Damped second order flow applied to image denoising

Abstract In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementa...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 84; no. 6; pp. 1082 - 1111
Main Authors Baravdish, G, Svensson, O, Gulliksson, M, Zhang, Y
Format Journal Article
LanguageEnglish
Published Oxford University Press 27.12.2019
Subjects
damped Hamiltonian system
image denoising
inverse problems
Nonlinear flow
p-Laplace
p-parabolic
regularization
Störmer–Verlet
symplectic method
parabolic
inverse problems
regularization
damped Hamiltonian system
symplectic method
Störmer–Verlet
image denoising
nonlinear flow
Laplace
Stormer-Verlet
p-parabolic
p-Laplace
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Summary:Abstract In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF.
ISSN:0272-4960
1464-3634
1464-3634
DOI:10.1093/imamat/hxz027