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| Médium: | Preprint |
| Vydáno: |
2000
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| Témata: | |
| On-line přístup: | https://arxiv.org/abs/math/0010242 |
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| _version_ | 1866912655185281024 |
|---|---|
| author | Strohmer, Thomas |
| author_facet | Strohmer, Thomas |
| contents | We 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0010242 |
| institution | arXiv |
| publishDate | 2000 |
| record_format | arxiv |
| spellingShingle | Numerical Analysis of the Non-uniform Sampling Problem Strohmer, Thomas Numerical Analysis 65T40, 65F22, 42A10, 94A12 We 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. |
| title | Numerical Analysis of the Non-uniform Sampling Problem |
| topic | Numerical Analysis 65T40, 65F22, 42A10, 94A12 |
| url | https://arxiv.org/abs/math/0010242 |