Four-Dimensional Tomographic Reconstruction by Time Domain Decomposition

Abstract

For classical tomography, it is essential that the sample does not change during the acquisition of one tomographic rotation. We derived and successfully implemented a tomographic reconstruction method, which relaxes this requirement of quasi-static samples. In the present paper, dynamic tomographic data sets are decomposed in the temporal domain by projecting to a lower dimensional subspace of basis functions and deploying an additional L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We adopted the primal-dual algorithm of Chambolle and Pock for solving the projected regularization problem and tested it on synthetic data containing different motion types. The proposed implementation on modern GPU systems demonstrates the applicability of the method for processing real data sets.