The success of the guided-wave damage inspection technology depends not only on the generation and measurement of desired waveforms but also on the signal processing of the measured waves, but less attention has been paid to the latter. This research aims to develop an efficient signal processing technique especially suitable for the current guided-wave technology. To achieve this objective, the use of a two-stage matching pursuit approach based on the Gabor dictionary is proposed. Instead of truncated sine pulses commonly used in waveguide inspection, Gabor pulses, the modulated Gaussian pulses, are chosen as the elastic energy carrier to facilitate the matching pursuit algorithm. To extract meaningful waves out of noisy signals, a two-stage matching pursuit strategy is developed, which consists of the following: rough approximations with a set of predetermined parameters characterizing the Gabor pulse, and fine adjustments of the parameters by optimization. The parameters estimated from measured longitudinal elastic waves can be then directly used to assess not only the location but also the size of a crack in a rod. For the estimation of the crack size, in particular, Love's theory is incorporated in the matching pursuit analysis. Several experiments were conducted to verify the validity of the proposed approach in damage assessment.