Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty

Understand

The optimal reconstruction of cosmic metric perturbations and other signals requires knowledge of their power spectra and other parameters.

• If these are not known a priori, they have to be measured simultaneously from the same data used for the signal reconstruction.
• We formulate the general problem of signal inference in the presence of unknown parameters within the framework of information field theory.
• We develop a generic parameter uncertainty renormalized estimation (PURE) technique and address the problem of reconstructing Gaussian signals with unknown power-spectrum with five different approaches: (i) separate maximum-a-posteriori power spectrum measurement and subsequent reconstruction, (ii) maximum-a-posteriori power reconstruction with marginalized power-spectrum, (iii) maximizing the joint posterior of signal and spectrum, (iv) guessing the spectrum from the variance in the Wiener filter map, and (v) renormalization flow analysis of the field theoretical problem providing the PURE filter.