOV) of a camera is the region where the camera can cover without any obstacles. It is given by:  
\[\phi=tan^{-1}\left(\frac{W_{s}}{2f_{i}}\right) \tag{39}\]  
and must satisfy a minimum threshold \(\phi_{th}\) that depends on the radius \(radius^{target}\) of the target object as well as its distance \(d_{i}^{target}\) from the camera sensor, given in [15] as:  
\[\phi_{th}=\frac{radius^{target}}{d_{i}^{target}} \tag{40}\]  
The _depth of field_ (DOF) is the difference between the distance of the front edge and the rear edge of a focused object. There is a far limit \(Dep_{f}^{i}\) and a near limit \(Dep_{n}^{i}\) that describe the DOF of node \(i\). They depend on the diaphragm \(Diaf_{i}\) of camera \(i\)'s lens, the focal length \(f_{i}\) and the distance \(d_{i}^{target}\) between the camera node \(i\). They are given as:  
\[Dep_{n}^{i}=\frac{d_{i}^{target}f_{i}^{2}Diaf_{i}}{Diaf_{i}f_{i}^{2}+cf_{i} \left(d_{i}^{target}-f_{i}\right)}\] (41a) where \[c\] here is the circle of confusion diameter [39]. The input variance \[\sigma_{th}^{2}\] of the capture target image decreases with the distance \[d_{i}^{target}\]. The authors were able to fit it acceptably by an exponential function given as: \[\sigma_{input}^{2}=e^{-0.06d_{i}^{target}} \tag{42}\]and the variance \(\sigma^{2}_{output}\) of the output image was derived in [15] as:  
\[\sigma^{2}_{output}=e^{-0.06d_{i}^{target}}\left(0.03N_{b_{i}}^{0.4}+0.91\right) \tag{43}\]  
where \(N_{b_{i}}\) is the number of bits per pixel that camera \(i\) uses for image quantization.