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，來自安徽大學、山東師范大學聯合研究團隊發表了一篇題為Optimized adaptive Savitzky-Golay filtering algorithm based on deeplearning network for absorption spectroscopy的研究論文。

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）是大氣中的主要污染物，源自自然光照、排放和工業排放。長時間暴露于NO₂與呼吸問題的風險增加有關。NO₂在大氣中產生的二次污染物可能導致光化學煙霧和酸雨。激光光譜學，如吸收光譜、熒光光譜和拉曼光譜，在物理學、化學、生物學和材料科學中發揮著日益重要的作用。它為追蹤具有靈敏度、選擇性和快速響應的氣體分析提供了強大的平臺。激光吸收光譜已被用于NO₂的定量分析。然而，測得的氣體吸收光譜數據通常受到各種噪聲的污染，如隨機和相干噪聲，這可能扭曲有效吸收光譜并影響檢測靈敏度。

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 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）濾波算法因其參數較少、操作速度較快且保留了光譜的高度和形狀而受到關注。此外，可以在一個簡單的步驟中計算導數和平滑的光譜。Rivolo和Nagel開發了一種自適應S-G平滑算法，逐點選擇最佳濾波參數。通過簡單的多變量閾值方法，S-G濾波器可以去除連續葡萄糖監測（CGM）信號中的所有類型噪聲，并進一步用于檢測低血糖/高血糖事件。S-G平滑濾波器廣泛用于平滑傅立葉變換紅外光譜的光譜，可消除隨機地震噪聲、遙感圖像融合和脈動波的處理。

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 平滑濾波器的性能取決于多項式階數和窗口大小的適當折中。然而，在實際應用中，噪聲源和吸收光譜是未知的。在固定的窗口大小和多項式階數下獲得最佳的濾波效果是困難的。為解決這個問題，我們提出了一種優化的自適應S-G算法，將深度學習（DL）網絡與傳統的S-G濾波結合起來，以提高測量系統的性能。

實驗設置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.

圖1展示了實驗設置，包括光源、帶有氣體壓力控制器的多通道吸收池、一系列鏡子、探測器和計算機。

Fig. 1. Experimental device diagram.

寧波海爾欣光電科技有限公司為此項目提供了量子級聯激光器（型號：QC-Qube™ 全功能迷你量子級聯激光發射頭）。激光器由溫度控制器控制，最大峰值輸出功率為30 mW，由電流控制器控制，工作在~6.2 mm，通過鈣氟化物（CaF2）鏡子的輻射與追蹤激光（可見紅光，波長632.8 nm）共線，使用氧化鋅硒（ZnSe）分束器。光束進入具有2 m有效光程的多通道池，通過流量控制器和氣體池入口和出口的隔膜泵控制池中的壓力。典型頻率為100 Hz的三角波用作掃描信號。在296 K的溫度下，波數從1630.1調至1630.42 cm^-1。使用熱電冷卻的汞鎘鎵探測器進行信號檢測，該探測器使用75 mm焦距的平凸透鏡。DAQ卡探測器放置在探測器旁邊，將數據傳輸到計算機，數據由LabVIEW程序進行實時分析。

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.

結論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.

在這項研究中，我們開發了一種改進的Savitzky-Golay（S-G）濾波算法，用于去噪氮氧化物（NO2）的吸收光譜。我們引入了深度學習（DL）網絡到傳統的S-G濾波算法中，以實時調整窗口大小和多項式階數。DL網絡的自適應和跟蹤反饋能夠有效解決數字信號處理中選擇輸入濾波器參數的盲目性。我們將優化后的自適應S-G濾波算法與多信號平均濾波（MAF）算法進行比較，以展示其性能。優化后的S-G濾波算法被用于檢測氮氧化物在基于中量子級聯激光器（QCL）的氣體傳感器系統中的應用。實驗結果表明，該算法獲得了5倍的靈敏度增強，表明新開發的算法可以生成高質量的氣體吸收光譜，適用于大氣環境監測和呼吸氣檢測等應用。

reference參考來源：

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

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