Abstract
In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximum-smoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space B q α (L p), the optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space W α(L 2), the optimization reduces to a simple weighted least-squares problem. An optional wavelet shrinkage regularization step makes the algorithm suitable for even noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.
| Original language | English (US) |
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| Title of host publication | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 1645-1648 |
| Number of pages | 4 |
| Volume | 3 |
| State | Published - 1999 |
| Event | Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99) - Phoenix, AZ, USA Duration: Mar 15 1999 → Mar 19 1999 |
Other
| Other | Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99) |
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| City | Phoenix, AZ, USA |
| Period | 3/15/99 → 3/19/99 |
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering
- Acoustics and Ultrasonics