BEADS Baseline Estimation And Denoising with Sparsity

Remove baseline, background or drift and random noise from (positive and) sparse signals (analytical chemistry, chromatographic peaks)

BEADS jointly addresses the problem of simultaneous baseline/trend/drift correction and (Gaussian, Poisson) noise reduction for 1D signals. It was designed for positive and sparse signals arising in analytical chemistry: chromatography, Raman spectroscopy, infrared, XRD, mass spectrometry, etc.). The baseline corresponds to slow-varying trends, instrumental drifts or background offset. The proposed BEADS baseline filtering algorithm is based on modeling of a series of (chromatogram) peaks as mostly positive, sparse with sparse derivatives, and on modeling the baseline as a low-pass signal. A convex optimization problems formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function, similar to a regularized l1 norm is utilized. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. It implements the method published in the paper "Chromatogram baseline estimation and denoising using sparsity (BEADS)", by Xiaoran Ning, Ivan W. Selesnick, Laurent Duval, in Chemometrics and Intelligent Laboratory Systems, December 2014, http://dx.doi.org/10.1016/j.chemolab.2014.09.014
The ZIP file contains two Matlab functions:
* a demonstration script (example.m);
* the main function (beads.m),
and an html readme help.
BEADS has since been used in 1D and 2D (GCxGC) chromatography, Raman spectroscopy, high-resolution mass spectrometry for astronomical hyperspectral data, electroencephalogram (EEG), electrocardiogram (ECG), arabic script analysis, power signal detrending for monitoring. Other uses, implementations in Python, R and C++ are provided at the BEADS page:
http://www.laurent-duval.eu/siva-beads-baseline-background-removal-filtering-sparsity.html