EMSC

EMSC corrects multiplicative scatter effects and additive baseline variations in spectral data. For each row, the spectrum is modeled as a scaled reference spectrum combined with a polynomial baseline. The fitted baseline is subtracted, and the result is divided by the fitted reference coefficient.

The EMSC app lets users apply the method and choose the reference and polynomial order, inspect the correction, apply it to all rows, and export the result.

Start

addpath('path/to/EMSC')
EMSC_test
app = EMSC(spectra);

The constructor also accepts a struct:

input.data = spectra;
input.wavelength = wavelength;
input.reference = reference;      % optional custom reference
app = EMSC(input);

The empty constructor opens the data selector. If no x-axis is supplied, channel numbers are used.

Input

Purpose	Accepted values
Spectra	Numeric matrix, or data/spectra in a struct
X-axis	wavelength/wavelengths, optional
Custom reference	reference/customReference, optional

Values must be real and finite. The x-axis must have one value per channel and must increase or decrease without repeats. A reference must have one value per channel. Without a custom reference, the app uses the mean or median spectrum.

Method

For each spectrum y, the app compares it with a reference spectrum r and fits:

y = b*r + c0 + c1*x + ... + cp*x^p + residual

The additive and polynomial terms describe the baseline and the coefficient b describes the overall scale of the sample. The corrected result is:

(y - (c0 + c1*x + ... + cp*x^p)) / b

The x-axis is scaled before the polynomial is fitted. The calculation uses a stable matrix solve and rejects designs that do not contain enough independent information, or have a zero or very small multiplicative coefficient.

Parameter	Values	Default
Polynomial order	0 to 6	2
Reference	Mean, median, or custom	Mean

Result

After Apply, app.getData() returns:

• data and spectra: corrected matrix
• wavelength and wavelengths: x-axis values
• reference: reference used for the correction
• multiplicativeCoefficients and nuisanceCoefficients
• metadata: method, parameters, source, rank, and condition estimate

The preview shows one selected sample, and the sample selector can be used to inspect other rows. Result plotting can still show the mean or multiple corrected spectra. This does not change the full exported matrix. Export checks MATLAB variable names and asks before overwriting an existing variable.

Example data and checks

EMSC_test.m creates spectra, wavelength, and reference with known scatter and polynomial baseline effects:

EMSC_test
app = EMSC(spectra);

Run Code Analyzer from this folder:

checkcode('EMSC.m', '-id')
checkcode('business_logic/@EMSCCorrector/EMSCCorrector.m', '-id')
checkcode('business_logic/@EMSCDataValidator/EMSCDataValidator.m', '-id')

MATLAB R2022a or later is required. No additional toolbox is needed.

Reference

Martens, H. and Stark, E. (1991). Extended multiplicative signal correction and spectral interference subtraction. Journal of Pharmaceutical and Biomedical Analysis, 9(8), 625-635.

License: MIT