  The recently proposed relaxed binaural beamforming (RBB) optimization problem
provides a flexible trade-off between noise suppression and binaural-cue
preservation of the sound sources in the acoustic scene. It minimizes the
output noise power, under the constraints which guarantee that the target
remains unchanged after processing and the binaural-cue distortions of the
acoustic sources will be less than a user-defined threshold. However, the RBB
problem is a computationally demanding non-convex optimization problem. The
only existing suboptimal method which approximately solves the RBB is a
successive convex optimization (SCO) method which, typically, requires to solve
multiple convex optimization problems per frequency bin, in order to converge.
Convergence is achieved when all constraints of the RBB optimization problem
are satisfied. In this paper, we propose a semi-definite convex relaxation
(SDCR) of the RBB optimization problem. The proposed suboptimal SDCR method
solves a single convex optimization problem per frequency bin, resulting in a
much lower computational complexity than the SCO method. Unlike the SCO method,
the SDCR method does not guarantee user-controlled upper-bounded binaural-cue
distortions. To tackle this problem we also propose a suboptimal hybrid method
which combines the SDCR and SCO methods. Instrumental measures combined with a
listening test show that the SDCR and hybrid methods achieve significantly
lower computational complexity than the SCO method, and in most cases better
trade-off between predicted intelligibility and binaural-cue preservation than
the SCO method.
