LAsLS Command-Line: Local Asymmetric Least Squares Baseline Correction

Standalone MATLAB function for Local Asymmetric Least Squares (LAsLS) baseline correction. LAsLS extends Asymmetric Least Squares (AsLS) by allowing different asymmetry parameters (pVals) and smoothing penalties (lambdasAsym) within user-defined intervals. Outside these intervals, symmetric weighting and a uniform smoothing penalty (lambdaWhit) are applied. A global first-derivative penalty (mu) enforces baseline tension across the full signal.

The baseline is estimated via Iteratively Reweighted Least Squares (IRLS):

(W + D' * diag(lambdaVec) * D + mu * L' * L) * baseline = W * y

Reference: Eilers, P. H. C., & Boelens, H. F. M. (2005). Baseline correction with asymmetric least squares smoothing. Leiden University Medical Centre Report, 1(1), 5.

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Usage

[baseline, weights] = LASLS_CL(y, intervals, pVals, lambdasAsym, lambdaWhit, mu, maxIter, tol);

Inputs

Parameter	Type	Description
y	(n x 1) vector	Input signal
intervals	(m x 2) matrix or cell	Each row defines [startIdx, endIdx] of a peak region
pVals	(m x 1) vector	Asymmetry parameter for each interval (small values ignore peaks)
lambdasAsym	(m x 1) vector	Local smoothing penalty for each interval
lambdaWhit	scalar	Smoothing penalty outside intervals
mu	scalar	Global first-derivative penalty (baseline tension)
maxIter	scalar	Maximum IRLS iterations
tol	scalar	Convergence tolerance (relative baseline change)

Outputs

Output	Type	Description
baseline	(n x 1) vector	Estimated baseline
weights	(n x 1) vector	Final IRLS weights

Example

y = rand(100,1)*10;
intervals = [10 20; 40 50];
pVals = [0.01; 0.001];
lambdasAsym = [1e4; 2e5];
lambdaWhit = 100;
mu = 1e3;
maxIter = 50;
tol = 1e-6;
[baseline, weights] = LASLS_CL(y, intervals, pVals, lambdasAsym, lambdaWhit, mu, maxIter, tol);

See test_LASLS_CL.m for a complete working example with synthetic data and visualization.

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Contents

File	Description
LASLS_CL.m	LAsLS baseline correction function
test_LASLS_CL.m	Test script with synthetic data, plots, and MSE evaluation

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Installation

Add to your MATLAB path:

addpath('path/to/LASLS_CL');

Dependencies

Built-in MATLAB functions only: spdiags, matrix division (\), norm.

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License

Released under the MIT License.

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Authors

• Adrian Gomez-Sanchez -- Universitat de Barcelona & Lovelace's Square, Barcelona, Spain
• Berta Torres-Cobos -- University of Copenhagen, Denmark & Lovelace's Square, Barcelona, Spain
• Rodrigo Rocha de Oliveira -- Universitat de Barcelona & Lovelace's Square, Barcelona, Spain