Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982a%26a...112..181p&link_type=abstract
Astronomy and Astrophysics, Vol.112, P. 181, 1982
Astronomy and Astrophysics
Astrophysics
Scientific paper
The problem of formulating a two-dimensional maximum entropy spectral density is examined. It is shown that the derivative of the two-dimensional entropy rate with respect to the autocorrelations are related to the spectral density. However, the entropy density cannot be related to the error powers of a single prediction-error filter as it can in the one-dimensional case. Rather, it was found to be a function of all the error powers of a set of two- dimensional predictors. The expression relating the entropy and prediction-error filtering contains limits in each of the x and y directions. The maximum entropy principle cannot be used to approximate the x and y limits simultaneously and it is necessary to make a maximum likelihood type of assumption in at least one direction. Nevertheless, the resolutions in the spectral estimates, thus obtained, are superior to those in spectra determined by traditional techniques. It is not clear how the maximum entropy principle can be applied to both directions simultaneously.
This work has significant astronomical impact since it is analogous to the problem of constructing a spatial radio brightness distribution from the measured values of its two-dimensional Fourier transform. In this context, the radio measurements correspond to the sample autocorrelations and the two-dimensional distribution of intensity corresponds to the spectral density. It is important to reconstruct the astronomical image which is consistent with the known data and at the same time, makes minimal assumptions about those data which are unavailable.
Pendrel Vv. J.
Smylie Douglas E.
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