拉曼成像是一种无损伤、 无需标记的光谱成像技术, 它可以提供样品的不同组分的分子指纹信息以及空间分布特征, 相比其他成像技术有着更重要的应用。 但是拉曼散射的截面积小, 灵敏度低, 加上在很多实验中为了观察某些组分的动态分布而缩短扫描时间, 导致最终得到的成像数据被噪声干扰, 因此往往需要对信号进行去噪处理。 常规的算法一般都是基于一个给定的数学模型对光谱进行处理, 容易造成过滤波, 使得信号失真； 另外, 在处理拉曼成像数据时, 常规算法往往是对数据进行逐条光谱去噪, 从而忽略了多条光谱之间的相互关系, 导致最终的拉曼图像仍然受许多噪点干扰。 因此, 提出了一种基于奇异值分解和中位数绝对偏差的拉曼成像的信号处理方法, 用于拉曼成像数据的去噪处理。 该方法首先对拉曼成像数据进行奇异值分解, 获得一个奇异值矩阵与两个正交矩阵； 然后通过中位数绝对偏差法对奇异值矩阵中的各奇异值进行离群值检测, 选取前k个被连续标记的离群值作为要保留的奇异值, 并将其余的奇异值赋值为零, 得到新的奇异值矩阵； 最后用新的奇异值矩阵与两个正交矩阵重新求解得到去噪后的拉曼成像数据。 实验中, 首先验证了中位数绝对偏差法确定前k个奇异值的正确性, 其次分别从处理后的图像质量和信号波形两方面对比了该算法与常规算法的去噪效果。 结果证明, 中位数绝对偏差法可以快速地确定出合理的k值大小, 而且, 依据该k值处理后的成像数据不仅在成像质量上消除了大量的噪点, 使得组分的空间分布特征清晰可见, 也在信号波形上较完美地保留了微小谱峰, 并恢复光谱信号。 该算法不同于常规算法, 能同时对整个拉曼成像数据进行处理, 并保留光谱之间的统计特征, 是一种更加有效的拉曼成像数据的去噪方法。

Raman imaging is a noninvasive, marker-free spectral imaging technique that provides molecular fingerprinting and spatial distribution of different components of a sample, and is more important than other imaging techniques. However, the Raman scattering has a small cross-sectional area and low sensitivity. In addition, in many experiments, in order to observe the dynamic distribution of certain components, the scanning time is shortened, and the resulting imaging data are disturbed by noise, so it is often necessary to denoise the signal. Conventional algorithms generally process the spectrum based on a given mathematical model, which is likely to cause excessive filtering and distortion of the signal. In addition, when processing Raman imaging data, conventional algorithms tend to denoise the data one by one. This neglects the relationship between multiple spectra, resulting in the final Raman image still being disturbed by many noises. Therefore, a signal processing method based on singular value decomposition (SVD) and median absolute deviation (MAD) is proposed for denoising Raman imaging data. Firstly, the singular value decomposition is performed on the Raman imaging data to obtain a singular value matrix and two orthogonal matrices. Then, all singular values in the singular value matrix are detected by the median absolute deviation method. The consecutively labeled outliers are used as singular values to be preserved, and the remaining singular values are assigned to zero to obtain a new singular value matrix. Finally, the new singular value matrix and two orthogonal matrices are solved again to obtain a denoised Raman imaging data. In the experiment, we first verify the correctness of the median absolute deviation method in determining the k value, and then the proposed algorithm is compared with the conventional algorithm from the aspects of image quality and signal waveform. The results show that the median absolute deviation method can quickly determine a reasonable value, and the imaging data processed according to this value not only eliminate a lot of noise in the imaging quality, but also make the spatial distribution characteristics of the components clearly visible. The tiny peaks are also perfectly preserved on the signal waveform and the spectral signal is recovered. This algorithm is different from the conventional algorithm in that it can process the entire Raman imaging data at the same time and preserve the statistical features between the spectra. It is a more effective denoising method for Raman imaging data.