Reconstruction of GPR Signals by Spectral Analysis of the SVD Components of the Data Matrix

This letter considers the problem of reconstructing total-time responses from noisy data collected by ground-penetrating radar (GPR). The well-known singularity expansion method (SEM) - a theory - for late-time response representation is generalized to establish a matrix model (data matrix) representing total-time responses of radar scattering waveforms. Using singular value decomposition of the data matrix - an intermediate processing technique, we present an approach to model-order determination and successfully reconstruct the total-time responses. The model order is quantitatively selected by spectral analysis of left singular vectors of the data matrix and of the emitted waveform. The most important discoveries in this letter are as follows: (1) the GPR upper frequency can be used as a criterion for the selection of left singular vectors of the data matrix, and (2) the left singular vectors of the data matrix, which should not be neglected, tend to be predominantly low-pass functions and also provide valuable information for model-order determination.