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This paper considers the problem of interpolating signals defined on graphs.A major presumption considered by many previous approaches to this problem hasbeen lowpass/ band-limitedness of the underlying graph signal. However,inspired by the findings on sparse signal reconstruction, we consider the graphsignal to be rather sparse/compressible in the Graph Fourier Transform (GFT)domain and propose the Iterative Method with Adaptive Thresholding for GraphInterpolation (IMATGI) algorithm for sparsity promoting interpolation of theunderlying graph signal.We analytically prove convergence of the proposedalgorithm. We also demonstrate efficient performance of the proposed IMATGIalgorithm in reconstructing randomly generated sparse graph signals. Finally,we consider the widely desirable application of recommendation systems and showby simulations that IMATGI outperforms state-of-the-art algorithms on thebenchmark datasets in this application.

Interpolation of Sparse Graph Signals by Sequential Adaptive Thresholds