Blind multispectral image decomposition by 3D nonnegative tensor factorization

Alpha-divergence-based nonnegative tensor factorization (NTF) is applied to blind multispectral image (MSI) decomposition. The matrix of spectral profiles and the matrix of spatial distributions of the materials resident in the image are identified from the factors in Tucker3 and PARAFAC models. NTF preserves local structure in the MSI that is lost as a result of vectorization of the image when nonnegative matrix factorization (NMF)- or independent component analysis (ICA)-based decompositions are used. Moreover, NTF based on the PARAFAC model is unique up to permutation and scale under mild conditions. To achieve this, NMF- and ICA-based factorizations, respectively, require enforcement of sparseness (orthogonality) and statistical independence constraints on the spatial distributions of the materials resident in the MSI, and these conditions do not hold. We demonstrate efficiency of the NTF-based factorization in relation to NMF- and ICA-based factorizations on blind decomposition of the experimental MSI with the known ground truth.