The map R^{2T} to W^T via C^T factorization is continuous in operator topologies, so R_j^{2T} converging implies the potential q_j converging to q in H^{-2}(Ω^T).
A Lipschitz stable reconstruction formula for the inverse problem for the wave equation.arXiv:1210.1094v1 [math.AP] 3 Oct 2012
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On a stability of time-optimal version of the Boundary Control method
The map R^{2T} to W^T via C^T factorization is continuous in operator topologies, so R_j^{2T} converging implies the potential q_j converging to q in H^{-2}(Ω^T).