Compressed Sensing (CS) techniques are used to measure and reconstruct surface dynamical processes with a helium spin-echo spectrometer for the first time. Helium atom scattering is a well established method for examining the surface structure and dynamics of materials at atomic sized resolution and the spin-echo technique opens up the possibility of compressing the data acquisition process. CS methods demonstrating the compressibility of spin-echo spectra are presented for several measurements. Recent developments on structured multilevel sampling that are empirically and theoretically shown to substantially improve upon the state of the art CS techniques are implemented. In addition, wavelet based CS approximations, founded on a new continuous CS approach, are used to construct continuous spectra. In order to measure both surface diffusion and surface phonons, which appear usually on different energy scales, standard CS techniques are not sufficient. However, the new continuous CS wavelet approach allows simultaneous analysis of surface phonons and molecular diffusion while reducing acquisition times substantially. The developed methodology is not exclusive to Helium atom scattering and can also be applied to other scattering frameworks such as neutron spin-echo and Raman spectroscopy.