Physical Wavelet Frame Algorithm And Its Application To GPR Signal Processing

Ground penetrating radar (GPR) system has been an effective measure to exploring shallow sub-surface. And has been playing an important role in railway, bridge, tunnel, geological prospecting, urban construction, pipes and cable detection, archaeological studies etc. The Direct wave is the main interfere of radar signal, attenuation or removing the direct wave is always the hotspot of research in this domain.Wavelet transform is an analysis method for non-stationary signal ,which overcomes the disadvantages of traditional Fourier analysis.It has both the time domain and the the frequency domainand ang has been widely used in practical applications. The result of wavelet transform depend on not only the signal but also the wavelet function that you choose. The more maching between the mother wavelet and the analysed signal, the more the consentrated is its energy distribution in time–scale domain. This is the theory basis of wavelet denoising used in this paper.Firstly, the 1-D Marr wavelet transform is proposed and performed by the MATLAB basis on the wavelet frame theory. As a example, the chirp signal is analyzed and reconstrued by the wavelet transform. Secondly, the 2-D physical wavelet function which best matches the point target scattering GPR singal is chosed as the mother wavelet , and then, the noised GPR synthetic data is analysed and used the thresholding algorithm. It is demonstrated that the 2-D physical wavelet is a suitable tool for denoising the noised GPR data, even though the poor SNR ratio data.By forcing some constraints upon the parameters of the 2-D physical wavelets, the new type analyzing wavelets is obtained, which best match the GPR direct wave. With the proposed new wavelets, the wavelet transform is applied to the GPR data, the direct wave is reconstructed and then reduced form the GPR data. Efficiency of the method is demonstrated by the real GPR data. Compared with the technique by the 2-D directional continue wavelet transform, the technique by the 2-D physical wavelets frame algorithm is very effective.