Nonlinear Wavelet Image Processing: Variational Problems, Compression, and Noise Removal through Wavelet Shrinkage (1996)
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| Venue: | IEEE Trans. Image Processing |
| Citations: | 137 - 8 self |
BibTeX
@ARTICLE{Chambolle96nonlinearwavelet,
author = {Antonin Chambolle and Ronald A. DeVore and Nam-yong Lee and Bradley J. Lucier},
title = {Nonlinear Wavelet Image Processing: Variational Problems, Compression, and Noise Removal through Wavelet Shrinkage},
journal = {IEEE Trans. Image Processing},
year = {1996},
volume = {7},
pages = {319--335}
}
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Abstract
This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; in particular, we show that wavelet shrinkage can be considered the exact minimizer of the following problem: given an image F defined on a square I, minimize over all g in the Besov space B 1 1 (L1 (I)) the functional #F - g# 2 L 2 (I) + ##g# B 1 1 (L 1 (I)) .Weusethetheoryof nonlinear wavelet image compression in L2 (I) to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i.i.d., mean zero, Gaussian noise. A new signal-tonoise ratio, which we claim more accurately reflects the visual perception of noise in images, arises in this derivation. We present extensive computations that support the hypothesis that near-optimal shrinkage parameters can be derived if one knows (or can estimate) only two parameters about an image F:thelarge...
