Adaptive Least Mean Squares Estimation of Graph Signals
This work addresses the challenge of efficiently estimating signals on graphs for applications like cognitive networks, representing an incremental improvement by adapting existing LMS methods to graph-based contexts.
The paper tackles the problem of adaptive estimation of graph signals by proposing a least mean squares (LMS) strategy that enables reconstruction and tracking from limited observations with guaranteed mean-square error performance, validated through numerical results and applied to power spatial density cartography in cognitive networks.
The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.