Regularization by dynamic programming

Abstract. We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization properties and also obtain rates of convergence for our methods. A numerical example concerning a dynamical electrical impedance tomogra-phy (EIT) problem is used to illustrate the theoretical results. Key words. Regularization, dynamic programming, inverse problems, Hamilton–Jacobi equation, electrical impedance tomography, dynamic inverse problems. AMS classification. 35R30, 47A52, 49N05, 49L20. 1