基于自动卡尔曼滤波的一维恒星光谱小波收缩去噪
Automatic Kalman-Filter-based Wavelet Shrinkage Denoising of 1D Stellar Spectra
摘要：
提出了一种基于小波收缩和自适应卡尔曼阈值的一维恒星光谱去噪非参数方法。小波收缩去噪涉及将离散小波变换（DWT）应用于输入信号，在变换域中“收缩”某些频率分量，然后将逆DWT应用于减少的分量。该过程的性能受基小波的选择、分解层数和阈值函数的影响。通常，这些参数是通过“试错法”来选择的，这在很大程度上取决于被降噪的数据的属性。在这里，我们介绍了一种自适应卡尔曼滤波器为基础的阈值方法，消除了需要选择的分解层次的数量。我们使用'Haar'小波基，我们发现这是最适合的一维恒星光谱。我们引入各种水平的泊松噪声合成PHOENIX光谱，并测试几种常见的去噪方法对我们自己的性能。它在噪声抑制和峰形保持方面被证明是优越的。我们希望它也可以用于自动和准确地过滤低信噪比的星系和类星体光谱，如SDSS，盖亚，LSST，PESSTO，VANDELS，LEGA-C和DESI的调查。
英文摘要：
We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the Discrete Wavelet Transform (DWT) to the input signal, `shrinking' certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by `trial and error', which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the `Haar' wavelet basis, which we found to be the best-suited for 1D stellar spectra. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI.
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