Processing Stationary Noise
SIAM Journal on Imaging Sciences(2014)
摘要
Additive or multiplicative stationary noise recently became an
important issue in applied fields such as microscopy or satellite
imaging. Relatively few works address the design of dedicated
denoising methods compared to the usual white noise setting. We
recently proposed a variational algorithm to tackle this issue. In
this paper, we analyze this problem from a statistical point of
view and provide deterministic properties of the solutions of the
associated variational problems. In the first part of this work,
we demonstrate that in many practical problems, the noise can be
assimilated to a colored Gaussian noise. We provide a quantitative
measure of the distance between a stationary process and the
corresponding Gaussian process. In the second part, we focus on
the Gaussian setting and analyze denoising methods which consist
in minimizing the sum of a total variation term and an $l^2$ data
fidelity term. While the constrained formulation of this problem
allows us to easily tune the parameters, the Lagrangian
formulation can be solved more efficiently since the problem is
strongly convex. Our second contribution consists in providing
analytical values of the regularization parameter in order to
approximately reach a given noise level.
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关键词
stationary noise,Berry--Esseen theorem,Morozov principle,negative norm models,destriping,convex analysis and optimization,94A08,65K10,49M29,60F05
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