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

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

2010-02-15

arxiv.org/abs/1002.2928v3

Phys.Rev.D83:105014,2011

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

21 pages, 5 figures, accepted by PRD

Scientific paper

10.1103/PhysRevD.83.105014

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. In all cases, the reconstruction can be described or approximated as Wiener filter operations with assumed signal spectra derived from the data according to the same recipe, but with differing coefficients. All of these filters, except the renormalized one, exhibit a perception threshold in case of a Jeffreys prior for the unknown spectrum. Data modes, with variance below this threshold do not affect the signal reconstruction at all. Filter (iv) seems to be similar to the so called Karhune-Loeve and Feldman-Kaiser-Peacock estimators for galaxy power spectra used in cosmology, which therefore should also exhibit a marginal perception threshold if correctly implemented. We present statistical performance tests and show that the PURE filter is superior to the others.

Affiliated with

Also associated with

No associations

Rating

Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-146432