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A nonlinear multigrid method for total variation minimization from image restoration. (English) Zbl 1129.65046
Summary: Image restoration has been an active research topic and variational formulations are particularly effective in high quality recovery. Although there exist many modelling and theoretical results, available iterative solvers are not yet robust in solving such modeling equations. Recent attempts on developing optimisation multigrid methods have been based on first order conditions. Different from this idea, this paper proposes to use piecewise linear function spanned subspace correction to design a multilevel method for directly solving the total variation minimisation. Our method appears to be more robust than the primal-dual method by {\it T. F. Chan, G. H. Golub}, and {\it P. Mulet} [SIAM J. Sci. Comput. 20, No. 6, 1964--1977 (1999; Zbl 0929.68118)] previously found reliable. Supporting numerical results are presented.

MSC:
65K10Optimization techniques (numerical methods)
49J20Optimal control problems with PDE (existence)
49M27Decomposition methods in calculus of variations
94A08Image processing (compression, reconstruction, etc.)
68U10Image processing (computing aspects)
65F10Iterative methods for linear systems
Software:
KELLEY
WorldCat.org
Full Text: DOI
References:
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