ADI SPLITTING SCHEMES FOR A FOURTH-ORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATION FROM IMAGE PROCESSING

被引：12

作者：

Calatroni, Luca ^{[1
]}

Duering, Bertram ^{[2
]}

Schoenlieb, Carola-Bibiane ^{[3
]}

机构：

[1] Univ Cambridge, Cambridge Ctr Anal, Cambridge CB3 0WA, England

[2] Univ Sussex, Dept Math, Brighton BN1 9QH, E Sussex, England

[3] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

ADI splitting; higher-order nonlinear diffusion; total variation; image processing; TOTAL VARIATION MINIMIZATION; DIFFUSION-EQUATIONS; DECOMPOSITION; STABILITY; RESTORATION; CURVATURE; SPACE;

D O I：

10.3934/dcds.2014.34.931

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H-1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

引用

页码：931 / 957

页数：27

共 55 条

[1]

Ambrosio L., 2000, Oxford Mathematical Monographs

[2]

[Anonymous], MATH TABLES OTHER AI

[3] Constrained and SNR-based solutions for TV-Hilbert space image denoising [J].

Aujol, Jean-Francois ;

Gilboa, Guy .

JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2006, 26 (1-2) :217-237

[4] Dual norms and image decomposition models [J].

Aujol, JF ;

Chambolle, A .

INTERNATIONAL JOURNAL OF COMPUTER VISION, 2005, 63 (01) :85-104

[5]

Barash D., 2006, LECT NOTES COMPUTER, V2106, P281

[6]

Benning M., 2011, THESIS U MUNSTER

[7]

Benning M., 2013, LNCS

[8] Regularized Regression and Density Estimation based on Optimal Transport [J].

Burger, Martin ;

Franek, Marzena ;

Schoenlieb, Carola-Bibiane .

APPLIED MATHEMATICS RESEARCH EXPRESS, 2012, 2012 (02) :209-253

[9] Cahn-Hilliard Inpainting and a Generalization for Grayvalue Images [J].

Burger, Martin ;

He, Lin ;

Schoenlieb, Carola-Bibiane .

SIAM JOURNAL ON IMAGING SCIENCES, 2009, 2 (04) :1129-1167

[10] Image recovery via total variation minimization and related problems [J].

Chambolle, A ;

Lions, PL .

NUMERISCHE MATHEMATIK, 1997, 76 (02) :167-188

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