| The multi object fiber spectroscopic telescope can obtain massive spectra from different celestial bodies simultaneously. After the transmission through the spectrometer by the optical fibers, the two-dimensional (2-D) spectral images are gained from the CCD cameras. Then the spectral data are processed by the fiber spectral processing system and the spectral treatment results are output and restored.The accuracy of the multi-fiber spectral processing system is related to the utilization rate, accuracy, and the integrity of the spectral data, and the obtained data have vital importance to the follow-up astronomy research. Therefore, it has great significance and value to desigh a reasonable spectral processing system and improve its accuracy.The dissertation first introduces the mechenism of the multi-object fiber spectroscopic telescope and the data types and characteristics of the acquired spectra. Then, taking LAMOST as an example, the formation mechanism of the 2-D spectra is analysised, and a multi-fiber spectral processing system based on 2-D models and algorithms is redesigned according to the formation mechanism. Next, the research focus on two kernel modules of the spectral processing system:spectrum extraction and sky subtraction, and the sparse representation and convex optimization algorithms are applied to them, respectively. From this, two kinds of spectrum extraction methods based on 2-D models, a sky subtraction algorithm based on homogeneity constraint and sparsity constraint on Nonnegtive Matrix Factorization (NMF) and a 2-D modeling sky subtraction algorithm based on Principal Component Analysis (PCA) are put forward.The main work and innovation points of this dissertation are listed as follows:1. Research and design a multi-fiber spectral processing system on LAMOST based on 2-D models and algorithms. The core of the design is on the basis of the formation mechanism of the 2-D spectra. The spectral informations on both the spatial orientation and the wavelength orientation are considered, maintaining the integrity of the spectral data. All of the algorithms of the kernel modules are based on 2-D models. Thereby, the dimension reduction process——spectrum extraction, which reduce the original one-dimensional (1-D) spectra from the 2-D spectra, is put in the end of the kernel modules. After the preprocessing steps——bias subtracting, cosmic ray detection, fiber tracing, etc. firstly, wavelength calibration based on 2-D model and flux calibration are carried on. Secondly, sky subtraction based on 2-D algorithm is carried out. Then, spectrum extraction by 2-D models is performanced, restoring the original 1-D input spectra from the 2-D spectral images. Finally, the subsequent processing steps——spectra combination, etc. are done, and the 1-D spectra are output.2. Research the algorithms of the spectrum extraction kernel module. Two kinds of spectrum extraction algorithms based on 2-D models are put forward. The 2-D spectrum extraction algorithms contain two main steps:building the 2-D point spread function (PSF) matrix which simulate the spectral contours; establish the spectrum extraction equations and evaluate the optimal solution. In view of the fact that the spectral contours obey gaussian distributions in both the spatial and the wavelength orientations, a modified 2-D Gaussian spectrum extraction method is proposed. The PSF matrix is built by 2-D Gaussian models. The high correlation between the profile signals and the non correlation between the signals and the noised are utilized to estimate the parameters of the 2-D Gaussian models by the least squares method. The parameters of the spatial orientation and the wavelength orientation are estimated through the corresponding 2-D flat-field spectra and the 2-D calibration lamp spectra, respectively. In addition, taking the asymmetry of the actual contour into account, a more flexible, with stronger adaptability spectrum extraction method based on 2-D exponential polynomial model is proposed. In both the spatial orientation and the wavelength orientation, two exponential polynomials are spliced, respectively, building the 2-D exponential polynomial model to constitute the PSF matrix. The polynomial coefficients are estimated respectively by the least squares method through the sampling spectral contours of the corresponding 2-D flat-field spectra and the 2-D calibration lamp spectra. Accomplishing the building of the PSF matrix, the spectrum extraction matrix equations are established according to the formation mechanism of the 2-D spectra. The difficulty lies in the accurate estimation on the solutions of the spectrum extraction equations. This dissertation innovatively proposes using the Barzilai-Borwein gradient projection sparse reconstruction (GPSR-BB) algorithm to evaluate the optimal solutions of the spectrum extraction equations. The proposed method solves the ringing problem caused by directly calculating the inverse of the matrix, getting a fairly precise estimation of the original 1-D input spectra. Thus the 2-D spectrum extraction algorithms are completed.3. Research the sky subtraction algorithms with high precision. Two kinds of high-accuracy sky subtraction algorithms are put forward. Firstly, from the skylight modeling algorithm itself, according to the characteristics of sky emission lines, that the sky emission lines have sparse distribution and different sky spectra have much the same flux on the same wavelength position, a Nonnegative Matrix Factorization (NMF) algorithm with homogeneity constraint and sparsity constraint is proposed and applied to sky background modeling. Then the designed NMF is utilized onto the sky spectra sampling matrix and the object spectra sampling matrix, respectively, to do training and testing, constructing the sky model. The sky subtraction process is completed by subtracting the constructed sky flux from the object spectra. Secondly, from the 2-D sky modeling, taking full advantage of the spectral information in both the spatial orientation and the wavelength orientation, the 2-D modeling sky subtraction method based on PCA is proposed. Making PCA on the sky spectra sampling matrix and projecting the obtained eigenvectors onto the object spectra sampling matrix, the 2-D sky model is constructed. The sky subtraction process is accomplished by subtracting the constructed 2-D sky flux from the 2-D object spectra.In view of the similarity of the mechanism of the multi-object fiber spectroscopic telescopes, the spectral processing flow and the algorithms of the kernel modules are experimented on LAMOST data to verify the validity and superiority. Meanwhile, they are also applicable on other multi-object fiber spectroscopic telescopes. So the methods proposed in the dissertation has certain reference and application value. |
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