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Analysis of non-stationary signals in dispersive media: contribution of compressive sensing techniques for interference managemenet


Directeur de thèse :     Cornel IOANA

École doctorale : Electronique, electrotechnique, automatique, traitement du signal (EEATS)

Spécialité : Signal, image, parole, télécoms

Structure de rattachement : Université Grenoble Alpes

Établissement d'origine : IMPERIAL COLLEGE - LONDRES

Financement(s) : bourse attribuée par un gouvernement étranger ; Sans financement


Date d'entrée en thèse : 01/09/2017

Date de soutenance : 04/06/2021


Composition du jury :
IOANA Cornel, Maitre de conférence, directeur de thèse, Université Grenoble Alpes
DAKOVIC Milos, Professeur, co-directeur de thèse, Université du Monténégro
FLANDRIN Patrick, Professeur, rapporteur, CNRS
RICHARD Cédric, Professeur, rapporteur, Université Côte d'Azur
GAUSSIER Eric, Professeur, examinateur, Université Grenoble Alpes
LERGA Jonatan, Professeur, examinateur, Université de Rijeka
MARS Jérôme, Professeur, invité, Université Grenoble Alpes
OROVIC Irena, Professeur, invité, Université du Monténégro


Résumé : In signal processing, the theory behind compressive sensing presented a successful sampling technique in various fields. Using a small number of measurements for the acquisition improves the efficiency of storage, memory, and transmission of signals. Since numerous signals in nature can be represented as sparse in some representation domain, the technique showed massive potential in many areas such as medicine, telecommunications, radar, and sonar systems. Although very successful, compressive sensing is not yet fully developed and implemented in underwater acoustics. Acoustic signals transmitted through water introduce many complex characteristics making their analysis challenging and difficult. The process of transmitting and receiving signals through shallow water environment is a representative example of a signal transmission through dispersive channel. The non-stationary nature of such signals leads to the time-frequency signal analysis as well developed theory suitable for non-stationary signal processing. Within the compressive sensing framework, it is important to emphasize that the non-stationary signals are only approximately sparse or nonsparse in the corresponding transformation domain. Since the compressive sensing reconstruction methods intrinsically relies on the sparsity, the reconstruction of approximately sparse or non-sparse signals will produce an error that should be considered in the calculations and applications. The main contributions of this thesis are in extending and adjusting the compressive sensing methods and results to the non-stationary signals, with application to the acoustic and sonar signals. This can include dispersive media propagation. In particular, the exact expected error of the reconstruction of non-stationary signals in time-frequency analysis using the compressive sensing methods is derived. The decomposition and reconstruction of signals in sonar systems and dispersive underwater channels using time-frequency approaches are presented. Various sequences used in the sonar imaging are considered from the point of the compressive sensing based reconstruction, including a reduced set of measurements or highly corrupted samples and real-world scenario setup. All of the presented theoretical results are followed by numerous examples. Application of the proposed methods and obtained theoretical results to image reconstruction and denoising problems is also presented as an example that developed tools and theoretical results are important not only for underwater acoustic systems. The algorithms used to achieve the main results in the thesis are given in the Appendix.

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