The present dissertation is divided in two parts. In the first one, we address two inverse problems, namely compressed sensing (CS) and speech denoising, through the lens of the analysis sparsity model. To that end, we leverage ideas from time-frequency analysis and introduce a new redundant analysis operator associated to a Gabor frame, which efficiently sparsifies the signals of interest. Subsequently, we employ an iterative method for solving both problems and perform a numerical comparison of our analysis operator to state-of-the-art Gabor analysis operators, on both synthetic and real-world data. Our experimental results indicate improved performance when our proposed framework is employed to solve both inverse problems, since it outperforms all other Gabor transforms, consistently for all datasets. In the second part of this dissertation, we resolve the CS problem by employing the newly-introduced field of deep unfolding, which stems from the interpretation of classic iterative a ...
The present dissertation is divided in two parts. In the first one, we address two inverse problems, namely compressed sensing (CS) and speech denoising, through the lens of the analysis sparsity model. To that end, we leverage ideas from time-frequency analysis and introduce a new redundant analysis operator associated to a Gabor frame, which efficiently sparsifies the signals of interest. Subsequently, we employ an iterative method for solving both problems and perform a numerical comparison of our analysis operator to state-of-the-art Gabor analysis operators, on both synthetic and real-world data. Our experimental results indicate improved performance when our proposed framework is employed to solve both inverse problems, since it outperforms all other Gabor transforms, consistently for all datasets. In the second part of this dissertation, we resolve the CS problem by employing the newly-introduced field of deep unfolding, which stems from the interpretation of classic iterative algorithms as deep neural networks. In order to do so, we ``unfold'' the iterations of two state-of-the-art algorithms, traditionally employed to solve the analysis-sparsity-based CS problem, into layers of neural networks. The latter jointly learn corresponding decoders and redundant sparsifying analysis operators. Our main novelty is attributed not only to the development of these two unfolding networks, but also to the estimation of the generalization error produced by each one of them. Regarding the latter, we take advan
Μέθοδοι επαναληπτικές και μάθησης συναντούν τον πλεονασμό στην επεξεργασία σήματος
ανάλυσης σχετιζόμενο με ένα πλαίσιο Gabor, ώστε να αναπαραστήσουμε όσο αραιότερα γίνtage of chaining techniques, in order to upper bound the Rademacher complexity of each network's hypothesis class. Then, we leverage this estimate so as to deliver the desired generalization error bounds. Finally, we conduct several experiments -- on synthetic and real-world datasets -- validating our derived theory and compare our proposed unfolding networks to a state-of-the-art one. As illustrated by the experimental results, both our unfolding networks outperform the baseline, consistently for all datasets.
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Θεοχάρης Θεοχάρης Γιαννόπουλος Απόστολος Νοτάρης Σωτήριος Παναγάκης Ιωάννης Εμίρης Ιωάννης Πολυδορίδης Νικόλαος Μερτικόπουλος Παναγιώτης
Επιστημονικό πεδίο
Φυσικές Επιστήμες ➨ or transforms, consistently for all datasets. In the second part of thCF%80%CE%B9%CF%83%CF%84%CE%AE%CE%BC%CE%B7+%CE%97%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%BF%CE%BD%CE%B9%CE%BA%CF%8E%CE%BD+%CE%A5%CF%80%CE%BF%CE%BB%CE%BF%CE%B3%CE%B9%CF%83%CF%84%CF%8E%CE%BD+%CE%BA%CE%B1%CE%B9+%CE%A0%CE%BB%CE%B7%CF%81%CE%BF%CF%86%CE%BF%CF%81%CE%B9%CE%BA%CE%AE">Επιστήμη Ηλεκτρονικών Υπολογιστών και Πληροφορική ➨ parsity-based CS problem, into layers of neural networks. The latter jointly learn corresponding decoders and redundant sparsifying analysis operators. Our main novelty is attributed not only to the development of these two unfolding networks, but also to the estimation of the generalization error produced by each one of them. Regarding the latter, we take advan
Όλα τα τεκμήρια στο ΕΑΔΔ προστατεύονται από πνευματικά δικαιώματα.
Αφορά στους συνδεδεμένους στο σύστημα χρήστες οι οποίοι έχουν αλληλεπιδράσει με τη διδακτορική διατριβή. Ως επί το πλείστον, αφορά τις μεταφορτώσεις. Πηγή: Εθνικό Αρχείο Διδακτορικών Διατριβών.
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