Ricerc@Sapienza

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean-square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided.

The goal of this work is to devise least mean square (LMS) strategies for online recovery of time-varying signals defined over dynamic graphs, which are observed over a (randomly) time-varying subset of vertices. We also derive a mean-square analysis illustrating the effect of graph variations and sampling on the reconstruction performance.

We study centralized interpolation of bandlimited graph signals at a fusion center (FC), when sampled data are transmitted over rate-constrained links. In such a scenario, the performance of the reconstruction task is inevitably affected by several sources of errors such as observation noise and quantization due to source encoding. In this paper, we propose two strategies for optimally selecting transmission powers, quantization bits, and the sampling set, with the aim of interpolating a graph signal with guaranteed performance.

The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples collected over a selected set of vertices. Then, we describe some sampling design criteria proposed in the literature to mitigate the effect of noise and model mismatching when performing graph signal recovery.

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly) time-varying subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely the least mean squares (LMS) and the recursive least squares (RLS) adaptive estimation strategies. For both methods, a detailed mean-square analysis illustrates the effect of random sampling on the adaptive reconstruction capability and the steady-state performance.

A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model.