GPR imaging method based on the phase shift migration and the least-square matching pursuits

A ground penetrating radar (GPR) imaging method is proposed based on the combination of the phase shift migration method and the least-square based matching pursuit algorithm (LSMP), which produces the amplitude spectrum and the phase spectrum of the migrated data. The non-uniform fast Fourier transform (NUFFT) is incorporated into the phase shift migration method to evaluate the inverse FFT more accurately and more efficiently than the conventional methods, which requires the interpolation of non-uniformly sampled data in wave-number space before the regular FFT can be applied. The LSMP, in which the least-squares concept is introduced to the matching pursuit algorithm to avoiding the greedy search of the optimal atom in the atom dictionary, is applied to implement efficiently the spectral decomposition of the migrated data based on analytic trace and analytic wavelets. The combined method proposed in this paper is tested on numerical simulated data and field data. The results show that, compared to the phase shift migration, the combined method has an advantage of suppressing random noise and improving the GPR imaging quality greatly, and the detection and localization of GPR objects can be enhanced from low signal to noise ratio data by combing the amplitude spectrum and the phase spectrum.