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This work proposes distributed recursive least squares (RLS) strategies for adaptive reconstruction and learning of signals defined over graphs. First, we introduce a centralized RLS estimation strategy with probabilistic sampling, and we propose a sparse sensing method that selects the sampling probability at each node in the graph in order to guarantee adaptive signal reconstruction and a target...
We present the theory of sequences of random graphs and their convergence to limit objects. Sequences of random dense graphs are shown to converge to their limit objects in both their structural properties and their spectra. The limit objects are bounded symmetric functions on [0,1]2. The kernel functions define an equivalence class and thus identify collections of large random graphs who are spectrally...
In this paper, the focus is on optimal sensor placement and power rating selection for parameter estimation in wireless sensor networks (WSNs). We take into account the amount of energy harvested by the sensing nodes, communication link quality, and the observation accuracy at the sensor level. In particular, the aim is to reconstruct the estimation parameter with minimum error at a fusion center...
Despite their widespread use for the analysis of graph data, current graph filters are designed for graph signals that do not change over time, and thus they cannot simultaneously process time and graph frequency content in an adequate manner. This work presents ARMA2D, an autoregressive moving average graph-temporal filter that captures jointly the signal variations over the graph and time. By its...
A new scheme to sample signals defined on the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the so-called graph-shift operator. Instead of using the value of the signal observed at a subset of nodes to recover the signal in the entire graph, the sampling scheme...
New schemes to recover signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. The schemes are designed within the framework of linear shift-invariant graph filters and consider that the seeding signals are injected only at a subset...
Existing methods for smart data reduction are typically sensitive to outlier data that do not follow postulated data models. We propose robust censoring as a joint approach unifying the concepts of robust learning and data censoring. We focus on linear inverse problems and formulate robust censoring through a sparse sensing operator, which is a non-convex bilinear problem. We propose two solvers,...
Covariance estimation from compressive samples has become particularly attractive for two main reasons. First, many applications do not require the signal itself, and second-order statistics are oftentimes sufficient. The resulting requirement on the sampling rate of the original signal can therefore be reduced. Second, signal recovery from compressive samples leads to underdetermined systems which...
Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. Weighted and structured generalizations of the TLS approach are further motivated in several signal processing and system identification related problems. On the other hand, modern...
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