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A primal‐dual method for the Meyer model of cartoon and texture decomposition
Author(s) -
Wen YouWei,
Sun HaiWei,
Ng Michael K.
Publication year - 2019
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.2224
Subject(s) - minimax , mathematics , dual norm , norm (philosophy) , minification , saddle point , dual (grammatical number) , mathematical optimization , saddle , algorithm , discrete mathematics , geometry , art , literature , political science , law , banach space
Summary In this paper, we study the original Meyer model of cartoon and texture decomposition in image processing. The model, which is a minimization problem, contains an l 1 ‐based TV‐norm and an l ∞ ‐based G ‐norm. The main idea of this paper is to use the dual formulation to represent both TV‐norm and G ‐norm. The resulting minimization problem of the Meyer model can be given as a minimax problem. A first‐order primal‐dual algorithm can be developed to compute the saddle point of the minimax problem. The convergence of the proposed algorithm is theoretically shown. Numerical results are presented to show that the original Meyer model can decompose better cartoon and texture components than the other testing methods.