Blind decomposition of low‐dimensional multi‐spectral image by sparse component analysis

A multilayer hierarchical alternating least square nonnegative matrix factorization approach has been applied to blind decomposition of low‐dimensional multi‐spectral image. The method performs blind decomposition exploiting spectral diversity and spatial sparsity between materials present in the image and, unlike many blind source separation methods, is invariant with respect to statistical (in)dependence among spatial distributions of the materials. As opposed to many existing blind source separation algorithms, the method is capable of estimating the unknown number of materials present in the image. This number can be less than, equal to, or greater than the number of spectral bands. The method is validated on underdetermined blind source separation problems associated with blind decomposition of experimental red‐green‐blue images composed of four materials. Achieved performance has been superior when compared against methods based on minimization of the ℓ1‐norm: linear programming and interior‐point methods. In addition to tumor demarcation, as demonstrated in the paper, other areas that can also benefit from the proposed method include cell, chemical, and tissue imaging. Copyright © 2009 John Wiley & Sons, Ltd.

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

[2]  José M. Bioucas-Dias,et al.  Does independent component analysis play a role in unmixing hyperspectral data? , 2005, IEEE Trans. Geosci. Remote. Sens..

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

[4]  Chein-I Chang,et al.  Linear spectral random mixture analysis for hyperspectral imagery , 2002, IEEE Trans. Geosci. Remote. Sens..

[5]  Andrzej Cichocki,et al.  Nonnegative matrix factorization with constrained second-order optimization , 2007, Signal Process..

[6]  Andrzej Cichocki,et al.  Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization , 2007, ICA.

[7]  Ivica Kopriva,et al.  Visualization of basal cell carcinoma by fluorescence diagnosis and independent component analysis. , 2007, Photodiagnosis and photodynamic therapy.

[8]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[9]  Qian Du,et al.  Independent-component analysis for hyperspectral remote sensing imagery classification , 2006 .

[10]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[11]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[12]  Liqing Zhang,et al.  Flexible Component Analysis for Sparse, Smooth, Nonnegative Coding or Representation , 2007, ICONIP.

[13]  Ivica Kopriva,et al.  Unsupervised decomposition of low-intensity low-dimensional multi-spectral fluorescent images for tumour demarcation , 2009, Medical Image Anal..

[14]  J. Settle,et al.  Linear mixing and the estimation of ground cover proportions , 1993 .

[15]  Yuanqing Li,et al.  Analysis of Sparse Representation and Blind Source Separation , 2004, Neural Computation.

[16]  Qian Du,et al.  Automated Target Detection and Discrimination Using Constrained Kurtosis Maximization , 2008, IEEE Geoscience and Remote Sensing Letters.

[17]  David Luengo,et al.  A general solution to blind inverse problems for sparse input signals , 2005, Neurocomputing.

[18]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[19]  Paul E. Johnson,et al.  Spectral mixture modeling: A new analysis of rock and soil types at the Viking Lander 1 Site , 1986 .

[20]  Michael Zibulevsky,et al.  Underdetermined blind source separation using sparse representations , 2001, Signal Process..

[21]  Edmund R. Malinowski,et al.  Determination of the number of factors and the experimental error in a data matrix , 1977 .

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

[23]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[24]  Christian Jutten,et al.  Estimating the mixing matrix in Sparse Component Analysis (SCA) based on partial k-dimensional subspace clustering , 2008, Neurocomputing.

[25]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[26]  José M. Bioucas-Dias,et al.  Vertex component analysis: a fast algorithm to unmix hyperspectral data , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[27]  Chein-I Chang,et al.  Estimation of number of spectrally distinct signal sources in hyperspectral imagery , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[28]  E. M. Winter,et al.  Anomaly detection from hyperspectral imagery , 2002, IEEE Signal Process. Mag..

[29]  R. Springett,et al.  Fluorescence Photodiagnostics and Photobleaching Studies of Cancerous Lesions using Ratio Imaging and Spectroscopic Techniques , 2000, Lasers in Medical Science.

[30]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

[31]  Andrzej Cichocki,et al.  Multilayer Nonnegative Matrix Factorization Using Projected Gradient Approaches , 2007, Int. J. Neural Syst..

[32]  Bernd J Pichler,et al.  A hyperspectral fluorescence system for 3D in vivo optical imaging , 2006, Physics in medicine and biology.

[33]  Michael D. Morris,et al.  Estimating the number of pure chemical components in a mixture by maximum likelihood , 2007 .

[34]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[35]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[36]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

[37]  S. Amari,et al.  Nonnegative Matrix and Tensor Factorization [Lecture Notes] , 2008, IEEE Signal Processing Magazine.

[38]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[39]  Michael P. Friedlander,et al.  Probing the Pareto Frontier for Basis Pursuit Solutions , 2008, SIAM J. Sci. Comput..

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

[41]  Daniel W. C. Ho,et al.  Underdetermined blind source separation based on sparse representation , 2006, IEEE Transactions on Signal Processing.

[42]  Carin Sandberg,et al.  Fluorescence contrast and threshold limit: implications for photodynamic diagnosis of basal cell carcinoma. , 2003, Journal of photochemistry and photobiology. B, Biology.

[43]  H Stepp,et al.  Diagnosing Cancer in Vivo , 2001, Science.