Iterative Reconstruction of Images from Incomplete Spectral Data

摘要

In various branches of engineering and science, one is confronted withmeasurements resulting in incomplete spectral data. The aim is to reconstruct to original data in the best possible way. This report investigates a few iterative techniques to accomplish this. The reconstruction problem can be viewed as solving an integral equation of the first kind. In turn, this equation can be rewritten into a equivalent integral equation of the second kind. This equation can be solved by using a Neumann type iterative method. It is shown that this scheme will converge and that it is equivalent to the socalled method of alternating orthogonal projections. The integral equation of the first kind can be taken 'as is' and tackled by an appropriate conjugate gradient scheme. Again, convergence of this scheme is shown. Finally a few illustrative numerical examples are presented and discussed.