Denoising total scattering data using Compressed Sensing

To obtain the best resolution for any measurement there is an ever-present challenge to achieve maximal differentiation between signal and noise over as fine of sampling dimensions as possible. In diffraction science these issues are particularly pervasive when analyzing small crystals, systems with diffuse scattering, or other systems in which the signal of interest is extremely weak and incident flux and instrument time is limited. We here demonstrate that the tool of compressed sensing, which has successfully been applied to photography, facial recognition, and medical imaging, can be effectively applied to diffraction images to dramatically improve the signal-to-noise ratio (SNR) in a data-driven fashion without the need for additional measurements or modification of existing hardware. We outline a technique that leverages compressive sensing to bootstrap a single diffraction measurement into an effectively arbitrary number of virtual measurements, thereby providing a means of super-resolution imaging.