This paper focuses on new signal processing algorithms customized for an air coupled Ultra-Wideband (UWB) Ground Penetrating Radar (GPR) system targeting highway pavements and bridge deck inspections. The GPR hardware consists of a high-voltage pulse generator, a high speed 8 GSps real time data acquisition unit, and a customized field-programmable gate array (FPGA) control element. In comparison to most existing GPR system with low survey speeds, this system can survey at normal highway speed (60 mph) with a high horizontal resolution of up to 10 scans per centimeter. Due to the complexity and uncertainty of subsurface media, the GPR signal processing is important but challenging. In this GPR system, an adaptive GPR signal processing algorithm using Curvelet Transform, 2D high pass filtering and exponential scaling is proposed to alleviate noise and clutter while the subsurface features are preserved and enhanced. First, Curvelet Transform is used to remove the environmental and systematic noises while maintain the range resolution of the B-Scan image. Then, mathematical models for cylinder-shaped object and clutter are built. A two-dimension (2D) filter based on these models removes clutter and enhances the hyperbola feature in a B-Scan image. Finally, an exponential scaling method is applied to compensate the signal attenuation in subsurface materials and to improve the desired signal feature. For performance test and validation, rebar detection experiments and subsurface feature inspection in laboratory and field configurations are performed.