Recently, a collaborative research team from Information Materials and Intelligent Sensing Laboratory of Anhui Province, Key Laboratory of Opto-Electronic Information Acquisition and Manipulation of Ministry of Education, and Shandong Normal University published a research paper titled Optimized adaptive Savitzky-Golay filtering algorithm based on deeplearning network for absorption spectroscopy.

近日，来自安徽大学、山东师范大学联合研究团队发表了一篇题为Optimized adaptive Savitzky-Golay filtering algorithm based on deeplearning network for absorption spectroscopy的研究论文。

研究背景 Research Background

Nitrogen oxide (NO2) is a major pollutant in the atmosphere,resulting from natural lighting, exhaust, and industrial emissions. Short- and long-term exposure to NO2 is linked with an increased risk of respiratory problems. Secondary pollutants produced by NO2 in the atmosphere can cause photochemical smog and acid rain. Laser spectroscopy such as absorption spectroscopy, fluorescence spectrum, and Raman spectrum play progressively essential roles in physics, chemistry, biology, and material science. It offers a powerful platform for tracing gas analysis with extremely high sensitivity, selectivity, and fast response. Laser absorption spectroscopy has been used for quantitative analysis of NO2. However, the measured gas absorption spectra data are usually contaminated by various noise, such as random and coherent noises, which can warp the valid absorption spectrum and affect the detection sensitivity.

氮氧化物（NO2）是大气中的主要污染物，源自自然光照、排放和工业排放。长时间暴露于NO2与呼吸问题的风险增加有关。NO2在大气中产生的二次污染物可能导致光化学烟雾和酸雨。激光光谱学，如吸收光谱、荧光光谱和拉曼光谱，在物理学、化学、生物学和材料科学中发挥着日益重要的作用。它为追踪具有极高灵敏度、选择性和快速响应的气体分析提供了强大的平台。激光吸收光谱已被用于NO2的定量分析。然而，测得的气体吸收光谱数据通常受到各种噪声的污染，如随机和相干噪声，这可能扭曲有效吸收光谱并影响检测灵敏度。

The Savitzky–Golay (S–G) filtering algorithm has recently attracted attention for spectral filtering because it has fewer parameters, faster operating speed, and preserves the height and shape of spectra. Moreover, the derivatives and smoothed spectra can be calculated in a simple step. Rivolo and Nagel developed an adaptive S–G smoothing algorithm that point wise selects the best filter parameters. With simple multivariate thresholding methods, the S–G filter can remove all types of noises in continuous glucose monitoring (CGM) signal and further process for detecting hypo/hyperglycemic events. The S–G smoothing filter is widely used to smooth the spectrum of the Fourier transform infrared spectrum that can eliminate random seismic noise, remote sensing image merging, and process pulse wave.

最近，Savitzky-Golay（S-G）滤波算法因其参数较少、操作速度较快且保留了光谱的高度和形状而受到关注。此外，可以在一个简单的步骤中计算导数和平滑的光谱。Rivolo和Nagel开发了一种自适应S-G平滑算法，逐点选择最佳滤波参数。通过简单的多变量阈值方法，S-G滤波器可以去除连续葡萄糖监测（CGM）信号中的所有类型噪声，并进一步用于检测低血糖/高血糖事件。S-G平滑滤波器广泛用于平滑傅立叶变换红外光谱的光谱，可消除随机地震噪声、遥感图像融合和脉动波的处理。

The performance of S–G smoothing filter depends on the proper compromise of the polynomial order and window size. However,the noise sources and absorption spectra are unknown in a real application. Obtaining the optimal filtering effect with fixed window size and polynomial degree is difficult. To address this issue,we proposed an optimized adaptive S–G algorithm that combined the deep learning (DL) network with traditional S–G filtering to improve the measurement system performance.

S–G 平滑滤波器的性能取决于多项式阶数和窗口大小的适当折中。然而，在实际应用中，噪声源和吸收光谱是未知的。在固定的窗口大小和多项式阶数下获得最佳的滤波效果是困难的。为解决这个问题，我们提出了一种优化的自适应S-G算法，将深度学习（DL）网络与传统的S-G滤波结合起来，以提高测量系统的性能。

