The Curvelet Transform in the analysis of 2-D GPR data: Signal enhancement and extraction of orientation-and-scale-dependent information

The utility of the CT in processing noisy GPR data is investigated with software based on the Fast Discrete CT and adapted for use with a set of interactive driver functions that compute and display the curvelet decomposition and then allow the manipulation of data (wavefront) components at different scales and angles via the corresponding manipulation (cancellation or restoration) of their associated curvelets. The method is demonstrated with data from archaeometric, geotechnical and hydrogeological surveys, contaminated by high levels of noise, or featuring straight and curved reflections in complex propagation media, or both. It is shown that the CT is very effective in enhancing the S/N ratio by isolating and cancelling directional noise wavefronts of any scale and angle of emergence, sometimes with surgical precision and with particular reference to clutter. It can as successfully be used to retrieve waveforms of specific scale and geometry for further scrutiny, also with surgical precision, as for instance distinguish signals from small and large aperture fractures and faults, different phases of fracturing and faulting, bedding etc. Moreover, it can be useful in investigating the characteristics of signal propagation (hence material properties), albeit indirectly. This is possible because signal attenuation and temporal localization are closely associated, so that scale and spatio-temporal localization are also closely related. Thus, interfaces embedded in low attenuation domains will tend to produce sharp reflections and fine-scale localization. Conversely, interfaces in high attenuation domains will tend to produce dull reflections with broad localization.