Observability of Laplace's equation on the cylindrical domain

Abstract

The problem of observability of a dynamical system that is governed by a partial differential equation is considered. The aim of this paper is to formulate the problem under the assumption of an idealized geometry; coaxial cylinder representing the human torso and cardiac surface. An analytical solution in the form of generalized Fourier series is obtained under this assumption. Finally, the reconstruction of the solution of Laplace's equation from discrete measurements on the boundary is discussed and a numerical algorithm is developed to treat this ill-posed problem.

This problem arises in the determination of the electropotential of the epicardial surface from discrete measurements on the torso.