Anthoine, Sandrine (2005) Different wavelet-based approaches for the separation of noisy and blurred mixtures of components. Application to astrophysical data. PhD thesis Program in Applied and Computational Mathematics, Program in Applied and Computational Mathematics, EP/X p.129.
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Abstract
This thesis addresses the problem of separating image components that have different structure, when several observations of blurred mixtures of these components are available. In the image processing literature, the deblurring problem has !
been well described for a single component in a single image and the separation problem mainly studied without blurring. In this thesis, the full problem is addressed globally, the separation being done simultaneously with the denoising and deblurring of the data, by generalizing methods that exist for the enhancement of a single image.
The first result is a mathematical analysis of a heuristic iterative algorithm for the enhancement of a single image. This algorithm is proved to be convergent but not regularizing; a modification is introduced that restores this property. The main object of this thesis is to develop and compare two methods for the multi-components/multi-observations problem: the first method uses functional spaces to describe the signals; the second method models the local statistical properties of the signals. Both methods use wavelet frames to simplify the description of the data.
Both algorithms are evaluated with regards to a particular astrophysical problem: the reconstruction of clusters of galaxies by the extraction of their Sunyaev-Zel'dovich effect in multifrequency measurements of the Cosmic Microwave Background anisotropies. Realistic simulations are studied. It is shown that both methods yield clusters maps of sufficient quality for subsequent cosmological studies when the resolution of the observations is high and the level of noise moderate. Then some limiting factor are pointed out.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Mallat, Stephane |
| Date: | August 2005 |
| Board of examiners: | Vincent, Poor and Elena, Pierpaoli and Ivan, Selesnick and Peter, Ramadge and Daubechies, Ingrid |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | Program in Applied and Computational Mathematics |
| Collection (Fonds): | EP/X |
| Institution: | EP/X |
| Department: | Program in Applied and Computational Mathematics |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Signal estimation, Detection, Wavelets, Statistical, Variational approach, Separation, Deconvolution, Astrophysics., Estimation, Detection de signaux, Ondelettes, Approche statistique, Variationnelle, Séparation, Déconvolution, Astrophysique |
| ID Code: | 1556 |
|---|---|
| Deposited By: | Nadine Garnier |
| Deposited On: | 17 February 2006 |
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