| Suppose we wish to reconstruct a signal or image given samples of its discrete Fourier transform. The quality of the reconstruction depends upon the choice of samples. Given the sampling locations, a set containing the support of the image, a bound on the measurement error, and the region of interest to be reconstructed, one can calculate an error bound for the reconstruction. By minimizing this bound with respect to the choice of sampling locations, the optimal sampling scheme is identified.; We pursue three minimization strategies. First, traditional combinatorial optimization procedures are explored and a branch-and-probability-bound procedure in the spirit of Zhigljavsky's global optimization technique is proposed. Then approximation methods suggested by the formulation of the error bound are derived. Finally, we look for situations in which the optimal sampling scheme may be produced without a search. |
