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Title
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Contributions to some validated exponential analysis applications
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Author
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Abstract
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| Latest advances in exponential analysis include a multivariate method and a Validated EXPonential Analysis (VEXPA) add on. The multivariate method can recover an n-term, d-dimensional exponential model from merely O((d + 1)n) regularly collected samples, which is substantially fewer than other Prony-based multivariate methods would require. This method breaks the curse of dimensionality hence decreases the computation cost dramatically. The VEXPA method is built on a sub-Nyquist version of Prony's method. The validation technique can automatically deduce the sparsity n in the model and validate the estimated results, which is very useful under low signal-to-noise ratio conditions. We expect that these developments can be used to overcome some of the current computational obstacles in classical exponential analysis. These computational problems are behind some of today's industrial challenges, especially when the data is sparse in one or other sense. The goal of this thesis is to investigate the new possibilities in certain signal and image processing applications. We explore real world applications, from one-dimensional (1-D) to three-dimensional (3- D) space. In 1-D space, we deal with non-stationary signals, which are encountered widely in many engineering applications. We present a validated exponential analysis add-on for a variety of modulated signals. Our experiment results demonstrate the advantages in a number of practical applications. As for the problem of two-dimensional image analysis, we introduce an exponential analysis based decomposition method for texture decomposition. The usefulness of the method is investigated in two vision applications, namely texture classiffcation and defect detection. In the 3-D space, exponential analysis plays a fundamental role in inverse synthetic aperture radar (ISAR) imaging. Our method can effciently recover a large set of scattering centers from a set of noisy data. i |
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Language
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English
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Publication
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Antwerp
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University of Antwerp, Faculty of Science, Department of Computer Science
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2021
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Volume/pages
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x, 95 p.
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Note
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Cuyt, Annie [Supervisor]
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Lee, Wen-Shin [Supervisor]
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Full text (open access)
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