Blind deconvolution via sparsity maximization applied to GPR data

ABSTRACT In measuring thin layer thickness of asphalt pavements using GPR, the sparse reflectivity series representing the layered structure of the pavement is convolved with the radar wavelet. This convolution results in masking closely spaced reflections. An ideal deconvolution retrieves the reflectivity series, and thus improves the time resolution and facilitates quantitative data interpretation. In this paper, we cast the convolutional model as a multidimensional data model which renders blind deconvolution via independent component analysis possible. We use a nonlinearity related to the double exponential density whose heavy-tailed nature provides further insight into the sparse nature of the reflectivity series. The method is tested on synthetic and real GPR data from a thin PVC slab. The results show the accuracy of the time delay estimates and verify the high resolution capability of the proposed approach.