A study of identifibility for blind source separation via non-orthogonal joint diagonalization

The problem of blind source separation (BSS) using joint diagonalization of a set of non-unitary eigen-matrices that are obtained with the observed signal vector sequence is addressed in this paper. A theoretical study is conducted of the identifiability of joint diagonalization of non-orthogonal matrices so as to generalize some known results for the orthogonal case. In particular, a mathematical proof is provided for essential uniqueness of general joint diagonalization, that is to say, all the estimated mixing matrices extracted from the non-unitary eigen-matrix group are essentially equal within an arbitrary permutation and scaling. The non-orthogonal identifiability theorem given in this paper serves as a mathematical foundation for the BSS methods based on the non-orthogonal joint diagonalization.