Article
Non-Linear Model Based Regularisation for the Sound Field Synthesis Problem (en)
* Presenting author
Abstract:
The sound field synthesis (SFS) problem is described with a first kind Fredholm integral equation, typically aiming at finding the optimum driving weights for the loudspeakers, which are arranged as a dense reproduction setup. This constitutes an ill-posed, inverse problem, which for numerical driven approaches, needs to be discretised. Such problems can now be tackled with neural network (NN) regression models. Recently in the literature, the NN-based mapping from sound pressure to optimised acoustic source strengths and the NN-based mapping from given reference source strengths to optimised source strengths have been dealt with by using different loss functions and NN architectures. An important issue of the SFS problem is the regularisation of the solution, a well-known feature of traditional pressure matching approaches. In this paper we discuss the fundamental similarities and differences of having the regularisation learned from large data for non-linear vs. linear inversion. For that we initially utilise 2D free-field SFS using circular loudspeaker arrays and complex-valued NN models trained with synthesised data. The linear combination of the discrete SFS pressure matching problem’s singular vectors for differently optimum driving sources give insights to the different regularisations, their robustness and generalisation.