微引力透镜数据的小波变换：去噪、提取本征脉动与行星信号
Wavelet transforms of microlensing data: Denoising, extracting intrinsic pulsations, and planetary signals
AI总结：
本研究将离散与连续小波变换应用于微引力透镜数据去噪，验证了去噪效果对采样率的依赖性，确定了不同数据下的最优小波族，并实现了被噪声掩盖的本征脉动与行星信号的提取与识别。
摘要：
小波是一类用于描述噪声等瞬态、非平稳变化的波形函数。本研究探讨了对微引力透镜数据进行离散小波变换（DWT）与连续小波变换（CWT）的优势，用于数据去噪，以及提取被噪声掩盖的行星信号和本征脉动信号。我们首先生成合成微引力透镜数据，并对其应用小波去噪方法。对于这些基于OGLE测光精度、带有理想高斯噪声的模拟微引力透镜数据，使用DWT去噪可将数据与真实模型的标准差降低0.044–0.048星等。利用去噪后数据重建真实模型与行星信号的效率强烈依赖于观测采样率：当采样间隔从15分钟降至6小时时，效率从37%下降至0.01%。随后我们对OGLE团队发现的100个微引力透镜事件进行了去噪处理。平均而言，对这些数据进行小波去噪后，数据相对于最佳拟合模型的标准差与约化卡方（χ²ₙ）分别改善了0.023星等和1.16。在模拟数据与OGLE数据中，表现最优的小波（分别基于去噪后数据的最高信噪比峰值（SNR_max）、最高皮尔逊相关系数或最低均方根误差（RMSE）判定）分别属于“Symlet（对称）”和“Biorthogonal（双正交）”小波族。在部分去噪后的数据中，出现了原始数据中被噪声掩盖的恒星本征脉动或类行星小偏差信号。不过，与尖锐信号相比，DWT去噪更易重建较为平缓、宽幅的行星信号；CWT与三维频率-功率-时间图可辅助判断尖锐信号的存在。
英文摘要：
Wavelets are waveform functions that describe transient and unstable variations, such as noises. In this work, we study the advantages of discrete and continuous wavelet transforms (DWT and CWT) of microlensing data to denoise them and extract their planetary signals and intrinsic pulsations hidden by noises. We first generate synthetic microlensing data and apply wavelet denoising to them. For these simulated microlensing data with ideally Gaussian nosies based on the OGLE photometric accuracy, denoising with DWT reduces standard deviations of data from real models by $0.044$-$0.048$ mag. The efficiency to regenerate real models and planetary signals with denoised data strongly depends on the observing cadence and decreases from $37\%$ to $0.01\%$ by worsening cadence from $15$ min to $6$ hrs. We then apply denoising on $100$ microlensing events discovered by the OGLE group. On average, wavelet denoising for these data improves standard deviations and $χ^{2}_{\rm n}$ of data with respect to the best-fitted models by $0.023$ mag, and $1.16$, respectively. The best-performing wavelets (based on either the highest signal-to-noise ratio's peak ($\rm{SNR}_{\rm{max}}$), or the highest Pearson's correlation, or the lowest Root Mean Squared Error (RMSE) for denoised data) are from 'Symlet', and 'Biorthogonal' wavelets families in simulated, and OGLE data, respectively. In some denoised data, intrinsic stellar pulsations or small planetary-like deviations appear which were covered with noises in raw data. However, through DWT denoising rather flattened and wide planetary signals could be reconstructed than sharp signals. CWT and 3D frequency-power-time maps could advise about the existence of sharp signals.
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