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This correspondence points out a technical error in Proposition 4 of the paper [1]. Because of this error, the proofs of Lemma 3, Theorem 1, Theorem 3, Proposition 2, and Theorem 4 in that paper are no longer valid. We provide counterexamples to Proposition 4 and discuss where the flaw in its proof lies. We also provide numerical evidence indicating that Lemma 3, Theorem 1, and Proposition 2 are likely to be false. Since the proof of Theorem 4 depends on the validity of Proposition 4, we propose an amendment to the statement of Theorem 4 of the paper using convergence in operator norm and prove this rigorously. In addition, we also provide a construction that guarantees convergence in the sense of Proposition 4.

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We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional scalar-valued graph signal, multichannel graph signal, and discrete-and continuous-time graph signals, allowing us to build a unified theory of graph random processes. We introduce the notion of joint wide-sense stationarity in this generalized GSP framework, which allows us to characterize a graph random process as a combination of uncorrelated oscillation modes across both the vertex and Hilbert space domains. We elucidate the relationship between the notions of wide-sense stationarity in different domains, and derive the Wiener filters for denoising and signal completion under this framework. Numerical experiments on both real and synthetic datasets demonstrate the utility of our generalized approach in achieving better estimation performance compared to traditional GSP or the time-vertex framework.

We consider a probabilistic model for graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. We introduce the notion of joint wide-sense stationarity in this generalized GSP (GGSP) framework, which allows us to characterize a random graph process as a combination of uncorrelated oscillation modes across both the vertex and Hilbert space domains. We also propose a method for joint power spectral density estimation in case of missing features. Experiment results corroborate the effectiveness of our estimation approach.