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| Content Provider | Springer Nature Link |
|---|---|
| Author | Plonka, Gerlind Heinen, Dennis |
| Copyright Year | 2012 |
| Abstract | We propose a new algorithm for denoising of multivariate function values given at scattered points in $${\mathbb{R}^{d}}$$ . The method is based on the one-dimensional wavelet transform that is applied along suitably chosen path vectors at each transform level. The idea can be seen as a generalization of the relaxed easy path wavelet transform by Plonka (Multiscale Model Simul 7:1474–1496, 2009) to the case of multivariate scattered data. The choice of the path vectors is crucial for the success of the algorithm. We propose two adaptive path constructions that take the distribution of the scattered points as well as the corresponding function values into account. Further, we present some theoretical results on the wavelet transform along path vectors in order to indicate that the wavelet shrinkage along path vectors can really remove noise. The numerical results show the efficiency of the proposed denoising method. |
| Ending Page | 354 |
| Page Count | 18 |
| Starting Page | 337 |
| File Format | |
| ISSN | 14226383 |
| e-ISSN | 14209012 |
| Journal | Results in Mathematics |
| Issue Number | 3 |
| Volume Number | 62 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2012-08-18 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Wavelets Image processing path vectors Mathematics Scattered data denoising wavelet shrinkage easy path wavelet transform Wavelets and other special systems |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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