Nonorthogonal joint diagonalization with diagonal constraints

Joint diagonalization has attracted much attention and many algorithms have been presented by far. However, some ambiguities still exist in the objective functions for joint diagonalization. In this paper, some criterion are proposed to eliminate above ambiguities at first, and then a new objective function which satisfies these criterion is presented. The new objective function introduces diagonal constraints for joint diagonalization, thus the trivial and unbalance solutions are excluded easily. Exactly jointly diagonalizable theorem is built to interpret the reasonableness of the new objective function and the conjugate gradient method is used to provide fast and reliable convergence. Finally, nonorthogonal joint diagonalization algorithm with diagonal constraints (DDiag) is developed. Simulations show that DDiag is efficient and robust.