Efficient Denoising of Multidimensional GPR Data Based on Fast Dictionary Learning

Denoising plays a fundamental role in ground penetrating radar (GPR) data processing and determines the effect of anomaly extraction, inversion imaging, and other subsequent processing. In recent years, the sparse dictionary representation method k-singular value decomposition (K-SVD) based on K-means, which can adaptively change the basis function according to the data, has become a hotspot in the field of image denoising and data reconstruction. Nevertheless, the SVD is a time-consuming calculation, especially unacceptable in multidimensional problems; we introduce a dictionary learning method based on the sequential generalized K-means (SGK), where the dictionary atoms are updated by the arithmetic average of several training signals instead of a great deal of SVD calculation in K-SVD. We establish a 3-D road simulation model and conduct finite-difference time-domain forward numerical simulation to acquire 3-D GPR data. Through three sets of experiments on 3-D numerical examples and 3-D field data, the results show that both dictionary learning algorithms can successfully remove random noise from GPR data even at a lower input signal-to-noise ratio. The clutter interference in the random medium forward data can be effectively eliminated simultaneously, and both denoising methods exhibit promising applications in 3-D field data. However, the SGK method solves the serious problem of computational efficiency to a certain extent. The computational acceleration ratio of SGK remains consistently above 7.5x that of the K-SVD algorithm in multigroup experiments, with only a marginal decline in denoising performance.