Multiresolution analysis based on Mallat pyramidal algorithm applied to GPR data

The implementation of the Pyramidal Mallat algorithm to GPR data, according to the analysis of its transient nature, is proposed. This is a decomposition method of the discrete wavelet transform which introduces a variable and scalable wavelet length, with compact support and limited band in the frequency domain. GPR data were analyzed in a time-frequency plane and are synthesized at different levels of resolution through octaves of frequency allowing noise removal[7]. This technique allows the improvement of radargrams in urban areas since the characteristic noise mask the main reflectors. In those cases the application of the Discrete Fourier Transform, designed for data analysis in which the frequency does not vary with time, is limited. Discrete Wavelet Transform is an alternative tool for analysis of transient data because it determines that time corresponds to each frequency component and also allows to reconstruct the data in a sequence of successive approximation spaces, such as orthogonal subspaces. The binding of them define L²(R) and each orthogonal projection represents a level of data resolution. In this paper the results obtained for different types of wavelets from the Daubechies family are presented.