Sparse Component Analysis: A General Framework for Linear and Nonlinear Blind Source Separation and Mixture Identificati
In this chapter, we consider two closely related data processing tasks. The first one is Blind Source Separation (BSS), which consists in estimating a set of unknown source data (one-dimensional signals, images, ...) from observed mixtures of these data,
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Sparse Component Analysis: A General Framework for Linear and Nonlinear Blind Source Separation and Mixture Identification Yannick Deville
Abstract In this chapter, we consider two closely related data processing tasks. The first one is Blind Source Separation (BSS), which consists in estimating a set of unknown source data (one-dimensional signals, images, ...) from observed mixtures of these data, while the mixing operator has unknown parameter values. The second task is Blind Mixture Identification (BMI), which aims at estimating these unknown parameter values of the mixing operator. We provide a unified view and describe the latest extensions of the general framework that we have been developing for BSS and BMI since the beginning of the 2000s. This framework yields a wide range of BSS/BMI methods applicable to various types of sources (one-dimensional signals, images, ...) mixed according to various models (linear instantaneous, anechoic, full convolutive, nonlinear and especially linear-quadratic), possibly with non-negativity or sum-to-one constraints. This framework is based on the concept of joint sparsity of the source data, considered in various domains (original temporal or spatial domain, transformed representation in time-frequency or time-scale/wavelet domain, ...). More precisely, the proposed methods essentially require a few tiny zones, in mixed signals or in their transformed versions, where only one of the source “signals” is active, i.e., nonzero. They therefore set very limited constraints on source sparsity and could then be considered as “quasi-non-sparse component analysis” methods. Besides, unlike Independent Component Analysis methods, they are suited to correlated sources. We also discuss their application to various data processing functions, ranging from audio signal separation to unmixing of hyperspectral remote sensing images.
Y. Deville (B) Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, UPS-CNRS-OMP, 14 Avenue Edouard Belin, 31400 Toulouse, France e-mail: [email protected] G. R. Naik and W. Wang (eds.), Blind Source Separation, Signals and Communication Technology, DOI: 10.1007/978-3-642-55016-4_6, © Springer-Verlag Berlin Heidelberg 2014
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Y. Deville
6.1 Introduction In this chapter, we consider two closely related data processing tasks. The first one is Blind Source Separation (BSS), which is a generic signal processing problem, where the term “signal” is to be understood in a broad sense: it may especially refer to one-dimensional (1D) series (e.g., depending on a time or wavelength variable) or to two-dimensional (2D) data (e.g., images), but also to more general types of data. BSS consists in estimating a set of unknown “source signals” from observed mixtures of these data, while the mixing operator is most often only partly known: it is known to belong to a given linear or nonlinear class, but it has unknown parameter values. The second task that we consider is Blind Mixture Identification (BMI), which consists in
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