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Signal Representation with Optimal Subspace Graph Filtering

Signal representation is a prime problem in signal processing. In this paper, we propose a subspace graph filtering method for signal representation. We demonstrate an extended singular value decomposition (SVD) model of signal essentially is a subspace graph filtering, and build a bridge from SVD to graph filtering. A smoothing subspace graph filtering is sequentially learned in the space provided by SVD. In the experiments, we compare the signal restoration performance between the extended SVD and the proposed subspace graph filtering. It shows that clean signal can be better reconstructed from the noisy signal in our smoothing subspace than the SVD space, where the learned smoothed bases of graph filtering are more robust than the bases of SVD to cope with noise.