Abstract
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.
Highlights
Compressed Sensing (CS) techniques are used to measure and reconstruct surface dynamical processes with a helium spin-echo spectrometer for the first time
Helium Spin-Echo (HeSE) spectrsocopy is a novel technique[4,5] which combines the surface sensitivity and the inert, completely non-destructive nature of He atom scattering with the unprecedented energy resolution of the spin-echo method[6]
HeSE is the ideal tool for studying surface dynamical processes within a time window from sub-pico second up to nanosecond time scales
Summary
It is precisely because of this decomposition into slanted regions that the two-dimensional problem is often reduced to a one-dimensional one using the Fourier slice theorem: Instead of the two-dimensional (λi, λf). Since we know beforehand that an elastic peak lies along the line λi =λf we expect that an integration angle of α =π/4 will produce the best results for resolving this feature as a single spike With this projection, we can treat the problem (12) as a one-dimensional version of (10) with a new wavelength intensity function ρα(λ). For further explanation and numerical examples demonstrating the benefits of the continuous approach and the differences with the discrete approach, see[20,21,22]
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