Denoising Method for Raman Imaging Data Based on Singular Value Decomposition and Median Absolute Deviation
FAN Xian-guang1, 2, 3, WU Teng-da1, ZHI Yu-liang1, WANG Xin1, 2, 3*
1. Department of Instrumental and Electrical Engineering, School of Aerospace Engineering, Xiamen University, Xiamen 361005, China
2. Fujian Key Laboratory of Universities and Colleges for Transducer Technology, Xiamen 361005, China
3. Xiamen Key Laboratory of Optoelectronic Transducer Technology, Xiamen 361005, China
Abstract：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.
Key words：Denoising; Raman imaging; Singular value decomposition; Median absolute deviation
范贤光，吴腾达，支瑜亮，王 昕. 基于奇异值分解和中位数绝对偏差的拉曼成像数据去噪方法[J]. 光谱学与光谱分析, 2020, 40(02): 436-440.
FAN Xian-guang, WU Teng-da, ZHI Yu-liang, WANG Xin. Denoising Method for Raman Imaging Data Based on Singular Value Decomposition and Median Absolute Deviation. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2020, 40(02): 436-440.
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