Authors: J. Bobin
Language: IDL
Download: IDL
Description: The scripts required to compute the CMB map from WMAP and Planck data


Local-generalised morphological component analysis is an extension to GMCA. Similarly to GMCA it is a Blind Source Separation method which enforces sparsity. The novel aspect of LGMCA, however is that the mixing matrix changes across pixels allowing LMCA to deal with emissions sources which vary spatially.

Running LGMCA on the WMAP9 temperature products requires the main script and a selection of mandatory files, algorithm parameters and map parameters.



Authors: J. Bobin
Language: Matlab and Python
Download: Python | Matlab
Description: A toolbox for solving Blind Source Separation problems.



GMCALab is a set of Matlab toolboxes that focus on solving Blind Source Separation problems from multichannel/multispectral/hyperspectral data. In essence, multichannel data provide different observations of the same physical phenomena (e.g. multiple wavelengths, ), which are modeled as a linear combination of unknown elementary components or sources:

\(\mathbf{Y} = \mathbf{A}\mathbf{S},\)

where \(\mathbf{Y}\) is the data matrix, \(\mathbf{S}\) is the source matrix, and \(\mathbf{A}\) is the mixing matrix. The goal of blind source separation is to retrieve \(\mathbf{A}\) and \(\mathbf{S}\) from the knwoledge of the data only.

Generalized Morphological Component Analysis, a.k.a. GMCA, is a BSS method that enforces the sparsity of the sought-after sources:


A lightweight Matlab/Octave version of the GMCALab toolbox is available at this location. Illustrations are provide here.

Please check out the project's GitHub page.

It is worth noting that GMCA provides a very generic framework that has been extended to tackle different matrix factorization problems:

  • Non-negative matrix factorization with nGMCA
  • Separation of partially correlated sources with AMCA
  • The decomposition of hyperspectral data with HypGMCA (available soon)
  • The analysis of multichannel data in the presence of outliers with rAMCA at this location (updated the 14/06/16).
  • Robust BSS in transformed domains with tr-rGMCA . 

 We are now developping a python-based toolbox coined pyGMCALab, which is available at this location.

Blind separation of sparse sources in the presence of outliers


Authors: C.Chenot, J.Bobin
Journal: Signal Processing, Elsevier
Year: 2016
Download: Elsevier / Preprint





Blind Source Separation (BSS) plays a key role to analyze multichannel data since it aims at recovering unknown underlying elementary sources from observed linear mixtures in an unsupervised way. In a large number of applications, multichannel measurements contain corrupted entries, which are highly detrimental for most BSS techniques. In this article, we introduce a new {\it robust} BSS technique coined robust Adaptive Morphological Component Analysis (rAMCA). Based on sparse signal modeling, it makes profit of an alternate reweighting minimization technique that yields a robust estimation of the sources and the mixing matrix simultaneously with the removal of the spurious outliers. Numerical experiments are provided that illustrate the robustness of this new algorithm with respect to aberrant outliers on a wide range of blind separation instances. In contrast to current robust BSS methods, the rAMCA algorithm is shown to perform very well when the number of observations is close or equal to the number of sources.

CMB reconstruction from the WMAP and Planck PR2 data


Authors:  J. Bobin, F. Sureau and J. -L. Starck
Journal: A&A
Year: 2015
Download: ADS | arXiv


In this article, we describe a new estimate of the Cosmic Microwave Background (CMB) intensity map reconstructed by a joint analysis of the full Planck 2015 data (PR2) and WMAP nine-years. It provides more than a mere update of the CMB map introduced in (Bobin et al. 2014b) since it benefits from an improvement of the component separation method L-GMCA (Local-Generalized Morphological Component Analysis) that allows the efficient separation of correlated components (Bobin et al. 2015). Based on the most recent CMB data, we further confirm previous results (Bobin et al. 2014b) showing that the proposed CMB map estimate exhibits appealing characteristics for astrophysical and cosmological applications: i) it is a full sky map that did not require any inpainting or interpolation post-processing, ii) foreground contamination is showed to be very low even on the galactic center, iii) it does not exhibit any detectable trace of thermal SZ contamination. We show that its power spectrum is in good agreement with the Planck PR2 official theoretical best-fit power spectrum. Finally, following the principle of reproducible research, we provide the codes to reproduce the L-GMCA, which makes it the only reproducible CMB map.

Robust Sparse Blind Source Separation


Authors: C.Chenot, J.Bobin and J. Rapin
Journal: IEEE SPL 
Year: Nov. 2015
Download: IEEE Arxiv


Blind source separation is a widely used technique to analyze multichannel data. In many real-world applications, its results can be significantly hampered by the presence of unknown outliers. In this paper, a novel algorithm coined rGMCA (robust Generalized Morphological Component Analysis) is introduced to retrieve sparse sources in the presence of outliers. It explicitly estimates the sources, the mixing matrix, and the outliers. It also takes advantage of the estimation of the outliers to further implement a weighting scheme, which provides a highly robust separation procedure. Numerical experiments demonstrate the efficiency of rGMCA to estimate the mixing matrix in comparison with standard BSS techniques.