Matching Pursuits (MP), a technique for signal decomposition using a dictionary of functions, is applied to ground penetrating radar (GPR) signals in order to remove noise and clutter included in the signals and to extract target responses. A wave-based dictionary composed of wavefronts and resonances is employed. Noise reduction performance and the removal of ground-surface reflection are evaluated through numerical simulations. The results show that the MP approach performs well and offers an effective method for feature extraction from GPR signals.