Low Rank Regularized Equivalent Source Method for Sound Field Reconstruction

Abstract

Aiming at the numerical instability problem that probably exists in the process of calculating the equivalent source strengths, this paper proposes a low rank regularized equivalent source method to improve the anti-noise characteristics and sound field reconstruction accuracy under the condition of low SNR by the means of multiple measurements. In the method, a matrix that contains certain multiply measured data vectors on the hologram surface is firstly composed. After that, a low rank matrix recovery problem of computing the equivalent source strengths is established by minimizing a convex optimization function. Furthermore, the l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf> norm is simultaneously added to the noise matrix formed by multiple noise vectors corresponding to the measurements to make the matrix more column sparse for suppressing the influence of the noise on the reconstruction accuracy. Numerical simulation results show that the proposed method can obtain higher reconstruction accuracy than the equivalent source method with Tikhonov regularization and prove the effectiveness and robustness of the method.