Docente
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DI LORENZO PAOLO
(programma)
Part I: Signal Processing
Definition of signals, signal properties, discrete representations, Fourier transforms, filtering, images, discrete cosine transform, applications to audio signals and images
Part II: Processing over graphs
Algebraic graph theory, graph properties, connectivity
Graph features: degree centrality, eigenvector centrality, PageRank, betweeness, modularity
Graph models: random graphs, random geometric graphs, small worlds graphs, scale-free graphs
Independence graphs: Markov networks, Bayes networks, Gaussian Markov Random Fields
Operations on graphs: partitioning
Signals defined on graphs
Filtering and sampling signals over graphs
Prediction of processes over graphs
Part III: Distributed optimization over networks
Review of convex optimization
Compressive Sensing
Algorithms for sparsity constrained problems
Primal and dual decomposition
Alternating direction method of multipliers
Consensus problems
Sharing problems
Part IV: Examples of application
Graph-based methods for machine learning
Distributed detection and estimation in wireless sensor networks
Radio resource allocation in communication networks
Sampling of energy distribution systems
![](/images/icon-multipage.png) 1) Vetterli, Martin, Jelena Kovačević, and Vivek K. Goyal. Foundations of signal processing. Cambridge University Press, 2014.
2) Newman, Mark. Networks: an introduction. Oxford university press, 2010.
3) S. Barbarossa, “Signal Processing over Graphs”
4) S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004;
5) S. Foucart and R. Holger, A mathematical introduction to compressive sensing, Basel: Birkhäuser, 2013.
6) Boyd, Stephen, et al. "Distributed optimization and statistical learning via the alternating direction method of multipliers." Foundations and Trends® in Machine learning 3.1 (2011): 1-122.
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