Fondamenti di teoria dei segnali, concetti di base di elaborazione dei segnali e delle immagini, campionamento Teoria algebrica dei grafi, principali proprietà, indici di centralità di un grafo, modelli di grafi aleatori: Erods-Renyi, grafi geometrici aleatori, small-world e grafi scale-free Modelli di indipendenza condizionale, grafi di Markov e Bayes Partizionamento di un grafo, teoria spettrale dei grafi Segnali definiti su grafo, filtraggio e campionamento su grafo, predizione Ottimizzazione convessa, decomposizione primaria e duale, condizioni KKT, compressive sensing ADMM, ottimizzazione distribuita: algoritmi di consenso, algoritmi di condivisione Applicazioni: Algoritmi di machine learning basati su grafi, reti di sensori, allocazione delle risorse radio nelle reti di comunicazione

M. Vetterli et al., “Foundations of Signal Processing” M.E.J. Newman, “Networks: An Introduction” S. Barbarossa, “Signal Processing over Graphs” S. Boyd et al. “Convex Optimization” S. Boyd et al. “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers”

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

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.