We will report on significant improvements of some of the algorithms for reconstruction of band-limited signals from non-uniform sampling sets. Although the methods apply in principle to any dimension we shall put special emphasis in this report on the application to band-limited images. Especially the combination of the ideas of the Adaptive Weights Method suggested by Feichtinger and Gröchenig with the conjugate gradient approach is better than the methods described so far in the literature, sometimes by several orders of magnitude. There is also experimental evidence that a combination of the steepest descent method with the use of a suitable relaxation parameter gives very often a highly efficient reconstruction method. In case of product sampled images successive 1D reconstruction performs best. Several examples illustrate the results.

Keywords: algorithms, irregular sampling, numerical work

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