Background Estimation in Chemical Spectra

This program estimates the background (or baseline) of optical spectra by the polynomial minimizing a cost function. If the cost function was quadratic, the solution is the least squares estimation, which is not appropriate in this problem. Instead, we need to use of non-quadratic cost function such as the symmetrical Huber function, the symmetrical truncated quadratic or their respective asymmetrical shape.

The next figure shows a screenshot of the program, with an example of a background estimation (in red) on a simulated spectrum (in blue). The polynomial order is set to 4, and the cost function is the asymmetric truncated quadratic with threshold equals 0.08.


The program backcor is the new version of the former backest (released in 2008). The main difference is the avaibility of a graphical user interface (of course, it can be not used).

The program is written in Matlab and should work with Matlab 6 (or higher). The ZIP file to download contains two Matlab script:

  • demo allows you to run the program with a simulated spectrum;
  • backcor is the main function which can be run with or without a graphical user interface.

Type help backcor in Matlab to get the syntax of the function.

Download - Matlab version, 4.7 kb, 11/2012.


  • Développement de méthodes de traitement de signaux spectroscopiques : estimation de la ligne de base et du spectre de raies. V. Mazet. Ph.D. thesis, University Henri Poincaré, Nancy 1. Defended on 01/12/2005.
  • Background removal from spectra by designing and minimising a non-quadratic cost function. V. Mazet, C. Carteret, D. Brie, J. Idier, B. Humbert. Chemometrics and Intelligent Laboratory Systems, vol. 76, no. 2, p. 121-133, april 2005.
  • Baseline Spectrum Estimation using Half-Quadratic Minimization. V. Mazet, D. Brie, J. Idier. EUSIPCO 2004, p. 305-308, 6-10 september 2004, Vienna, Austria.
  • Estimation de l'arrière-plan de spectres par différentes méthodes dérivées des moindres carrés. V. Mazet, J. Idier, D. Brie, B. Humbert, C. Carteret. Chimiométrie 2003, 3-4 december 2003, Paris, France.