Compressed Sensing of Compton Profiles for Fermi Surface Reconstruction: Concept and Implementation

Compton scattering is a well-established technique that can provide detailed information about electronic states in solids. Making use of the principle of tomography, it is possible to determine the Fermi surface from sets of Compton-scattering data with different scattering axes. Practical applications, however, are limited due to long acquisition time required for measuring along enough number of scattering directions. Here, we propose to overcome this difficulty using compressed sensing. Taking advantage of a hidden sparsity in the momentum distribution, we are able to reconstruct the three-dimensional momentum distribution of bcc-Li, and identify the Fermi surface with as little as 14 directions of scattering data with unprecedented accuracy. This compressed-sensing approach will permit further wider applications of the Compton scattering experiments.