Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage

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 B1 1(L1(I)) the functional F − g 2 L2(I) + λ g B1 1 (L1(I)). We use the theory of 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 : the largest α ...

• Type: Journal
• Year: 1998
• Where: TIP
• Authors: Antonin Chambolle, Ronald A. DeVore, Nam-Yong Lee, Bradley J. Lucier
• Keywords: Image, Shrinkage Parameter, TIP 1998, Variational Problems