| In this dissertation, the super-resolution method that we use for image restoration is the Poisson Maximum A-Posteriori (MAP) super-resolution algorithm of Hunt, computed with an iterative form. This algorithm is similar to the Maximum Likelihood of Holmes, which is derived from an Expectation/Maximization (EM) computation. Image restoration of point source data is our focus. This is because most astronomical data can be regarded as multiple point source data with a very dark background. The statistical limits imposed by photon noise on the resolution obtained by our algorithm are investigated. We improve the performance of the super-resolution algorithm by including the additional information of the spatial constraints. This is achieved by applying the well-known CLEAN algorithm, which is widely used in astronomy, to create regions of support for the potential point sources. Real and simulated data are included in this paper. The point spread function (psf) of a diffraction limited optical system is used for the simulated data. The real data is two dimensional optical image data from the Hubble Space Telescope. |
