Damped second order flow applied to image denoising

G. Baravdish; O. Svensson; M. Gulliksson; Y. Zhang

doi:10.1093/imamat/hxz027

Damped second order flow applied to image denoising

G. Baravdish, O. Svensson, M. Gulliksson, Y. Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1082-1111
Number of pages	30
Journal	IMA Journal of Applied Mathematics
Volume	84
Issue number	6
DOIs	https://doi.org/10.1093/imamat/hxz027
Publication status	Published - 27 Dec 2019

Keywords

Störmer-Verlet
damped Hamiltonian system
image denoising
inverse problems
nonlinear flow
p-Laplace
p-parabolic
regularization
symplectic method

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10.1093/imamat/hxz027

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title = "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 implementation, based on the St{\"o}rmer-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.",

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AU - Baravdish, G.

AU - Svensson, O.

AU - Gulliksson, M.

AU - Zhang, Y.

PY - 2019/12/27

Y1 - 2019/12/27

N2 - 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.

AB - 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.

KW - Störmer-Verlet

KW - damped Hamiltonian system

KW - image denoising

KW - inverse problems

KW - nonlinear flow

KW - p-Laplace

KW - p-parabolic

KW - regularization

KW - symplectic method

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VL - 84

SP - 1082

EP - 1111

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 6

ER -

Damped second order flow applied to image denoising

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Keywords

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