An Alternative Proof for the Identifiability of Independent Vector Analysis Using Second Order Statistics

Dana Lahat (1) , Christian Jutten (1)

1 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing

In this paper, we present an alternative proof for characterizing the (non-) identifiability conditions of independent vector analysis (IVA). IVA extends blind source separation (BSS) to several mixtures by taking into account statistical dependencies across mixtures. We focus on IVA in the presence of real Gaussian data with temporally independent and identically distributed samples. This model is always non-identifiable when each mixture is considered separately. However, it can be shown to be generically identifiable within the IVA framework. Our proof differs from previous ones by being based on direct factorization of a closed-form expression for the Fisher information matrix (FIM). Our analysis is based on a rigorous linear algebraic formulation, and leads to a new type of factorization of a structured matrix. Therefore, the proposed approach is of potential interest for a broader range of problems.

Mots clés: Blind source separation; independent vector analysis; uniqueness; matrix factorization; data fusion

Domaines: Traitement du signal et de l'image [eess.SP]

Dana Lahat, Christian Jutten. An Alternative Proof for the Identifiability of Independent Vector Analysis Using Second Order Statistics. 2015. ⟨hal-01212027v1⟩