| Summary: | 碩士 === 國立清華大學 === 通訊工程研究所 === 100 === MUSE (Multi-Unit Spectroscopic Explorer) is a wide-field integral field spectrograph at the Very Large Telescope (VLT) for the European Southern Observatory (ESO) under construction and it is an optical instrument to be used to obtain spectra of astronomical objects over a two-dimensional field of view. Hence, MUSE will provide three-dimensional hyperspectral data cube with two spatial axes and a wavelength axis. However, due to the high noise level and the three-dimensional translation variant blur function, detection and analysis of astrophysical sources from the forthcoming MUSE instrument is of greatest challenge. In this thesis, we tackle this challenging task by studying how to accurately estimate the spectra of very distant galaxies and the corresponding abundance maps (or proportional contribution of each galaxy over the field of view affected by spatial blur). We first use some realistic hypotheses of MUSE to reformulate the data convolution model into a set of linear mixing models corresponding to different, disjoint spectral frames. Based on the linear mixing models, we propose a spatial-spectral unmixing (SSU) algorithm to detect and characterize the galaxy spectra. In each spectral frame, the SSU algorithm identifies the pure galaxy regions with a theoretical guarantee, and estimate galaxy spectra based on a sparse approximation assumption. Then, the inversion process is applied to estimate the abundances associated with the spectra estimates. The full galaxy spectra can finally be recovered by concatenating the spectra estimates associated with all the spectral frames through an advisable permutation. Some computer simulations are performed to demonstrate the efficacy of the proposed SSU algorithm.
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