Maximum contrast analysis for nonnegative blind source separation

In this paper, we propose a maximum contrast analysis (MCA) method for nonnegative blind source separation, where both the mixing matrix and the source signals are nonnegative. We first show that the contrast degree of the source signals is greater than that of the mixed signals. Motivated by this observation, we propose an MCA-based cost function. It is further shown that the separation matrix can be obtained by maximizing the proposed cost function. Then we derive an iterative determinant maximization algorithm for estimating the separation matrix. In the case of two sources, a closed-form solution exists and is derived. Unlike most existing blind source separation methods, the proposed MCA method needs neither the independence assumption, nor the sparseness requirement of the sources. The effectiveness of the new method is illustrated by experiments using X-ray images, remote sensing images, infrared spectral images, and real-world fluorescence microscopy images.

[1]  Aapo Hyvrinen,et al.  Fast and Robust Fixed-Point Algorithms , 1999 .

[2]  James V. Stone.  Blind Source Separation Using Temporal Predictability , 2001, Neural Computation.

[3]  Dennis R. Morgan,et al.  Permutation inconsistency in blind speech separation: investigation and solutions , 2005, IEEE Transactions on Speech and Audio Processing.

[4]  Soo-Young Lee.  Blind Source Separation and Independent Component Analysis: A Review , 2005 .

[5]  Chong-Yung Chi,et al.  Nonnegative Least-Correlated Component Analysis for Separation of Dependent Sources by Volume Maximization , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Andrzej Cichocki,et al.  New Algorithms for Non-Negative Matrix Factorization in Applications to Blind Source Separation , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[7]  Chong-Yung Chi,et al.  Blind Separation of Multichannel Biomedical Image Patterns by Non-negative Least-Correlated Component Analysis , 2006, PRIB.

[8]  Hairong Qi,et al.  Endmember Extraction From Highly Mixed Data Using Minimum Volume Constrained Nonnegative Matrix Factorization , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[9]  Mohamed-Jalal Fadili,et al.  Sparsity and Morphological Diversity in Blind Source Separation , 2007, IEEE Transactions on Image Processing.

[10]  Jean-Luc Starck,et al.  Blind Source Separation: the Sparsity Revolution , 2008 .

[11]  Van Khanh Nguyen,et al.  Blind Separation of Mutually Correlated Sources Using Precoders , 2010, IEEE Transactions on Neural Networks.

[12]  Andrzej Cichocki,et al.  Improved M-FOCUSS Algorithm With Overlapping Blocks for Locally Smooth Sparse Signals , 2008, IEEE Transactions on Signal Processing.

[13]  Sen Jia,et al.  Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[14]  Wensheng Yu,et al.  Blind source separation based on phase and frequency redundancy of cyclostationary signals , 2004 .

[15]  Dietrich Lehmann,et al.  Nonsmooth nonnegative matrix factorization (nsNMF) , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Emanuele Salerno,et al.  Blind spectral unmixing by local maximization of non-Gaussianity , 2008, Signal Process..

[17]  Terrence J. Sejnowski,et al.  Slow Feature Analysis: Unsupervised Learning of Invariances , 2002, Neural Computation.

[18]  Roy E. Marsten,et al.  Feature Article - Interior Point Methods for Linear Programming: Computational State of the Art , 1994, INFORMS J. Comput..

[19]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[20]  Ignacio Santamaría,et al.  A spectral clustering approach to underdetermined postnonlinear blind source separation of sparse sources , 2006, IEEE Transactions on Neural Networks.

[21]  Guoqing Wang,et al.  Independent component analysis and its applications in signal processing for analytical chemistry , 2008 .

[22]  Chong-Yung Chi,et al.  A Convex Analysis Framework for Blind Separation of Non-Negative Sources , 2008, IEEE Transactions on Signal Processing.

[23]  Fabian J. Theis,et al.  Sparse component analysis and blind source separation of underdetermined mixtures , 2005, IEEE Transactions on Neural Networks.

[24]  Seungjin Choi.  Blind Source Separation and Independent Component Analysis : A Review , 2004 .

[25]  A. J. Bell,et al.  A Unifying Information-Theoretic Framework for Independent Component Analysis , 2000 .

[26]  Mineichi Kudo,et al.  Performance analysis of minimum /spl lscr//sub 1/-norm solutions for underdetermined source separation , 2004, IEEE Transactions on Signal Processing.

[27]  Hieu Minh Trinh,et al.  A new blind method for separating M+1 sources from M mixtures , 2010, Comput. Math. Appl..

[28]  Visa Koivunen,et al.  Identifiability, separability, and uniqueness of linear ICA models , 2004, IEEE Signal Processing Letters.

[29]  Yuanqing Li,et al.  Probability estimation for recoverability analysis of blind source separation based on sparse representation , 2006, IEEE Transactions on Information Theory.