A Convex Approximation of the Relaxed Binaural Beamforming Optimization Problem

TL;DR

This paper introduces a convex relaxation approach to solve the relaxed binaural beamforming optimization problem more efficiently, balancing noise reduction and binaural cue preservation with lower computational cost.

Contribution

It proposes a semi-definite convex relaxation method for RBB, reducing complexity, and a hybrid approach combining SDCR and SCO to improve performance.

Findings

SDCR achieves lower computational complexity than SCO.

Hybrid method balances noise suppression and binaural-cue preservation.

Experimental results show improved trade-offs over existing methods.

Abstract

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.