Automated weak signal extraction of hyperspectral Raman imaging data by adaptive low‐rank matrix approximation

Abstract

Hyperspectral Raman imaging has emerged as a promising spectroscopic tool that can provide spatial and molecular information of the sample in a label-free and noninvasive manner, which is very suitable to the biological and biomedical research. However, the intrinsically weak Raman scattering effect results in the low signal quality of the measured Raman spectra, which has largely limited the application of Raman imaging. In this paper, we develop an adaptive low-rank matrix approximation method to automatically extract the signal from the noisy hyperspectral Raman imaging data. After spike removal, the hyperspectral Raman imaging data are decomposed into a linear combination of submatrices by singular value decomposition. Next, the submatrices are classified into positive and negative groups according to the SNR contribution. The negative group, reflecting the instrumental noise, is discarded, and the positive group is used to reconstruct the denoised signal. We prove on the simulated data that this algorithm can significantly decrease the normalized mean noise error from 34.35% down to 1.9%. Such a strong denoising performance enables it to efficiently extract the signal from the noisy hyperspectral Raman imaging data, especially under the low SNR condition. We finally apply this algorithm to the fast speed Raman imaging of HeLa cell and surprisingly find that the slight difference of the spectra can be differentiated after signal extraction. This algorithm offers a promising tool in the Raman imaging and also can be extended to other spectroscopic imaging platforms such as fluorescent and IR spectroscopy.

Hybrid Principal Component Analysis Denoising Enables Rapid, Label-Free Morpho-Chemical Quantification of Individual Nanoliposomes

“…Despite these small discrepancies, our study still shows that, with the modest experimental effort of obtaining a small high-SNR training data set containing the expected spectral variability of future test data, hybrid PCA denoising permits higher throughput, accurate, and automated nanoparticle characterization and could be gainfully applied in the future to a wide variety of both synthetic and biological nanoparticles such as EVs. While biological nanoparticles are expected to have greater chemical variability and therefore may require an enlarged training data set compared to the liposome data presented here, the ability to accurately describe these spectra by a small number of principal components is a property common to most biological Raman data 38 and medicines. 39 ■ ASSOCIATED CONTENT * sı Supporting Information…”

Collaborative Low-Rank Matrix Approximation-Assisted Fast Hyperspectral Raman Imaging and Tip-Enhanced Raman Spectroscopic Imaging

“…Therefore, matrix A 1 after the collaborative factorization can be written as eq , which is not a strict orthogonal matrix factorization form. Next, the SNR contribution rule that was described in our previous work is used to select appropriate SVs with a positive contribution to reconstructing the clean data (Figure c). Finally, the high-SNR data matrix (Figure d) corresponding to the target matrix is obtained by the combination of the selected submatrices, as indicated in eq , where S is the selected index set of SVs and is the high-SNR data matrix. …”

“…The instrumental noise is obtained by removing the first principal component of the Au film spectra that were measured by the same instrument with the same experimental conditions. The detailed scheme of producing high-SNR data and instrumental noise can be found in ref . The bilayer WSe 2 sample was measured using a LabRam HR-800 (point scan, Horiba, Japan); the original data of bilayer WSe 2 , as well as the instrumental noise, was acquired with an integration time of 0.1 s/pixel, a 633 nm laser source, 1.25 mW/pixel, and air objective NA = 0.9, 1800 g/mm.…”

“…Recently, we proposed an algorithm named adaptive lowrank matrix approximation (ALRMA), which used the SNR contribution rule to screen the appropriate submatrices of SVD to approximate the clean data. 18 This method achieved superior performance in Raman imaging of single cells over the abovementioned methods that are widely used in the literature. Nonetheless, it is still very difficult to remove the instrumental noise residual in the SVD domain, which will be ultimately added into the denoised data, thus deteriorating the performance.…”

“…This method has achieved considerable denoising performance and has been successfully applied to the Raman imaging of materials, single cells, and others. − In addition, there are also many reports that use similar methods for the noise reduction of a natural image , and other applications. , However, both the denoising principle of SVD and the selection rule of appropriate submatrices have not been clearly explained. Recently, we proposed an algorithm named adaptive low-rank matrix approximation (ALRMA), which used the SNR contribution rule to screen the appropriate submatrices of SVD to approximate the clean data . This method achieved superior performance in Raman imaging of single cells over the abovementioned methods that are widely used in the literature.…”