The acoustic inverse problem in the framework of alternating direction method of multipliers

Abstract

Acoustic imaging is an important technique for sound source identification which is widely used in noise control and fault detection. It can be described as a method for reconstructing the amplitude and phase distribution of an acoustic field in a given plane. When the size of radiating object is huge and measurement environment is noisy, accuracy and efficiency of acoustic imaging algorithm deteriorate easily. In this paper, a novel computational framework is investigated to simplify the algorithm and balance computation speed with accuracy. It converts acoustic imaging into an inverse problem and then divides this problem into two parts including forward model and denoising model. This computation framework is based on the alternating direction method of multipliers, which makes parallel implementation and distributed optimization possible, especially for large scale measurements. It is assumed that the acoustic field is composed of a cluster of monopole sources and the equivalent source method is taken to solve the acoustic inverse problem. Both L2-norm penalization based on the minimal energy assumption and Lp-norm (0<p⩽1) penalization based on the sparsity hypothesis are taken in this framework. Thus, the regularization parameter in the algorithm, which balances the standard least square error and the norm of the source solution, can be coupled with some pre-existing methods incluing L-curve, GCV and Bayesian strategies. Different regularization parameters are proposed and the comparison is made in this paper. The proposed method provides a general and convenient method for different type of sound source priors and it is validated with an experiment.