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A fast full multigrid solver for applications in image processing
Author(s) -
Stürmer M.,
Köstler H.,
Rüde U.
Publication year - 2007
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.563
Subject(s) - multigrid method , solver , fast fourier transform , partial differential equation , discretization , mathematics , image processing , algorithm , elliptic partial differential equation , image (mathematics) , noise reduction , computer science , mathematical optimization , computer vision , mathematical analysis
We present a fast, cell‐centered multigrid solver and apply it to image denoising and non‐rigid diffusion‐based image registration. In both applications, real‐time performance is required in 3D and the multigrid method has to be compared with solvers based on fast Fourier transform (FFT). The optimization of the underlying variational approach results for image denoising directly in one time step of a parabolic linear heat equation, for image registration a non‐linear second‐order system of partial differential equations is obtained. This system is solved by a fixpoint iteration using a semi‐implicit time discretization, where each time step again results in an elliptic linear heat equation. The multigrid implementation comes close to real‐time performance for medium size medical images in 3D for both applications and is compared with a solver based on FFT using available libraries. Copyright © 2007 John Wiley & Sons, Ltd.