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Helium atom scattering (HAS) is a well established technique for examiningthe surface structure and dynamics of materials at atomic sized resolution. TheHAS technique Helium spin-echo spectroscopy opens up the possibility ofcompressing the data acquisition process. Compressed sensing (CS) methodsdemonstrating the compressibility of spin-echo spectra are presented. Inaddition, wavelet based CS approximations, founded on a new continuous CSapproach, are used to construct continuous spectra that are compatible withvariable transformations to the energy/momentum transfer domain. Moreover,recent developments on structured multilevel sampling that are empirically andtheoretically shown to substantially improve upon the state of the art CStechniques are implemented. These techniques are demonstrated on severalexamples including phonon spectra from a gold surface.

Continuous Compressed Sensing of Inelastic and Quasielastic Helium Atom Scattering Spectra