A fast algorithm for joint diagonalization with application to blind source separation

We present a new approach to approximate joint diagonalization of a set of matrices. The main advantages of our method are computational efficiency and generality. The algorithm is based on the Frobeniusnorm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non-orthogonal transformation. The iterative scheme of the algorithm inherits the key ideas from the classical Levenberg-Marquardt algorithm, re-interpreted for a multiplicative iteration update, which is more suitable for the joint diagonalization task than traditional additive iteration updates. The algorithm’s efficiency stems from the sparse approximation of the cost function. Extensive numerical simulations illustrate the performance of the algorithm by a comparison to other leading diagonalization methods and demonstrate its capability to perform blind source separation without requiring the usual pre-whitening of the data.