Before revision:  Our proof relies on a recent result on the stability of the associated deterministic inverse problem 10 , on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator.
After revision:  Our proof relies on a recent result on the stability of the associated deterministic inverse problem  , on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator.