Abstract
In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of finding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p α(L p), p ≥ 1, the optimization corresponds to convex programming in the wavelet domain. The algorithm simultaneously achieves signal interpolation and wavelet denoising, which makes it particularly suitable for noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.
| Original language | English (US) |
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| Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |
| Editors | M.A. Unser, A. Aldroubi, A.F. Laine |
| Pages | 16-27 |
| Number of pages | 12 |
| Volume | 5207 |
| Edition | 1 |
| State | Published - 2003 |
| Event | Wavelets: Applications in Signal and Image Processing X - San Diego, CA, United States Duration: Aug 4 2003 → Aug 8 2003 |
Other
| Other | Wavelets: Applications in Signal and Image Processing X |
|---|---|
| Country/Territory | United States |
| City | San Diego, CA |
| Period | 8/4/03 → 8/8/03 |
Keywords
- Besov
- Denoising
- Interpolation
- Regularization
- Wavelet
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Condensed Matter Physics