Continuous-time image reconstruction using differential equations for computed tomography

Multivalued Discrete Tomography Using Dynamical System That Describes Competition

“…Therefore, is definitely included as an equilibrium point of (9). We can rewrite the dynamical system in (9) as…”

“…In (9), without Ψ , the dynamics is based on gradient systems proposed for binary tomography inverse problems in [9,11]. In the former reference, a dynamical system is provided whose vector field resembles that of a logistic equation, and the convergence of solutions is demonstrated theoretically.…”

“…In this paper, we treat multivalued discrete tomography as an extension of the binary tomography problems addressed in [9,11]. Equation (9) shows that the proposed system, including the term (−Ψ ), is inspired by the generalized Lotka-Volterra equation [14] to ensure…”

“…Equation (9) shows that the proposed system, including the term (−Ψ ), is inspired by the generalized Lotka-Volterra equation [14] to ensure…”

“…Conventional methods for discrete tomography include the iterative reconstruction method involving an iterative algorithm and image segmentation [3], an optimization algorithm based on minimizing an energy function to discretize multiple intensity values [4], and various other methods [5][6][7][8]. In this paper, we propose a dynamical method based on the continuous-time optimization approach with nonlinear differential equations [9][10][11][12][13] that are capable of obtaining a desired tomographic image through convergence to a limit set of the differential equations. Our method utilizes the competition dynamics of generalized Lotka-Volterra systems [14] to solve the problem of multivalued discrete tomography.…”