Application of convex optimization to acoustical array signal processing

作者：Bai Mingsian R^*; Chen Ching Cheng

来源：Journal of Sound and Vibration, 2013, 332(25): 6596-6616.

DOI：10.1016/j.jsv.2013.07.020

This paper demonstrates that optimum weighting coefficients and inverse filters for microphone arrays can be accomplished, with the aid of a systematic methodology of mathematical programming. Both far-field and near-field array problems are formulated in terms of convex optimization formalism. Three application examples, including data-independent far-field array design, nearfield array design, and pressure field interpolation, are presented. In far-field array design, array coefficients are optimized to tradeoff Directivity Index for White Noise Gain or the coefficient norm, while in nearfield array convex optimization is applied to design Equivalent Source Method-based Nearfield Acoustical Holography. Numerical examples are given for designing a far-field two-dimensional random array comprised of thirty microphones. For far-field arrays, five design approaches, including a Delay-And-Sum beamformer, a Super Directivity Array, three optimal arrays designed using l(1), l(2), and 1(infinity) - norms, are compared. Numerical and experimental results have shown that sufficiently high White Noise Gain was crucial to robust performance of array against sensor mismatch and noise. For nearfield arrays, inverse filters were designed in light of Equivalent Source Method and convex optimization to reconstruct the velocity field on a baffled spherical piston source. The proposed neartield design is benchmarked by those designed using Truncated Singular Value Decomposition and Tikhonov Regularization, Compressive Sampling and convex optimization is applied to pressure field reconstruction, source separation and modal analysis with satisfactory performance in both near-field and far-field microphone arrays.

• 出版日期2013-12-9
• 单位清华大学