The wave-number-frequency spectra of a pressure field beneath a turbulent boundary layer is considered, with the aim of removing the effect of the measuring device. A rotating antenna of aligned microphones has been used in previous studies, and the measured spectra are shown to be a convolution of the true spectra with the transfer function of said antenna. Deconvolution algorithms that were previously developed for other fields of studies are presented. Test cases and processing of experimental data are used to assess their applicability. A hybrid approach of both deconvolution and interpolation, to artificially refine the azimuthal discretization, is found to be best at estimating both narrowband and broadband components of the spectra.