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Economic and financial decision-making may cause a significant impact on government, society, and industries. Due to the increasing volume of data, decision science has become an interdisciplinary field of study, supported by efficient methods and models of data analysis. Our contributions lie exactly in the intersection of signal processing, tensorial algebra, and decision science. More precisely, we introduce a novel approach in which the data taken into account in the decision process is modeled as a tensor.

In Nuclear Magnetic Resonance (NMR) spectroscopy, an efficient analysis and a relevant extraction of different molecule properties from a given chemical mixture are important tasks, especially when processing bidimensional NMR data. To that end, using a blind source separation approach based on a variational formulation seems to be a good strategy. However, the poor resolution of NMR spectra and their large dimension require a new and modern blind source separation method.

Signed graphs have recently been found to offer advantages over unsigned graphs in a variety of tasks. However, the problem of learning graph topologies has only been considered for the unsigned case. In this paper, we propose a conceptually simple and flexible approach to signed graph learning via signed smoothness metrics. Learning the graph amounts to solving a convex optimization problem, which we show can be reduced to an efficiently solvable quadratic problem. Applications to signal reconstruction and clustering corroborate the effectiveness of the proposed method.

Graph signal processing on directed graphs poses theoretical challenges since an eigendecomposition of filters is in general not available. Instead, Fourier analysis requires a Jordan decomposition and the frequency response is given by the Jordan normal form, whose computation is numerically unstable for large sizes. In this paper, we propose to replace a given adjacency shift A by a diagonalizable shift A D obtained via the Jordan-Chevalley decomposition.

A probability-theoretic problem under information
constraints for the concept of optimal control over a noisymemoryless channel is considered. For our Observer-Controller
block, i.e., the lossy joint-source-channel-coding (JSCC) scheme,
after providing the relative mathematical expressions, we propose a Blahut-Arimoto-type algorithm − which is, to the best
of our knowledge, for the first time. The algorithm efficiently finds the probability-mass-functions (PMFs) required for .....................

We present a novel sampling theorem, and prototypical applications, for Fourier-sparse lattice signals, i.e., data indexed by a finite semi-lattice. A semilattice is a partially ordered set endowed with a meet (or join) operation that returns the greatest lower bound (smallest upper bound) of two elements. Semilattices can be viewed as a special class of directed graphs with a strictly triangular adjacency matrix , which thus cannot be diagonalized.