ITERATIVE RECONSTRUCTION OF IMAGES FROM INCOMPLETE SPECTRAL DATA

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