Stability of independent vector analysis

Independent vector analysis (IVA) is a method for solving the permutation problem that is inherent in the frequency-domain independent component analysis for convoluted mixtures. IVA utilizes inner dependency among the frequency components of each source. It is formulated as a problem of minimizing a measure that represents difference between a prior probability density function (pdf) of the set of frequency components and the actual pdf of the output of the demixing process. Although the effectiveness of the IVA method has been demonstrated by many applications, there are very few mathematical analyses of the algorithm. This paper shows a remarkable proposition that proves the validity of IVA: if the desired demixing process minimizes the measure, any permuted one never becomes a local minimum.