基于匹配追踪的拉曼光谱信号重构算法

拉曼光谱技术是一种高灵敏度、无损伤、振动分子光谱技术，在医药、生物、分析化学等诸多领域有着重要的作用。然而，由于拉曼散射强度低，实际测得的拉曼信号容易被噪声所污染。特别是在较短的曝光时间，收集到的拉曼光谱的信噪比很低。因此，提出了一种基于匹配追踪算法的信号重构方法，用于提取低信噪比的拉曼信号。该方法首先通过阈值循环迭代的方法在平均谱上找出特征峰的位置、估计峰的区间。根据峰的位置区间等信息，用高斯密度函数生成字典。在噪声谱上，根据特征峰位置和区间，将其区分为有信号区间和无信号区间，在有信号区间上利用匹配追踪算法重构被噪声所掩盖的拉曼信号。该算法不仅能够很好的逼近掩盖在噪声中的拉曼信号，且在重构信号的过程中也会对基线进行扣除，无须作基线校正处理。在仿真和实验中对该算法与常规算法进行了比较，结果证明，该算法在低信噪比条件下能够较好的恢复拉曼信号。该算法不同于传统光谱去噪算法，能同时对拉曼光谱进行了基线扣除以及噪声的处理，且能取得较为理想的结果，不需要使用不同的算法对基线和噪声分别处理。其次，在算法上我们创造性地将匹配追踪算法用于拉曼光谱信号的稀疏逼近求解。

Signal Processing Method for Raman Spectra Based on Matching Pursuit

Raman spectroscopy, as a high sensitive, non-invasive vibrational molecular spectrocopy technique, plays a significant role in many fields such as pharmaceutical, biology and analytical chemistry etc. However, due to the weak Raman scattering intensity, the measured Raman signal is always contaminated by noise. Especially in the short exposure time, the SNR (signal to noise ratio) of collected Raman spectra is extremely low. Therefore, this paper proposed a signal reconstruction method based on matching pursuit algorithm, which is used to extract Raman signals from the low SNR Raman spectra. The method first finds the position of the characteristic peak on the average spectrum by threshold iterative method, and estimates the interval of the peak according to the location of the peak and peak interval, with a Gaussian density function to generate a dictionary. In the noise spectrum, according to the position and interval of the characteristic peak, it is divided into the signal interval and the non-signal interval. On the signal interval, the matching pursuit algorithm is used to reconstruct the Raman signal covered by noise. The algorithm not only can primely approximate the Raman signal which is covered in the noise, but also deducts the baseline in the procession of reconstructing the signal, and does not need any baseline correction further. The performances of the proposed algorithm and conventional algorithms were compared. The results show that the proposed algorithm can recover the Raman signals in the condition of low SNR. Different with the conventional de-noise algorithms, algorithm of this paper process the baselines and the random noises in Raman signals simultaneously, and the results have been proved good. So there is no need to use different algorithms to process the baselines and noises separately. Furthermore, in the aspect of algorithm, we creatively applied the matching pursuit algorithm to solve the sparse approximation of Raman signals.