A Frequency-Domain BSS Method Based on ℓ1 Norm, Unitary Constraint, and Cayley Transform

We propose a frequency-domain blind source separation method that uses (a) the ℓ
₁
norm of orthonormal vectors of estimated source signals as a sparsity measure and (b) Cayley transform for optimizing the objective function under the unitary constraint in the Riemannian geometry approach. The orthonormal vectors of estimated source signals, obtained by the sphering of observed mixed signals and the unitary constraint on the separation filters, enables us to use the ℓ
₁
norm properly as a sparsity measure. The Cayley transform enables us to handle the geometrical aspects of the unitary constraint efficiently. According to the simulation of a two-channel case, the proposed method achieved a 20-dB improvement in the source-to-interference ratio in a room with a reverberation time of T
₆₀
= 300ms.