Graph Filtering with Quantization over Random Time-varying Graphs

Distributed graph filters can be implemented over wireless sensor networks by means of cooperation and exchanges among nodes. However, in practice, the performance of such graph filters is deeply affected by the quantization errors that are accumulated when the messages are transmitted. The latter is paramount to overcome the limitations in terms of bandwidth and computation capabilities in sensor nodes. In addition to quantization errors, distributed graph filters are also affected by random packet losses due to interferences and background noise, leading to the degradation of the performance in terms of the filtering accuracy. In this work, we consider the problem of designing graph filters that are robust to quantized data and time-varying topologies. We propose an optimized method that minimizes the quantization error, while ensuring an accurate filtering over time-varying graph topologies. The efficiency of the proposed theoretical findings is validated by numerical results in random wireless sensor networks.