Volume 5, Issue 3
Finite Element Approximation for TV Regularization

Int. J. Numer. Anal. Mod., 5 (2008), pp. 516-526.

Published online: 2008-05

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• Abstract

In this paper, we will develop the convergence of the solution of TV-regularization equations with regularized parameter $\varepsilon \rightarrow 0$ in BV($\Omega$) for practical purposes. Originated from the effects of regularized parameter $\varepsilon$, the error rate of finite element approximation for TV-regularization equations will be controlled by the regularized parameter $\varepsilon^{-1}$ polynomially in the energy norm when using linearization technique and duality argument. And in the $L^p$-norm, the effect of regularized parameter $\varepsilon$ will be more extremely.

35B25, 35K57, 35Q99, 65M60, 65M12

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@Article{IJNAM-5-516, author = {Yao , Changhui}, title = {Finite Element Approximation for TV Regularization}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {3}, pages = {516--526}, abstract = {

In this paper, we will develop the convergence of the solution of TV-regularization equations with regularized parameter $\varepsilon \rightarrow 0$ in BV($\Omega$) for practical purposes. Originated from the effects of regularized parameter $\varepsilon$, the error rate of finite element approximation for TV-regularization equations will be controlled by the regularized parameter $\varepsilon^{-1}$ polynomially in the energy norm when using linearization technique and duality argument. And in the $L^p$-norm, the effect of regularized parameter $\varepsilon$ will be more extremely.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/824.html} }
TY - JOUR T1 - Finite Element Approximation for TV Regularization AU - Yao , Changhui JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 516 EP - 526 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/824.html KW - TV-regularization, regularized parameter, finite element method. AB -

In this paper, we will develop the convergence of the solution of TV-regularization equations with regularized parameter $\varepsilon \rightarrow 0$ in BV($\Omega$) for practical purposes. Originated from the effects of regularized parameter $\varepsilon$, the error rate of finite element approximation for TV-regularization equations will be controlled by the regularized parameter $\varepsilon^{-1}$ polynomially in the energy norm when using linearization technique and duality argument. And in the $L^p$-norm, the effect of regularized parameter $\varepsilon$ will be more extremely.

Changhui Yao. (1970). Finite Element Approximation for TV Regularization. International Journal of Numerical Analysis and Modeling. 5 (3). 516-526. doi:
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