This paper presents an iterative algorithm for reconstruction of dynamic non-monotonic process in a three-dimensional object (4D tomography) using only one projection per each time step. In this case, a priori knowledge about the unchanging (initial) structure of the object is used, and the processing of intermediate data at each iteration is performed in the projection data space. The proposed algorithm is compared with the previously proposed algorithm for monotonic processes and its extensions for non-monotonic processes, where the processing of intermediate data in the space of reconstructed objects is used. Virtual experiments have been conducted to reconstruct the dynamics of voxels values changes in time. The advantage of the new approach in both speed and quality of reconstruction is shown. The influence of the internal structure of dynamic regions on the reconstruction quality is investigated. The new 4D tomography algorithm presented in this paper shows the possibility of reconstructing a dynamic process in a three-dimensional volume using only one projection per time step, which can be useful in different fields of science such as materials science, geology, medicine, etc. The proposed algorithm is demonstrated on an unambiguous mathematical phantom, serving as a proof of concept. Its application to more complex or real experimental data will require further study and adaptation.
Grigoriev et al. (Wed,) studied this question.