Abstract
Wavelet image denoising practice has shown that the performance of simple estimators may be substantially improved by averaging these estimators over a collection of transformations such as translations or rotations. In this paper, we explain and quantify these empirical findings using estimation theory. We consider a general nonlinear observation model, analyze the estimation risk of transformation-averaged estimators, and derive an upper bound on the risk reduction due to transformation averaging. The bound is evaluated for several estimators, using different averaging strategies (including a randomized strategy) and different wavelet bases. The practical usefulness of the bound is established for standard image denoising examples.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 87-96 |
| Number of pages | 10 |
| Journal | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 5207 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2003 |
| Event | Wavelets: Applications in Signal and Image Processing X - San Diego, CA, United States Duration: Aug 4 2003 → Aug 8 2003 |
Keywords
- Estimation risk
- Invariance
- Transformation groups
- Wavelets
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering