PhD Graduate

PhD program:: XXXIII

advisor: Vittoria Bruni

Thesis title: Differential Entropy Based Methods for Thresholding in Wavelet Bases and Other Applications

In this thesis the problem of automatically selecting expansion coefficients of a function f(t) in a wavelet basis expansion is considered. The problem is approached through an information-theoretic point of view and three different differential entropy based measures are proposed to compare expansion coefficients in order to find the optimal subset. Several theoretical results about differential entropy of a function are developed in order to provide a solid theoretical framework to the proposed measures. A numerical scheme to compute the differential entropy of a function is presented and its stability and convergence properties are proved. Numerical experiments concerning different wavelet bases and frames are presented, and the behaviour of the proposed measures is compared to state of the art methods. Moreover, numerical experiments highlight a connection between the proposed measures and the well-known information measure Normalized Compression Distance (NCD). In addition, Fourier basis is considered, and an application to Fourier shape descriptors is developed. As a last contribute, the problem of locating time-frequency interferences in multicomponent signals is considered. A method for time-domain location of modes interferences is presented relying on a filtered energy signal. The optimal amount of filtering is automatically detected in a rate/distortion-like curve by means of the proposed information measures.

Research products

11573/1696446 - 2024 - Solution of the EEG inverse problem by random dipole sampling
Della Cioppa, Lorenzo; Tartaglione, Michela; Pascarella, Annalisa; Pitolli, Francesca - 01a Articolo in rivista
paper: INVERSE PROBLEMS (-Bristol : Institute of Physics, 1985 -Bristol IOP Publishing Limited) pp. - - issn: 0266-5611 - wos: WOS:001131946700001 (0) - scopus: (0)

11573/1458440 - 2020 - A multiscale energy-based time-domain approach for interference detection in non-stationary signals
Bruni, Vittoria; Della Cioppa, L.; Vitulano, D. - 04b Atto di convegno in volume
conference: 17th International Conference on Image Analysis and Recognition, ICIAR 2020 (prt)
book: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) - (978-3-030-50515-8; 978-3-030-50516-5)

11573/1341612 - 2020 - An automatic and parameter-free information-based method for sparse representation in wavelet bases
Bruni, Vittoria; Della Cioppa, Lorenzo; Vitulano, Domenico - 01a Articolo in rivista
paper: MATHEMATICS AND COMPUTERS IN SIMULATION (Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598) pp. 73-95 - issn: 0378-4754 - wos: WOS:000534533200006 (3) - scopus: 2-s2.0-85073062216 (6)

11573/1284663 - 2019 - A normalized Information based method for efficient signal representation
Bruni, V.; Della Cioppa, L.; Vitulano, D. - 04b Atto di convegno in volume
conference: MASCOT 2018 (Rome; Italy)
book: Proceedings of MASCOT 2018 - ()

11573/1216713 - 2018 - An entropy-based approach for shape description
Bruni, Vittoria; Della Cioppa, Lorenzo; Vitulano, Domenico - 04b Atto di convegno in volume
conference: Eusipco 2018 (Roma, Italia)
book: Proceedings of Eusipco 2018 - ()

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