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To obtain the best resolution for any measurement there is an ever-presentchallenge to achieve maximal differentiation between signal and noise over asfine of sampling dimensions as possible. In diffraction science these issuesare particularly pervasive when analyzing small crystals, systems with diffusescattering, or other systems in which the signal of interest is extremely weakand incident flux and instrument time is limited. We here demonstrate that thetool of compressed sensing, which has successfully been applied to photography,facial recognition, and medical imaging, can be effectively applied todiffraction images to dramatically improve the signal-to-noise ratio (SNR) in adata-driven fashion without the need for additional measurements ormodification of existing hardware. We outline a technique that leveragescompressive sensing to bootstrap a single diffraction measurement into aneffectively arbitrary number of virtual measurements, thereby providing a meansof super-resolution imaging.

Denoising total scattering data using Compressed Sensing