It is essential to extract high-fidelity surface waves in surface-wave surveys. Because reflections usually interfere with surface waves on X components in multicomponent seismic exploration, it is difficult to extract dispersion curves of surface waves. To make matters worse, the frequencies and velocities of higher-mode surface waves are close to those of PS-waves. A method for surface-wave extraction is proposed based on the morphological differences between surface waves and reflections. Frequency-domain high-resolution linear Radon transform (LRT) and time-domain high-resolution hyperbolic Radon transform (HRT) are used to represent surface waves and reflections, respectively. Then, a sparse representation problem based on morphological component analysis (MCA) is built and optimally solved to obtain high-fidelity surface waves. An advantage of our method is its ability to extract surface waves when their frequencies and velocities are close to those of reflections. Furthermore, the results of synthetic and field examples confirm that the proposed method can attenuate the distortion of surface-wave dispersive energy caused by reflections, which contributes to extraction of accurate dispersion curves.