Mathematics
Scientific paper
Feb 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...118..194n&link_type=abstract
Astronomy and Astrophysics, vol. 118, no. 1, Feb. 1983, p. 194-196.
Mathematics
7
Astronomical Maps, Brightness Distribution, Entropy, Polarized Light, Synthetic Apertures, Algorithms, Fourier Transformation, Iterative Solution, Matrices (Mathematics)
Scientific paper
In the maximum entropy method of reconstructing a brightness distribution B it has recently been recognized that a whole family of functions f(B) can be used in place of the usual choices f = ln B and f = -BlnB. In this note the authors suggest an analogous family of functions for polarized brightness distributions described by a correlation matrix Β. The entropy is shown to be the integral of the trace of f(Β) and reduces to the form given earlier by Ponsonby for the ln B case. The authors obtain an expression for the gradient of the entropy which is analogous to that for the unpolarized case and can be used in a similar way in an iterative scheme for finding the maximum entropy solution. Further, they show that the entropy is a convex function of the brightness matrix when farcsec<0, thus guaranteeing a unique maximum entropy solution consistent with the measurements.
Narayan Ramesh
Nityananda Rajaram
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