In applications such as social, energy, transportation, sensor, and neuronal networks, big data naturally reside on the vertices of graphs. Each vertex stores a sample, and the collection of these samples is referred to as a graph signal. The product of the network graph with the time series graph is considered as underlying structure for the evolution through time of graph signal “snapshots”. The framework of signal processing on graphs [4] extends concepts and methodologies from classical discrete signal processing. The task of sampling and recovery is one of the most critical topics in the signal processing community. In this talk, we present some localized iterative methods, obtained by modifying the Marvasti algorithm [2] in classical signal processing, for interpolating graph signals from only a partial set of samples, both in vertex and time domain. Our methods are also compared with other recent algorithms [3, 5] in order to study rate of convergence and computational efficiency [1]. The experimental results demonstrate the effectiveness of the proposed reconstruction methods in real world datasets and noisy scenarios.