Using learned priors to regularize the Helmholtz equation least-squares method

The Journal of the Acoustical Society of America, vol. 155, pp. 971–983

Abstract

The Helmholtz equation least-squares (HELS) method is a valuable tool for estimating equivalent sound sources of a radiating object. It solves an inverse problem by mapping measured pressures to a set of basis functions satisfying the Helmholtz equation in spherical coordinates. However, this problem is often ill-posed, necessitating additional regularization methods, in which often variations of Ridge or Lasso are used. These conventional methods do not explicitly consider the distribution underlying the source radiations (besides sparsity) and are often used in the context of obtaining only a point estimate, even in the presence of ambiguity in the data. In this work, we propose the use of empirical priors through a normalizing flow model to enhance the inversion results obtained with the HELS method. We first validate our approach using numerical data and subsequently demonstrate its superior performance in interpolating a measured violin directivity compared to Lasso and Ridge methods, even when optimal regularization parameters are selected.

Authors 3

1. Thiago Henrique Gomes Lobato

   HEAD Acoustics (Germany)

   Affiliation as printed

   HEAD acoustics GmbH 1 , Herzogenrath, 52134, Germany

2. Roland Sottek

   HEAD Acoustics (Germany)

   Affiliation as printed

   HEAD acoustics GmbH 1 , Herzogenrath, 52134, Germany

3. Michael Vorländer Aachen Institute for Hearing Technology and Acoustics

   RWTH Aachen University

   Affiliation as printed

   Institute for Hearing Technology and Acoustics, RWTH Aachen University 2 , Aachen, 52074, Germany