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29 March 2024
 
  » arxiv » math.NA/0010242

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Numerical Analysis of the Non-uniform Sampling Problem
Thomas Strohmer ;
Date 25 Oct 2000
Subject Numerical Analysis MSC-class: 65T40, 65F22, 42A10, 94A12 | math.NA
AbstractWe give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays a key role in the numerical solution of the non-uniform sampling problem. In the one approach (often proposed in the literature) the finite-dimensional model leads to an ill-posed problem even in very simple situations. The other approach that we consider leads to a well-posed problem that preserves important structural properties of the original infinite-dimensional problem and gives rise to efficient numerical algorithms. Furthermore a fast multilevel algorithm is presented that can reconstruct signals of unknown bandwidth from noisy non-uniformly spaced samples. We also discuss the design of efficient regularization methods for ill-conditioned reconstruction problems. Numerical examples from spectroscopy and exploration geophysics demonstrate the performance of the proposed methods.
Source arXiv, math.NA/0010242
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