MCRLLM: Multivariate Curve Resolution by Log-Likelihood Maximization.

X = CS
where
X(nxk): Spectroscopic data where n spectra acquired over k energy levels
C(nxa): Composition map based on a MCRLLM components
S(axk): Spectra of the a components as computed by MCRLLM

Method first presented in

Lavoie F.B., Braidy N. and Gosselin R. (2016) Including Noise Characteristics in MCR to improve Mapping and Component Extraction from Spectral Images, Chemometrics and Intelligent Laboratory Systems, 153, 40-50.

Input data

Algorithm is designed to treat 2D data X(nxk) where n spectra acquired over k energy levels.
A 3D spectral image X(n1,n2,k) can be reshaped to a 2D matrix X(n1xn2,k) prior to MCRLLM analysis. Composition maps can then be obtained by reshaping C(n1xn2,a) into 2D chemical maps C(n1,n2,a).

Examples

Two full examples, along with datasets, are provided in 'Download Files'.
Please refer to 'MCRLLM_example.pdf' for full details.

• Example 1: 1D spectral linescan of EELS data.
• Example 2: 2D spectral image of XPS data.

Compatibility

MCRLLM tested on Python 3.7 using the following modules:
Numpy 1.17.2
Scipy 1.3.1
Sklearn 0.21.3
Pysptools 0.15.0
Tqdm 4.36.1