Reconstruction of a polarized brightness distribution by the maximum entropy method

Abstract

A general expression for the entropy E of a polarized brightness map B is obtained in terms of a general function f. An expression is also obtained for the gradient of E with respect to unmeasured Fourier coefficients of B, and it is shown that the map B-max which maximizes E is f-prime (B-max) bandlimited. Iterative numerical schemes to obtain B-max can be developed from these results as for the scalar brightness case. It is shown that if f-double prime is less than zero, then there is only one solution for B-max which maximizes E. This will lend robustness to numerical algorithms since convergence to the unique solution is assured.