BEADS: Baseline Estimation And Denoising w/ Sparsity

Essentials:
BEADS paper : Baseline Estimation And Denoising w/ Sparsity
BEADS Matlab toolbox
BEADS Baseline toolbox at MatlabCentral
BEADS page: references, toolboxes and uses

Most signals and images can be split into broad classes of morphological features. There are five traditional classes, with potentially different names, although the dams are not fully waterproof:

• smooth parts: trends, backgrounds, wanders, continuums, biases, drifts or baselines,
• ruptures, discontinuities: contours, edges or jumps,
• harmonic parts: oscillations, resonances, geometric textures,
• hills: bumps, blobs or peaks,
• noises: un-modeled, more or less random, unstructured or stochastic.

In analytical chemistry,  many types of signals (chromatography, mass spectroscopy, Raman, NMR) resemble Fourier spectra: a quantity of positive bump-like peaks, representing the proportion of chemical compounds or atoms, over an instrumental baseline, with noise.

Individual  isolated peaks

Superimposed peaks

Sum of individual peaks

The present work (termed BEADS) combines a Baseline Estimation And Denoising. It features the use of the Sparsity of the peaks themselves, but also that of their higher-order derivatives. It also enforces positivity, with sparsity-promoting asymmetric L1 norms, or regularization thereof. A first version of the BEADS Matlab toolbox is provided. 

1D chromatogram with increasing baseline

Chromatogram baseline estimation and denoising using sparsity (BEADS), Xiaoran Ning, Ivan W. Selesnick, and Laurent Duval

Chemometrics and Intelligent Laboratory Systems, December 2014

Matlab toolbox: BEADS_toolbox.zip (v1.0)

This paper jointly addresses the problems of chromatogram baseline correction and noise reduction. The proposed approach is based on modeling the series of chromatogram peaks as sparse with sparse derivatives, and on modeling the baseline as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function is utilized. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods [Vincent Mazet's BackCor and airPLS] using both simulated and real chromatogram data, with Gaussian and Poisson noises

Asymmetric L1 penalty for positive signals

Keywords: baseline correction; baseline drift; sparse derivative; asymmetric penalty; low-pass filtering; convex optimization

• This paper jointly addresses the problems of chromatogram baseline correction and noise reduction.
• The series of chromatogram peaks are modeled as sparse with sparse derivatives.
• The baseline is modeled as a low-pass signal.
• A convex optimization problem is formulated so as to encapsulate these non-parametric models and a computationally efficient, iterative algorithm is developed.
• The performance is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data.

I would like to thank Vincent Mazet for excellent suggestions.