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Session 107 - Radio Astronomy and VLBI Instruments.
Display session, Thursday, January 16
Estimation of the true source emission signature from an observed data set corrupted by the detection process is a classical inverse problem arising in both imaging and spectroscopic observations. The data are generally distorted due to the finite spatial, spectral and/or temporal response of the instrument. Furthermore, noise can be introduced into the data via the detection process, and in some cases the data can be partially corrupted, saturated or even lost. If the number of observed data points is greater than or equal to the number of independent variables, the inverse problem is well-posed and can be uniquely solved if a feasible solution exists. In principle, maximum likelihood estimation (MLE) methods can be applied to problems of this type; in practice, numerical problems usually arise due to ill-conditioning. If the number of observed data points is less than the number of independent variables due to missing data, the problem is ill- posed and generally an infinite set of MLE solutions exist. We develop a maximum entropy method with MLE constraints suitable for both the ill- and well-posed cases. For the ill-posed case the method chooses out of the infinite set of MLE solutions that which has maximal entropy, i.e. the least informative solution, thereby mitigating against an over interpretation of the data. The MLE constraints also insure that, for the well- posed case, the solution must be the unique MLE solution if a feasible solution exists. This insures continuity across the boundary between the ill- and well-posed cases. This work suggests the possibility that maximum likelihood estimation theory may be interpreted as a subset of maximum entropy theory. Spectroscopic and imaging examples are shown as demonstrations.
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