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Signal Processing techniques for Raman spectroscopy
Transcript of Signal Processing techniques for Raman spectroscopy
Rock forming: Limestone, marble
Studied by CV Raman
Inelastic scattering of light
Signal processing techniques
in Raman spectroscopy
Case study: Calcite-dolomite mixtures
MNCN CSIC - FI UPM
Independent Component Analysis
Digital Filter Analysis
Spectra mixing for FastICA
2 concentration profile models
1. Peaks concentration profile
49x49 Raman spectra sampled on a rectangular area.
2. Random concentration profile
10x10 Raman spectra with random concentrations
Raman Spectra mixing
Spectra mixing for filter analysis
Independent Component Analysis (ICA)
Model follows the equation: x = As
Non-Gaussian, non overlapping.
IC physically interpretable.
Algorithm: FastICA for MATLAB
1. Prewhitening: PCA
2. Rotation: ICA
a) Initial b) Mixed c) Whitened
a) Principal components
b) Independent components
Calcite-dolomite demixing with ICA
1. Peaks concentration
2. Random concentration
Dot product: 0.99999
Both calcite 10% and dolomite 10%
Digital filter analysis
Time domain signal: Inverse FFT
Raman spectrum modelled as filter
Objective: Pole-zero representation
Digital filter models
1. AR model
2. ARMA model
ICA very good qualitative and quantitative separator.
Better than available methods.
Exact concentration profile estimator.
Raman spectra analysis as filter is possible.
Very interesting properties.
Need to confirm data with real samples.
Results should not diverge by much.