实验设置Experimental setup

Fig. 1 presents the experimental setup, which consists of anoptical source, a multi-pass cell with a gas pressure controller, a series of mirrors, a detector, and a computer. The laser source is a thermoelectrically cooled continuous-wave room-temperature quantum cascade laser (QC-Qube™, HealthyPhoton Co., Ltd.),which works with a maximum peak output power of 30 mW controlled by temperature controllers and operates at ~6.2 mm driven by current controllers. The radiation of QCL passes through theCaF2 mirror is co-aligned with the trace laser (visible red light at632.8 nm) using a zinc selenide (ZnSe) beam splitter. The beams go into the multipass cell with an effective optical path length of2 m, the pressure in multipass cell is controlled using the flow controller (Alicat Scientific, Inc, KM3100) and diaphragm pump (Pfeiffer Vacuum, MVP 010–3 DC) in the inlet and outlet of gas cell,respectively. A triangular wave at a typical frequency of 100 Hzis used as a scanning signal. The wave number is tuned from1630.1 to 1630.42 cm 1 at a temperature of 296 K. The signal is detected using a thermoelectric cooled mercury cadmium telluride detector (Vigo, VI-4TE-5), which uses a 75-mm focal-length planoconvex lens. A DAQ card detector (National Instruments, USB-6259) is placed next to detector to transmit the data to the computer, and the data is analyzed by the LabVIEW program in real time.

图1展示了实验设置，包括光源、带有气体压力控制器的多通道吸收池、一系列镜子、探测器和计算机。

Fig. 1. Experimental device diagram.

宁波海尔欣光电科技有限公司为此项目提供了量子级联激光器（型号：QC-Qube™ 全功能迷你量子级联激光发射头）。激光器由温度控制器控制，最大峰值输出功率为30 mW，由电流控制器控制，工作在~6.2 mm，通过钙氟化物（CaF2）镜子的辐射与追踪激光（可见红光，波长632.8 nm）共线，使用氧化锌硒（ZnSe）分束器。光束进入具有2 m有效光程的多通道池，通过流量控制器和气体池入口和出口的隔膜泵控制池中的压力。典型频率为100 Hz的三角波用作扫描信号。在296 K的温度下，波数从1630.1调至1630.42 cm-1。使用热电冷却的汞镉镓探测器进行信号检测，该探测器使用75 mm焦距的平凸透镜。DAQ卡探测器放置在探测器旁边，将数据传输到计算机，数据由LabVIEW程序进行实时分析。

QC-Qube™, HealthyPhoton Co., Ltd.

Fig. 2. Simulation of the NO2 gas absorption spectra of the ASGF and MAF algorithms (under the background of Gaussian noise), and the filtered results and the SNRs of different filtering methods.

Fig. 3. Simulation of the NO2 gas absorption spectra of the two filtering algorithms (under the background of Non-Gaussian noise), and the filtered results of different filtering methods.

结论Conclusion

An improved Savitzky–Golay (S–G) filtering algorithm was developed to denoise the absorption spectroscopy of nitrogen oxide (NO2). A deep learning (DL) network was introduced to the traditional S–G filtering algorithm to adjust the window size and polynomial order in real time. The self-adjusting and follow-up actions of DL network can effectively solve the blindness of selecting the input filter parameters in digital signal processing. The developed adaptive S–G filter algorithm is compared with the multisignal averaging filtering (MAF) algorithm to demonstrate its performance. The optimized S–G filtering algorithm is used to detect NO2 in a mid-quantum-cascade-laser (QCL) based gas sensor system. A sensitivity enhancement factor of 5 is obtained, indicating that the newly developed algorithm can generate a high-quality gas absorption spectrum for applications such as atmospheric environmental monitoring and exhaled breath detection.

在这项研究中，我们开发了一种改进的Savitzky-Golay（S-G）滤波算法，用于去噪氮氧化物（NO₂）的吸收光谱。我们引入了深度学习（DL）网络到传统的S-G滤波算法中，以实时调整窗口大小和多项式阶数。DL网络的自适应和跟踪反馈能够有效解决数字信号处理中选择输入滤波器参数的盲目性。我们将优化后的自适应S-G滤波算法与多信号平均滤波（MAF）算法进行比较，以展示其性能。优化后的S-G滤波算法被用于检测氮氧化物在基于中量子级联激光器（QCL）的气体传感器系统中的应用。实验结果表明，该算法获得了5倍的灵敏度增强，表明新开发的算法可以生成高质量的气体吸收光谱，适用于大气环境监测和呼吸气检测等应用。

reference参考来源：

Optimized adaptive Savitzky-Golay filtering algorithm based on deeplearning network for absorption spectroscopy,

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 263 (2021) 120187