Distortionless acoustic beamforming with enhanced sparsity based on reweighted ℓ1-norm minimization

Acoustic beamforming enables us to record a distant talker's speech signal from a certain direction while rejecting simultaneous interfering speech signals from other directions in the presence of noise using an array of microphones. It finds application in directional speech enhancement, 3-D sound/speech separation, video or teleconferencing, speech recognition in smart home devices etc. The most popular beamformer is the minimum power distortionless response (MPDR) beamformer which minimizes the power of the beamformer output while putting a distortionless constraint in the desired direction. To improve the performance of the MPDR beamformer, sparse beamformers which minimize the ℓ<inf>1</inf>-norm of the beamformer output while having the same distortionless constraint have been proposed. In this work, we propose a sparse beamformer based on a customized merit function for sparsity that provides a better approximation to the sparsity inducing ℓ<inf>0</inf>-norm than the ℓ<inf>1</inf>-norm thereby reducing the bias of the ℓ<inf>1</inf>-norm based sparse beamformers. The formulation of the proposed beamformer and the algorithm to solve the resulting sparse optimization problem are presented. Using various objective measures, simulation results show that the proposed acoustic beamformer performs better in reverberant room environments in eliminating interfering residuals and performs better in distant speech recognition applications.