Reconstructed power spectra from the inferred initial conditions from a BORG analysis with unknown foreground contamination for the robust likelihood (left panel) and the Poissonian likelihood (right panel) over the full range of Fourier modes considered in this work. The σ limit corresponds to the cosmic variance . The colour scale shows the evolution of the power spectrum with the sample number. The power spectra of the individual realizations, after the initial burn-in phase, from the robust likelihood analysis possess the correct power across all scales considered, demonstrating that the foregrounds have been properly accounted for. In contrast, the standard Poissonian analysis exhibits spurious power artefacts due to the unknown foreground contaminations, yielding excessive power on these scales.