A Convex Approximation of the Relaxed Binaural Beamforming Optimization Problem

The recently proposed relaxed binaural beamforming (RBB) optimization problem provides a flexible tradeoff 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 semidefinite 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 that 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 tradeoff between predicted intelligibility and binaural-cue preservation than the SCO method.