Abstract
We conduct an asymptotic risk analysis of the nonlocal means image denoising algorithm for the Horizon class of images that are piecewise constant with a sharp edge discontinuity. We prove that the mean square risk of an optimally tuned nonlocal means algorithm decays according to n- 1log1 /2+εn, for an n×n-pixel image with ε>0. This decay rate is an improvement over some of the predecessors of this algorithm, including the linear convolution filter, median filter, and the SUSAN filter, each of which provides a rate of only n- 2/3. It is also within a logarithmic factor from optimally tuned wavelet thresholding. However, it is still substantially lower than the optimal minimax rate of n- 4/3.
Original language | English (US) |
---|---|
Pages (from-to) | 370-387 |
Number of pages | 18 |
Journal | Applied and Computational Harmonic Analysis |
Volume | 33 |
Issue number | 3 |
DOIs | |
State | Published - Nov 2012 |
Keywords
- Denoising
- Horizon class
- Linear filter
- Minimax risk
- Nonlocal means
- SUSAN filter
- Wavelet thresholding
ASJC Scopus subject areas
- Applied Mathematics