Design of Graph Signal Sampling Matrices for Arbitrary Signal Subspaces

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.