Noise reduction and identification of subsurface radar images using recursive wavelet decomposition

Shape estimation and noise reduction are among most important issues in the signal processing of subsurface radars. The authors developed a noise reduction scheme based on a two-dimensional parabolic wavelet transform, which is designed to detect hyperbolic features associated to subsurface radar images. The major limitation of the proposed algorithm was that the parabolic wavelets do not give an orthogonal basis, which limits the reconstruction capability of the algorithm. The authors propose a scheme based on similar 2D wavelet bases, but employing the recursive non-orthogonal decomposition algorithm known as the matching pursuit. The idea is to repeat the procedure of fitting waveforms given in a redundant dictionary to the given waveform, and subtracting the best matched one recursively. The advantage is that the desired signal can be retrieved from a very noisy data if the waveform is included in the dictionary. The inherent problem of this procedure is a heavy computational load because a large number of iteration is needed. The authors develop schemes to substantially reduce the computation by customizing the algorithm to the signal processing of subsurface radars, and by taking into account the characteristics of the desired signals. The capability of the proposed algorithm in detecting various targets buried in the noise is evaluated based on simulated data for an attenuating and dispersive medium