Estimation risk of transformation-averaged estimators

Juan Liu; Pierre Moulin

doi:10.1117/12.508038

13 November 2003 Estimation risk of transformation-averaged estimators

Juan Liu, Pierre Moulin

Proceedings Volume 5207, Wavelets: Applications in Signal and Image Processing X; (2003) https://doi.org/10.1117/12.508038
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

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.

Citation Download Citation

Juan Liu and Pierre Moulin "Estimation risk of transformation-averaged estimators", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.508038

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