CWT-PLSR for Quantitative Analysis of Raman Spectrum Authors Shuo Li, James O Nyagilo, Dr. Digant P Dave and Dr. Jean Gao Emails shuo.li@mavs.uta.edu gao@uta.edu Presenter Dr. Jean Gao
Outline Introduction Raman Scattering and Raman Spectrum Introduction to SERS Cancer detection by SERS The State of the Art Method Partial Least Squares (PLS) Regression Problem for Raman spectrum Our Method CWT-PLS Regression 2/19
Raman Spectrum Raman Spectrum Raman scattering Rayleigh scattering Laser Material A 3/19
Surface-enhanced Raman Scattering The inherently weak magnitude of Raman scattering limits the sensitivity The SERS-nanoparticles, normally a silver or gold colloid or a substrate containing silver or gold, are designed to enhance the Raman spectra intensity 4/19
Cancer Detection [1] Antibody conjugated SERSnanoparticles, which can be attached to specific proteins in cancer cells, are injected into body. Cancer can be detected by imaging large amount of such nanoparticles gathered in certain place inside body by Raman imaging techniques. [1] C. Zavaleta, B. R. Smith, I. Walton, W. Doering, G. Davis, B. Shojaei, M. Natan and S. S. Gambhir, Multiplexed Imaging of Surface Enhanced Raman Scattering Nanotags in Living Mice Using Noninvasive Raman Spectroscopy, PNAS, Vol. 106, pp. 13511-13516, 2009. 5/19
Outline Introduction Raman Scattering and Raman Spectrum Introduction to SERS Cancer detection by SERS The State of the Art Method Partial Least Squares (PLS) Regression Problem for Raman spectrum Our Method CWT-PLS Regression 6/19
Three Properties of Raman Spectrum [1,2] Source spectra do not change when the pure materials are mixed into compounds; The mixture spectrum equals to the summation of the source spectra; Within certain range of concentrations, the intensities of source spectra are approximately linearly related to the concentrations of the pure material. [2] S. Keren, C. Zavaleta, Z. Cheng, A. de la Zerda, O. Gheysens and S. S. Gambhir, Noninvasive Molecular Imaging of Small Living Subjects Using Raman Spectroscopy, PNAS, Vol. 105, pp. 5844-5849, 2008. 7/19
Model for PLS Regression Calibration model X = Y S + E1 Dx Dy Dx Dx N X Y S E1 Multivariate regression model Y = X Θ + E; y' = x Θ Latent variable regression T = X W; Y = T Q + E 8/19
PLS Regression Find W= [w1,...,wk] by solving a constraint optimization problem W of PLSR gives more weights to the Raman shifts that have both big variances of intensities and high correlations with concentrations. And those Raman shifts are more likely to be the positions of main Raman peaks. Methods: PLS2 and SIMPLS 9/19
Limitation of PLSR Raman signal = Raman spectrum + Instable background Traditional PLSR only considers the intensities information of Raman signals without separating the Raman spectrum from the instable background. Motivation: Use only Raman Peaks (Raman spectrum) to do PLS regression 10/19
Outline Introduction Raman Scattering and Raman Spectrum Introduction to SERS Cancer detection by SERS The State of the Art Method Partial Least Squares (PLS) Regression Problem for Raman spectrum Our Method CWT-PLS Regression 11/19
Continuous Wavelet Transform (CWT) Definition of CWT: Example: Mexican hat wavelet function x(τ): one Raman signal τ : Raman shifts variable ψa,b(τ) : a series of wavelet functions a = 1,..., s : scale variable b = 1,...,Dx : translation variable C(a, b) : 2D matrix of wavelet coefficients. 12/19
Peaks Extraction The intensities of the Raman spectrum x(τ) at Raman peak region [τ1, τ2] can be represented as: x(τ) = P(τ) + B(τ) + G + E(τ) P(τ): Raman peak Background = B(τ) + G B(τ) : an odd function G : a constant E(τ): random noise Average CWT coefficients C 13/19
CWT-PLS Algorithm Training (1-5) Testing (6-8) 14/19
Experiment Data Sets Data sets description Average Mixture Raman spectra 15/19
Experiment Design Cross Validation on Duplicate testing spectra (CVD): All 5 duplicate spectra of the same mixing ratio are treated as the testing samples, and all the other mixture signals are treated as the training samples. Cross Validation on Average testing spectra (CVA): The average spectrum of the 5 duplicates with the same ratio is treated as the testing sample and all the other duplicate spectra are treated as training samples. Cross Validation on Average testing Average training spectra (CVAA): The average spectrum of the 5 duplicates with the same ratio is treated as the testing sample and all the other average spectra are treated as training samples 16/19
Experiment Results Definition of Square Root of Mean Squares Error (RMSE): Compare different methods 17/19
The Utilization of Raman Peaks 18/19
Thanks