A link between the decomposition of a third-order tensor in rank-(L,L,1) terms and Joint Block Diagonalization

In this paper, we show that the Block Component Decomposition in rank-(L,L,1) terms of a third-order tensor, referred to as BCD-(L,L,1), can be reformulated as a Joint Block Diagonalization (JBD) problem, provided that certain assumptions on the dimensions are satisfied. This JBD-based reformulation leads to a new uniqueness bound for the BCD-(L,L,1). We also propose a closed-form solution to solve exact JBD problems. For approximate JBD problems, this closed-form solution yields a good starting value for iterative optimization algorithms. The performance of our technique is illustrated by its application to blind CDMA signal separation.