Abstract
In various branches of engineering and science, one is confronted with measurements resulting in incomplete spectral data. The problem of the reconstruction of an image from such a data set can be formulated in terms of an integral equation of the first kind. Consequently, this equation can be converted into an equivalent integral equation of the second kind which can be solved by a Neumann-type iterative method. It is shown that this Neumann expansion is an error-reducing method and that it is equivalent to the Papoulis - Gerchberg algorithm for band-limited signal extrapolation. The integral equation can also be solved by employing a conjugate gradient iterative scheme. Again, convergence of this scheme is demonstrated. Finally a number of illustrative numerical examples are presented and discussed.
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