Bandlimited graph signals on an unweighted graph can be reconstructed by its local measurement, which is a generalization of decimation. Since most signals are weighted in real life, we extend and improve the iterative local measurement reconstruction (ILMR) by introducing the diffusion operators to reconstruct bandlimited signals on a weighted graph. We prove that the proposed reconstruction converges to the original signal. Moreover, the simulation results demonstrate that the improved algorithm has better convergence and has robustness against noise.
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