2020
DOI: 10.1109/tsp.2020.2974651
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Quaternion Non-Negative Matrix Factorization: Definition, Uniqueness, and Algorithm

Abstract: This article introduces quaternion non-negative matrix factorization (QNMF), which generalizes the usual nonnegative matrix factorization (NMF) to the case of polarized signals. Polarization information is represented by Stokes parameters, a set of 4 energetic parameters widely used in polarimetric imaging. QNMF relies on two key ingredients: (i) the algebraic representation of Stokes parameters thanks to quaternions and (ii) the exploitation of physical constraints on Stokes parameters. These constraints gene… Show more

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Cited by 20 publications
(17 citation statements)
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“…Activation maps are chosen such that the pure pixel condition is satisfied. Such conditions guarantee that the QNMF X 0 = W 0 H 0 satisfies the necessary uniqueness condition given in [6,Prop. 3].…”
Section: A Illustrationmentioning
confidence: 98%
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“…Activation maps are chosen such that the pure pixel condition is satisfied. Such conditions guarantee that the QNMF X 0 = W 0 H 0 satisfies the necessary uniqueness condition given in [6,Prop. 3].…”
Section: A Illustrationmentioning
confidence: 98%
“…Importantly, these two matrix factorization problems are not independent, for two reasons: (i) the activation matrix H is a common factor and (ii) the very nature of the polarization constraint (S) links the real and imaginary parts of the source matrix W. In full generality, QNMF greatly improves NMF model identifiablity by taking advantage of supporting polarization informationfundamental properties that can be measured in most optical imaging setups. From a theoretical perspective, we derive in [6] sufficient conditions (for P = 2 sources) and necessary uniqueness conditions (for P ≥ 2 sources). Compared to their NMF counterparts [11]- [14], these conditions appear far less restrictive -in particular, one may recover QNMF uniqueness even when sources never vanish, a case where NMF is known to be not unique.…”
Section: B Relation With Nmfmentioning
confidence: 99%
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