1210.6866 (Niels Oppermann et al.)

Reconstruction of Gaussian and log-normal fields with spectral smoothness    [PDF]

Niels Oppermann, Marco Selig, Michael R. Bell, Torsten A. Enßlin

We develop a method to infer log-normal random fields from measurement data affected by Gaussian noise. The log-normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders of magnitude. We use the formalism of minimum Gibbs free energy to derive an algorithm that uses the signal's correlation structure to regularize the reconstruction. The correlation structure, described by the signal's power spectrum, is thereby reconstructed from the same data set. We further introduce a prior for the power spectrum that enforces spectral smoothness. The appropriateness of this prior in different scenarios is discussed and its effects on the reconstruction's results are demonstrated. We validate the performance of our reconstruction algorithm in a series of one- and two-dimensional test cases with varying degrees of non-linearity and different noise levels.

View original: http://arxiv.org/abs/1210.6866