Sound Field Reproduction via the Alternating Direction Method of Multipliers Based Lasso Plus Regularized Least-Square

This paper proposes a 3-D sound field reproduction (SFR) approach through the combination of alternating direction method of multipliers (ADMM)-based least-absolute shrinkage and selection operator (Lasso) and regularized least square (LS). The proposed SFR method is split into two parts through the pressure matching optimization of loudspeaker positions and the computation of driving signals. At the first part, a plurality of candidate positions of loudspeakers in planar array is given and, then, the active speaker selection method is proposed based on ADMM complex Lasso algorithm for selecting the optimal loudspeaker positions. Afterwards, regularized LS is adopted to calculate the selected loudspeaker weights and control the total power. The numerical simulation experiments demonstrate that the proposed SFR scheme outperforms the existing sparse loudspeakers' placement and weight optimization algorithms especially in under-sampled sound fields. Meanwhile, the evaluations also confirmed that the proposed method could significantly reduce the computational complexity of the active loudspeaker selection compared to the state-of-the-art Lasso-based SFR. Effectively, the proposed method uses a relatively small number of loudspeakers for a satisfying reproduction quality.