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We propose a design method of sampling matrices for graph signals that guarantees perfect recovery for arbitrary graph signal subspaces. When the signal subspace is known, perfect reconstruction is always possible from the samples with an appropriately designed sampling matrix. However, most graph signal sampling methods so far design sampling matrices based on the bandlimited assumption and sometimes violates the perfect reconstruction condition for the other signal models. In this paper, we formulate an optimization problem for the design of the sampling matrix that guarantees perfect recovery, thanks to a generalized sampling framework for standard signals. In experiments with various signal models, our sampling matrix presents better reconstruction accuracy both for noiseless and noisy situations.

In this paper, we consider multi-channel sampling (MCS) for graph signals. We generally encounter full-band graph signals beyond the bandlimited ones in many applications, such as piecewise constant/smooth graph signals and union of bandlimited graph signals. Full-band graph signals can be represented by a mixture of multiple signals conforming to different generation models. This requires the analysis of graph signals via multiple sampling systems, i.e., MCS, while existing approaches only consider single-channel sampling. We develop a MCS framework based on generalized sampling. We also present a sampling set selection (SSS) method for the proposed MCS so that the graph signal is best recovered. Furthermore, we reveal that existing graph filter banks can be viewed as a special case of the proposed MCS. In signal recovery experiments, the proposed method exhibits the effectiveness of recovery for full-band graph signals. INDEX TERMS Multi-channel sampling, full-band graph signals, sampling set selection.

We propose a generalized sampling framework for stochastic graph signals. Stochastic graph signals are characterized by graph wide sense stationarity (GWSS) which is an extension of wide sense stationarity (WSS) for standard timedomain signals. In this paper, graph signals are assumed to satisfy the GWSS conditions and we study their sampling as well as recovery procedures. In generalized sampling, a correction filter is inserted between the sampling and reconstruction operators to compensate for non-ideal measurements. We propose a design method for the correction filters to reduce the mean-squared error (MSE) between the original and reconstructed graph signals. We derive the correction filters for two cases: The reconstruction filter is arbitrarily chosen or predefined. The proposed framework allows for arbitrary sampling methods, i.e., sampling in the vertex or graph frequency domain. We show that the graph spectral response of the resulting correction filter parallels that for generalized sampling for WSS signals if sampling is performed in the graph frequency domain. The effectiveness of our approach is validated via experiments by comparing its MSE with existing approaches.