Continuous-time image reconstruction using differential equations for computed tomography

An approach for reconstructing tomographic images based on the idea of continuous dynamical methods is presented. The method consists of a continuous-time image reconstruction (CIR) system described by differential equations for solving linear inverse problems. We theoretically demonstrate that the trajectories converge to a least squares solution to the linear inverse problem. An implementation of its equivalent electronic circuit is significantly faster than conventional discrete-time image reconstruction (DIR) systems executed in a digital computer. Moreover, the merits of our CIR are demonstrated on a tomographic inverse problem where simulated noisy projection data are generated from a known phantom. Here, we numerically demonstrate that the CIR system does not produce unphysical negative pixel values if one starts out with positive initial values. Besides, CIR also recovers the phantom with almost the same quality as DIR images.