# GPR Data Augmentation Methods by Incorporating Domain Knowledge
## 2 Methods
### Image Brightness Transformation Based on Gain Compensation  
The reflected signal features of the target are weak due to the attenuation of the EW when traveling through the medium, which is one of the most important challenging factors in the GPR automatic identification. Signal gain compensation is considered to be the time-varying enhancement of signal amplitude strength that can be used to compensate for the energy loss caused by EW attenuation [35]. The reflected signal was changing from weak to strong through the adjustment of the gain function, which caused the GPR images' brightness and contrasts to change.  
Three gain functions are most commonly used to process the GPR data depending on the target. The first method is automatic gain control (AGC), which is an automatic function applied to each single-channel wave of the GPR based on the difference between the maximum amplitude of all the traces and the average amplitude of the specific time window. This algorithm is a function to compensate for the amplitude difference between two traces, so it is necessary to select the time window carefully to prevent excessive noise in the section. The second method is spherical and exponential (SEC). This method compensates for the loss of the EW energy by the exponential function because it considers that the geometric diffusion effect attenuates the EW. The disadvantage of using SEC is highly related to the exponential gain factor which could hide the earlier time amplitudes [36]. The third method is inverse amplitude decay (IAD). A main amplitude decay function is calculated just like a data-adaptive filter. Then, each trace is applied by the inverse function. In addition, the gain function can also be set by expert experience, including simple constant, linear, and exponential gain functions to the signal. However, the choice of gain function type should depend on the physical model of the detected target. Considering the characteristics of road sub-surface distresses, we adopt the IAD gain compensation method.  
Figure 1: GPR data augmentation methods by incorporating domain knowledge: image brightness transformation based on gain compensation, image resolution transformations based on station spacing, and color space transformations based on radar signal mapping rules.  
Assuming that in a homogeneous medium, the EW amplitude at a distance from the transmitting antenna is:  
\[A=\frac{A_{0}}{r}e^{-at} \tag{1}\]  
In Equation (1), \(A_{0}\) is the raw amplitude without energy loss; \(\frac{1}{r}\) is the spreading factor; \(\alpha\) is the absorption coefficient of the medium; \(t\) is the travel time of the EW. So the real amplitude \(A_{0}\) is calculated as follows:  
\[A_{0}=Are^{at} \tag{2}\]  
In Equation (2), the real path of the reflected EW \(r=vt\), \(v\) is the speed of the EW, and the gain function is the coefficient of \(A\), then the gain function can be defined as Equation (3).  
\[W_{e}=vte^{at} \tag{3}\]  
After the gain function is determined, we select seven gain coefficients of 0.2, 0.4, 0.6, 0.8, 1.2, 1.4, and 1.6 for gain adjustment, the coefficient of 1.0 is the original GPR data. Figure 2 shows an example of the GPR image generated with different gain coefficients. Figure 2a is the original GPR image, and Figure 2b-h is the gain coefficients of 0.2, 0.4, 0.6, 0.8, 1.2, 1.4, and 1.6, respectively. It can be seen that the target features become more obvious when the gain coefficient increases.