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

Alpha- and beta-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.

nonnegative tensor factorization; nonlinear band expansion; magnetic resonance image; multi-spectral image

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