Bobin Jérôme, Starck Jean-Luc, Fadili Jalal, Moudden Yassir
DAPNIA/SEDI-SAP, Service d'Astrophysique, CEA/Saclay, 91191 Gif sur Yvette, France
IEEE Trans Image Process. 2007 Nov;16(11):2662-74. doi: 10.1109/tip.2007.906256.
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-caIled 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 emergedas 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.
在过去几年中，多通道传感器的发展激发了人们对多元数据相干处理方法的兴趣。一些具体问题已经得到解决，关于所谓的盲源分离（BSS）问题的大量文献证明了这一点。在这种情况下，正如先前工作所明确强调的，要检索的源呈现出一些可定量测量的差异是至关重要的。最近，稀疏性和形态多样性已成为BSS一种新颖且有效的差异源。在此，我们对源分离中稀疏性的使用给出一些新的重要见解，并概述形态多样性作为源之间差异或对比度来源的重要作用。本文介绍了一种新的BSS方法，即广义形态成分分析（GMCA），它利用最近的稀疏超完备或冗余信号表示，兼具形态多样性和稀疏性的优势。GMCA是一种快速高效的BSS方法。我们给出支持GMCA算法收敛的论据和讨论。给出了多元图像和信号处理中的数值结果，说明了GMCA的良好性能及其对噪声的鲁棒性。
