1. 山东大学(威海)机电与信息工程学院, 山东 威海 264209
2. 哈尔滨理工大学荣成学院, 山东 威海 264300
3. 中国科学院光学天文重点实验室, 国家天文台, 北京 100012
*通讯联系人 e-mail: pjc@sdu.edu.cn

A Method to Fit Low-Quality Stellar Spectrum
WU Ming-lei1,2, PAN Jing-chang1,*, YI Zhen-ping1, WEI Peng3
1. School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai, Weihai 264209, China;
2. Harbin University of Science and Technology at Rongcheng, Weihai 264300, China
3. Key Laboratory of Optical Astronomy, NAOC, Chinese Academy of Sciences, Beijing 100012, China
Abstract

The stellar continuum is a sort of spectrum whose light intensity changes continuously and smoothly with wavelength (frequency) due to blackbody radiation. Each observed spectrum contains continuous spectra, spectral lines and noises. The classification of stellar is mainly based on the spectral lines of the spectrum, relative intensity of the continuum and other characteristics of the spectrum. The distribution of the stellar continuum and the contour of the lines are determined by the stellar atmospheric parameter, so the stellar atmospheric parameter can be estimated from the continuum and the spectral lines. Therefore, the main problem of the spectral data processing is to extract the continuum and the lines. The current algorithms for stellar continuous spectral extraction are mainly polynomial approximation, median filtering, morphological filtering and wavelet filtering. However, these methods for the robustness of low-quality spectral processing are not very satisfying. Therefore, it is necessary to study a new algorithm for extracting the continuous spectrum from the low-quality spectra. In this paper, a fitting method for low-quality stellar spectrum based on Monte Carlo is proposed after careful analyses of low-quality stellar continuum. The method is used to automatically interpolate at the point where the spectrum is not in the range of the star spectrum with Monte Carlo, so each wavelength corresponds to a flow point, and then the low-order polynomial iterations are fitted to these flow points for obtaining the continuous spectrum. In order to verify the robustness of the algorithm for low-quality spectral continuum extraction with different SNRs, we use different SNRs to simulate different low-quality spectrum by adding different Gaussian white noise to the original spectrum. The result shows that the proposed algorithm has high accuracy and robustness to the fitting of low-quality spectrum with different SNRs.

Keyword: Low-quality spectrum; Spectrum continuum; Monte Carlo; Uniform distribution

1 方法介绍

1.1 数据点模拟

(1) 根据上下限(L, U), 对原始光谱点以统计窗为区间进行逐个筛选;

(2) 对未选取到的流量点利用蒙特卡罗在一定区间内进行模拟, 区间的间距就是D=U-L;

(3) 调用蒙特卡罗随机数发生器, 利用模拟的均匀分布在区间内产生随机数[8, 9]

$F=L+(U-L)×Rand(1, 1)$

(4) 对每一个窗口重复第二步, 直至重复的次数已达预定值;

(5) 对所有的随机数求平均值, 将这个平均值作为模拟的流量点值。

$U=55+h(s)-h(0)50[h(100)-h(0)]L=45+h(s)-h(0)50[h(100)-h(0)](1)$

1.2 多项式迭代拟合及归一化处理

(1)对波长WS和流量FS进行5阶多项式拟合, 利用最小二乘法得到连续谱FC, 然后对连续谱进行归一化Fn=FS/FC

(2)对归一化的光谱进行异常点的剔除, 去掉[m-3s, m+3s]范围外的点, 其中ms分别为FC的均值和标准差。

(3)重复步骤(1)和(2), 直到没有可去除的点为止[5]

1.3 原始光谱加噪声处理

(1) 对原始光谱的流量点进行插值;

(2) 产生均值为0, 标准差为1的正态分布随机数;

(3) 对第2步的随机数进行标准化

$y=y-mean(y)y=y/sqrt(yy')$

(4) 与第3步的随机数进行结合, 产生具有一定信噪比的噪声

$y=y/(10snr/20)$

(5) 产生服从N(f, y)正态分布的噪声

$f=f+y$

(6) 利用不同信噪比(文中选取SNR=1: 15)对第1步到第5步进行循环。

2 结果与讨论

 Figure Option 图1 方法流程图Fig.1 Method flow chart

 Figure Option 图2 SDSS不同种类光谱的拟合结果Fig.2 The fitting results of different spectral types from SDSS

 Figure Option 图3 不同信噪比的A类低质量光谱拟合Fig.3 Low-quality spectral fitting with different SNR of A-type

 Figure Option 图4 不同信噪比的低质量光谱拟合Fig.4 Low-quality spectral fitting with different SNRs

3 结论

The authors have declared that no competing interests exist.

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