Nonlinear Band Expansion and 3D Nonnegative Tensor Factorization for Blind Decomposition of Magnetic Resonance Image of the Brain

α- and β-divergence based nonnegative tensor factorization (NTF) is combined with nonlinear band expansion (NBE) for blind decomposition of the magnetic resonance image (MRI) of the brain. Concentrations and 3D tensor of spatial distributions of brain substances are identified from the Tucker3 model of the 3D MRI tensor. NBE enables to account for the presence of more brain substances than number of bands and, more important, to improve conditioning of the expanded matrix of concentrations of brain substances. Unlike matrix factorization methods NTF preserves local spatial structure in the MRI. Unlike ICA-, NTF-based factorization is insensitive to statistical dependence among spatial distributions of brain substances. Efficiency of the NBE-NTF algorithm is demonstrated over NBE-ICA and NTF-only algorithms on blind decomposition of the realistically simulated MRI of the brain.

[1]  Chein-I Chang,et al.  Band Expansion-Based Over-Complete Independent Component Analysis for Multispectral Processing of Magnetic Resonance Images , 2008, IEEE Transactions on Biomedical Engineering.

[2]  Andrzej Cichocki,et al.  Blind decomposition of low‐dimensional multi‐spectral image by sparse component analysis , 2009 .

[3]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

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

[5]  Chein-I. Chang.  Hyperspectral Data Exploitation: Theory and Applications , 2007 .

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

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

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

[9]  P. Tichavský,et al.  Efficient variant of algorithm fastica for independent component analysis attaining the cramer-RAO lower bound , 2005, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005.

[10]  Toshiharu Nakai,et al.  Application of independent component analysis to magnetic resonance imaging for enhancing the contrast of gray and white matter , 2004, NeuroImage.

[11]  José M. Bioucas-Dias,et al.  Does independent component analysis play a role in unmixing hyperspectral data? , 2003, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Erkki Oja,et al.  Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound , 2006, IEEE Transactions on Neural Networks.

[13]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

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

[15]  Alan C. Evans,et al.  MRI Simulation Based Evaluation and Classifications Methods , 1999, IEEE Trans. Medical Imaging.

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

[17]  A. Evans,et al.  MRI simulation-based evaluation of image-processing and classification methods , 1999, IEEE Transactions on Medical Imaging.

[18]  Andrzej Cichocki,et al.  Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations , 2009, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[19]  Andrzej Cichocki,et al.  Blind multispectral image decomposition by 3D nonnegative tensor factorization. , 2009, Optics letters.