Parameter Selection in Coupled Dynamical Systems for Tomographic Image Reconstruction

This study investigates the performance of image-reconstruction methods derived from coupled dynamical systems for solving linear inverse problems, focusing on how appropriate parameter selection enhances noise-suppression capability in tomographic image reconstruction. Our previous work has established the stability of linear and nonlinear variants of such systems on the basis of Lyapunov's theorem. However, the influence of parameter choice on reconstruction quality has not been fully clarified. To address this issue, we introduce a parameter adjustment strategy based on an optimization principle. Two complementary optimization strategies are considered. The first employs ground-truth images to determine optimal parameter values that serve as a numerical benchmark for evaluating reconstruction performance. The second relies solely on measured projection data, enabling practical application without prior knowledge of the true image. Numerical experiments using phantoms with relatively high noise levels demonstrate that appropriate parameter selection markedly improves reconstruction accuracy and robustness. These results clarify how properly tuned reconstruction methods derived from coupled dynamical systems can effectively exploit their inherent dynamics to achieve noise suppression in tomographic inverse problems.