Detection and extraction of orientation-and-scale-dependent information from two-dimensional GPR data with tuneable directional wavelet filters

摘要

The Ground Probing Radar (GPR) is a valuable tool for near surface geological, geotechnical, engineering, environmental, archaeological and other work. GPR images of the subsurface frequently contain geometric information (constant or variable-dip reflections) from various structures such as bedding, cracks, fractures, etc. Such features are frequently the target of the survey; however, they are usually not good reflectors and they are highly localized in time and in space. Their scale is therefore a factor significantly affecting their detectability. At the same time, the GPR method is very sensitive to broadband noise from buried small objects, electromagnetic anthropogenic activity and systemic factors, which frequently blurs the reflections from such targets.This paper introduces a method to de-noise GPR data and extract geometric information from scale-and-dip dependent structural features, based on one-dimensional B-Spline Wavelets, two-dimensional directional B-Spline Wavelet (BSW) Filters and two-dimensional Gabor Filters. A directional BSW Filter is built by sidewise arranging s identical one-dimensional wavelets of length L, tapering the s-parallel direction (span) with a suitable window function and rotating the resulting matrix to the desired orientation. The length L of the wavelet defines the temporal and spatial scale to be isolated and the span determines the length over which to smooth (spatial resolution). The Gabor Filter is generated by multiplying an elliptical Gaussian by a complex plane wave; at any orientation the temporal or spatial scale(s) to be isolated are determined by the wavelength λ of the plane wave and the spatial resolution by the spatial aspect ratio γ, which specifies the ellipticity of the support of the Gabor function. At any orientation, both types of filter may be tuned at any frequency or spatial wavenumber by varying the length or the wavelength respectively. The filters can be applied directly to two-dimensional radargrams, in which case they abstract information about given scales at given orientations. Alternatively, they can be rotated to different orientations under adaptive control, so that they remain tuned at a given frequency or wavenumber and the resulting images can be stacked in the LS sense, so as to obtain a complete representation of the input data at a given temporal or spatial scale.In addition to isolating geometrical information for further scrutiny, the proposed filtering methods can be used to enhance the S/N ratio in a manner particularly suitable for GPR data, because the frequency response of the filters mimics the frequency characteristics of the source wavelet. Finally, signal attenuation and temporal localization are closely associated: low attenuation interfaces tend to produce reflections rich in high frequencies and fine-scale localization as a function of time. Conversely, high attenuation interfaces will produce reflections rich in low frequencies and broad localization. Accordingly, the temporal localization characteristics of the filters may be exploited to investigate the characteristics of signal propagation (hence material properties). The method is shown to be very effective in extracting fine to coarse scale information from noisy data and is demonstrated with applications to noisy GPR data from archaeometric and geotechnical surveys.