Mathematical analysis of interpolation step of Omega - K Algorithm for GPR and its implementation

Ground-penetrating radar (GPR) is a mature remote sensing technique employed by engineers and scientists to obtain information from subsurface structures. These structures range from manmade objects, such as buried utilities, pavements, and unexploded ordnance, to geological formations. GPR data collection may be viewed as a mapping from the object space (x,y,z), characterized by the object's spatial location and reflectivity, to the image space. The image space may be viewed in the space-time domain (x,y,t), where the recorded scattered signals are displayed as a function of lateral position and time, or in the Omega-K domain (k
_x
,k
_y
,f), where the two image sets are related by spatial-temporal Fourier transforms (FTs). Additionally, data may be recorded in the space-frequency domain (x,y,f ), as would be the case with a frequency-domain GPR. Fourier transforms allow easy conversions between the three image domains.