基于FFT奇异值分解的光谱信号去噪算法

微型光谱仪在采集光谱信号过程中，光谱数据经常受到来自仪器光学系统和电子电路中的干扰出现噪声和光源特征峰，严重干扰了真实光谱信号的图谱特征，因此需要使用合理的预处理方法保留光谱信号中有用信号并尽可能过滤噪声信号同时将光源特征峰滤除，从而提高光谱信息定量分析的稳健性和准确性。并且在线检测系统要求尽可能减少人为参数选择对去噪效果的影响，奇异值分解经常应用于由系统电路引起的噪声去噪，奇异值降噪阶次的选取对提高信号信噪比十分关键，但是往往参数选取主要依赖经验调试和实验验证。因此，提出了一种基于奇异值重构信号分量频率的光谱信号去噪算法。该算法首先重构原始光谱信号单个奇异值分量信号，然后对每个奇异值分量信号作快速傅里叶变换，得到每个奇异值分量信号快速傅里叶变换结果中振幅最大所对应的频率值，最后按照奇异值递减方式对相应分量信号频率值进行一阶滞后差分，得到频率差分谱，研究表明，差分谱第一个谱峰值在大于设定阈值处所对应的奇异值即为奇异值分解降噪的有效阶次。结果表明：对包含多种重金属离子的溶液在线测量的紫外可见光谱信号，添加不同强度的随机噪声，并进行去噪处理，使用信噪比和均方根误差两个性能指标进行对比。所提算法相较于SG滤波算法和小波变换去噪算法信噪比分别提高了22.05%，10.88%，均方根误差分别降低了74.28%，41.29%。所提算法完全基于数据驱动，在处理真实紫外可见光谱信号中不仅抑制了噪声影响，而且将微型光谱仪的光源特征峰有效滤除，在紫外可见光谱信号的定量分析中具有较好的应用前景。

Denoising Algorithm of Spectral Signal Based on FFT SVD

In the process of collecting spectrum signals,the spectrum data is often interfered with by the optical system and electronic circuit of the instrument,which results in noise and characteristic peaks of the light source,and seriously interferes with the spectrum characteristic of the real spectrum signal.Therefore,it is necessary to use a reasonable preprocessing method to retain the useful signal in the spectrum signal,filter the noise signal as much as possible and filter the light source characteristic peak to improve the robustness and accuracy of the quantitative analysis of spectral information.Spectrum online detection system requires minimizing the influence of human parameter selection on the denoising effect.Singular value decomposition(SVD)is often applied to the denoising caused by the system circuit.The selection of the order of singular value denoising is very important to improve the signal-to-noise ratio.However,the selection of parameters mainly depends on empirical debugging and experimental verification.Therefore,this paper proposes a spectral signal denoising algorithm based on singular value reconstruction of signal component frequency.The algorithm firstly reconstructs the single singular value component signal of the original spectral signal.Then,the Fast Fourier Transform(FFT)of each singular value component signal is performed to obtain the frequency value corresponding to the maximum amplitude of each signal.Finally,according to the singular value decreasing mode,the first-order hysteresis difference of the corresponding component signal frequency value is carried out,and the frequency difference spectrum is obtained.The results show that the first peak value of the difference spectrum is the effective order of singular value decomposition denoising.Random noise of different intensity is added to the UV-Visible spectrum signal measured online of a solution containing a variety of metals,and the signal to noise ratio and root mean square error are compared.The results show that the proposed algorithm’s signal-to-noise ratio and root mean square error are 22.05%,10.88%and 74.28%,41.29%higher than those of SG filter and wavelet transform respectively.The proposed algorithm is fully data driven,which not only suppresses the noise effect in processing the real UV-Vis spectrum signal,but also effectively filters out the characteristic peak of the light source of the micro spectrometer,so it has a good application prospect in the quantitative analysis of UV-Vis spectrum signal.