Deconvolution on graphs via linear programming

Abstract

The main challenge addressed in this paper is to identify individual terms in a superposition of heat kernels on a graph. We establish geometric conditions on the vertices at which these heat kernels are centered and find bounds on the time parameter governing the evolution under the heat semigroup that guarantee a successful recovery. This result can be viewed as a type of deconvolution on a graph. A first main result addresses the setting of a common time parameter for all the heat kernels. We also treat a more general setting when the time parameter depends on the location at which the heat kernel is centered.