Continuous-time image reconstruction for binary tomography

Binary tomography is the process of reconstructing a binary image from a finite number of projections. We present a novel method for solving binary tomographic inverse problems using a continuous-time image reconstruction (CIR) system described by nonlinear differential equations based on the minimization of a double Kullback–Leibler divergence. We prove theoretically that the divergence measure monotonically decreases in time. Moreover, we demonstrate numerically that the quality of the reconstructed images of the nonlinear CIR system is better than those from an iterative reconstruction method.

► A continuous method for solving inverse problems in binary tomography is proposed.
► The convergence is proved based on minimization of a Kullback–Leibler divergence.
► The divergence measure monotonically decreases even in the ill-posed case.
► The quality of reconstructed images is better than those from an iterative method.