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