We present a new application of modern filtering techniques to ground-penetrating radar (GPR) data processing for coherent noise attenuation. We compare the performance of the discrete wavelet transform (DWT) and the linear Radon transform (τ-p) to classical time-space and Fourier domain methods using a synthetic model and real data. The synthetic example simulates problems such as system ringing and surface scattering, which are common in real cases. The field examples illustrate the removal of nearly horizontal but variable-amplitude noise features. In such situations, classical space-domain techniques require several trials before finding an appropriate averaging window size. Our comparative analysis indicates that the DWT method is better suited for local filtering than are 2D frequency-domain (f-k) techniques, although the latter are computationally efficient. Radon-based methods are slightly superior than the techniques previously used for local directional filtering, but they are slow and quite sensitive to the p-sampling rate, p-range, and sizes of the muting zone. Our results confirm that Radon and wavelet methods are effective in removing noise from GPR images with minimal distortions of the signal.