Blind separation of a large number of sparse sources

 

Authors: C. Kervazo, J. Bobin, C. Chenot
Journal: Signal Processing
Year: 2018
Download: Paper


Abstract

Blind Source Separation (BSS) is one of the major tools to analyze multispectral data with applications that range from astronomical to biomedical signal processing. Nevertheless, most BSS methods fail when the number of sources becomes large, typically exceeding a few tens. Since the ability to estimate large number of sources is paramount in a very wide range of applications, we introduce a new algorithm, coined block-Generalized Morphological Component Analysis (bGMCA) to specifically tackle sparse BSS problems when large number of sources need to be estimated. Sparse BSS being a challenging nonconvex inverse problem in nature, the role played by the algorithmic strategy is central, especially when many sources have to be estimated. For that purpose, the bGMCA algorithm builds upon block-coordinate descent with intermediate size blocks. Numerical experiments are provided that show the robustness of the bGMCA algorithm when the sources are numerous. Comparisons have been carried out on realistic simulations of spectroscopic data.

Blind separation of a large number of sparse sources

 

Authors: C. Kervazo, J. Bobin, C. Chenot
Journal: Signal Processing
Year: 2018
Download: Paper


Abstract

Blind Source Separation (BSS) is one of the major tools to analyze multispectral data with applications that range from astronomical to biomedical signal processing. Nevertheless, most BSS methods fail when the number of sources becomes large, typically exceeding a few tens. Since the ability to estimate large number of sources is paramount in a very wide range of applications, we introduce a new algorithm, coined block-Generalized Morphological Component Analysis (bGMCA) to specifically tackle sparse BSS problems when large number of sources need to be estimated. Sparse BSS being a challenging nonconvex inverse problem in nature, the role played by the algorithmic strategy is central, especially when many sources have to be estimated. For that purpose, the bGMCA algorithm builds upon block-coordinate descent with intermediate size blocks. Numerical experiments are provided that show the robustness of the bGMCA algorithm when the sources are numerous. Comparisons have been carried out on realistic simulations of spectroscopic data.

NMF with Sparse Regularizations in Transformed Domains

 

Authors: J. Rapin, J. Bobin, A. Larue, J.-L. Starck
Journal: SIAM
Year: 2014
Download: ADS | arXiv


Abstract

Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Sparsity is known to enhance such contrast between the sources while producing very robust approaches, especially to noise. In this paper we introduce a new algorithm in order to tackle the blind separation of non-negative sparse sources from noisy measurements. We first show that sparsity and non-negativity constraints have to be carefully applied on the sought-after solution. In fact, improperly constrained solutions are unlikely to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA (non-negative Generalized Morphological Component Analysis), makes use of proximal calculus techniques to provide properly constrained solutions. The performance of nGMCA compared to other state-of-the-art algorithms is demonstrated by numerical experiments encompassing a wide variety of settings, with negligible parameter tuning. In particular, nGMCA is shown to provide robustness to noise and performs well on synthetic mixtures of real NMR spectra.

Sparse and Non-Negative BSS for Noisy Data

 

Authors: J. Rapin, J. Bobin, A. Larue, J.-L. Starck
Journal: IEEE
Year: 2013
Download: ADS | arXiv


Abstract

Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Sparsity is known to enhance such contrast between the sources while producing very robust approaches, especially to noise. In this paper we introduce a new algorithm in order to tackle the blind separation of non-negative sparse sources from noisy measurements. We first show that sparsity and non-negativity constraints have to be carefully applied on the sought-after solution. In fact, improperly constrained solutions are unlikely to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA (non-negative Generalized Morphological Component Analysis), makes use of proximal calculus techniques to provide properly constrained solutions. The performance of nGMCA compared to other state-of-the-art algorithms is demonstrated by numerical experiments encompassing a wide variety of settings, with negligible parameter tuning. In particular, nGMCA is shown to provide robustness to noise and performs well on synthetic mixtures of real NMR spectra.

Hyperspectral BSS Using GMCA With Spatio-Spectral Sparsity Constraints

 

Authors: Y, Moudden, J. Bobin
Journal: IEEE
Year: 2014
Download: IEEE


Abstract

Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Sparsity is known to enhance such contrast between the sources while producing very robust approaches, especially to noise. In this paper we introduce a new algorithm in order to tackle the blind separation of non-negative sparse sources from noisy measurements. We first show that sparsity and non-negativity constraints have to be carefully applied on the sought-after solution. In fact, improperly constrained solutions are unlikely to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA (non-negative Generalized Morphological Component Analysis), makes use of proximal calculus techniques to provide properly constrained solutions. The performance of nGMCA compared to other state-of-the-art algorithms is demonstrated by numerical experiments encompassing a wide variety of settings, with negligible parameter tuning. In particular, nGMCA is shown to provide robustness to noise and performs well on synthetic mixtures of real NMR spectra.

Blind Source Separation: the Sparsity Revolution

 

Authors: J. Bobin, J.-L. Starck, Y. Moudden, J. M. Fadili
Journal: AIEP
Year: 2008
Download: HAL


Abstract

Over the last few years, the development of multi-channel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsity-based BSS method coined Generalized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyperspectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Numerical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation.

Sparsity and Morphological Diversity in Blind Source Separation

 

Authors: J. Bobin, J.-L. Starck, J. Fadili, Y. Moudden
Journal: IEEE
Year: 2007
Download: IEEE


Abstract

Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. Here, we give some new and essential insights into the use of sparsity in source separation, and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper introduces a new BSS method coined generalized morphological component analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient BSS method. We present arguments and a discussion supporting the convergence of the GMCA algorithm. Numerical results in multivariate image and signal processing are given illustrating the good performance of GMCA and its robustness to noise.

Morphological diversity and source separation

 

Authors: J. BobinY. Moudden, J.-L. Starck, M. Elad
Journal: IEEE
Year: 2006
Download: IEEE


Abstract

This letter describes a new method for blind source separation, adapted to the case of sources having different morphologies. We show that such morphological diversity leads to a new and very efficient separation method, even in the presence of noise. The algorithm, coined multichannel morphological component analysis (MMCA), is an extension of the morphological component analysis (MCA) method. The latter takes advantage of the sparse representation of structured data in large overcomplete dictionaries to separate features in the data based on their morphology. MCA has been shown to be an efficient technique in such problems as separating an image into texture and piecewise smooth parts or for inpainting applications. The proposed extension, MMCA, extends the above for multichannel data, achieving a better source separation in those circumstances. Furthermore, the new algorithm can efficiently achieve good separation in a noisy context where standard independent component analysis methods fail. The efficiency of the proposed scheme is confirmed in numerical experiments.