# Solution of ill-posed problem in plane wave decomposition for sound field reconstruction

## Palavras-chave:

room acoustics, inverse problems, plane wave decomposition, virtual microphone array, sound field reconstruction## Resumo

Plane-wave decomposition is a recently developed technique in the field of acoustics that stems from

an approximation in the inverse spatial tri-dimensional Fourier transform so that it considers that the sound field

is represented by the superposition of plane waves traveling in well-defined directions. The calculations for the

technique involve the solution of an ill-posed matrix equation, requiring a regularized solution for the least squares

problem. This paper will show the implementation of the plane wave decomposition using Tikhonov regularization

in the context of a simulated and a measured impedance tube. The classical L-curve algorithm and a fixed-point

algorithm for the calculation of the regularization parameter were investigated and compared with the goal of

defining which technique produces the least error in this scenario. The reconstructions of the transfer functions

in both the simulated case and the measured case were realised, with the fixed-point algorithm displaying an

advantage over the L-curve with respect to reconstruction errors in both scenarios.