X-ray data reconstruction from incomplete data sampling

For specific setups, a diffraction pattern can contain gaps or missing information. For example, that is the case when several detectors are used simultaneously, but a particular angular range is not covered between each detector. In this article, a procedure for the reconstruction of the missing signal is proposed. It is based on a modified Papoulis-Gerchberg algorithm that considers features of the diffraction pattern without loss of generality. The mathematical basis of the algorithm is presented, and several cases, simulated and experimental, are used to test the performance and robustness of the proposed solution.