Wavenumber spectrum determination for aeroacoustic applications using FISTA

This conference paper deals with computational methods to determine the wavenumber spectrum of acoustical data measured by a phased microphone array. Such problems occur e.g. within the analysis of pressure fluctuations due to a turbulent boundary layer on a surface such as a wind-tunnel wall or the skin of an aircraft. The problem is closely related to the deconvolution of dirty beamforming maps in wavenumber domain, which seeks to determine the wavenumber spectrum by removing the influence of the shift-invariant point spread function from the beamforming result. Firstly, we recall how this task can be formulated as a minimization problem and then discuss a specific solver for this problem, provided by the framework of the generalized FISTA algorithm. The resulting method takes advantage of the convolutional structure of the gradient of the data misfit functional and allows further for a flexible regularization with L1 and L2 penalties as well as a nonnegativity constraint. Finally, the presented algorithmic framework is demonstrated with numerical examples