Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 1/2016

21.11.2015

Block Decomposition Methods for Total Variation by Primal–Dual Stitching

verfasst von: Chang-Ock Lee, Jong Ho Lee, Hyenkyun Woo, Sangwoon Yun

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Due to the advance of image capturing devices, huge size of images are available in our daily life. As a consequence the processing of large scale image data is highly demanded. Since the total variation (TV) is kind of de facto standard in image processing, we consider block decomposition methods for TV based variational models to handle large scale images. Unfortunately, TV is non-separable and non-smooth and it thus is challenging to solve TV based variational models in a block decomposition. In this paper, we introduce a primal–dual stitching (PDS) method to efficiently process the TV based variational models in the block decomposition framework. To characterize TV in the block decomposition framework, we only focus on the proximal map of TV function. Empirically, we have observed that the proposed PDS based block decomposition framework outperforms other state-of-art methods such as Bregman operator splitting based approach in terms of computational speed.
Vorheriger Artikel Numerical Identification of the Fractional Derivatives in the Two-Dimensional Fractional Cable Equation
Nächster Artikel Symmetric Coupling of LDG–FEM and DG–BEM

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
It is inspired from an image stitching method in [25].
 
2
As shown in Theorem 3, the sequential method (i.e., BD-S) with \({\textit{subMaxIt}}=1\) and \(\omega =1\) corresponds to the method (i.e., PLAD) without using block decomposition.
 
3
Note that one iteration condition is used in coordinate optimization only with primal variable to find a solution of fused Lasso problem [10].
 
4
Note that the original PLAD algorithm in [27] linearizes fidelity term and augmented term at the same time. However, since the fidelity term of the proxTV model (1) is a simple proximal term, the original PLAD method is up to constant equal to (40), which we called PLAD in this paper.
 
Literatur
1.
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)MathSciNetCrossRefMATH
2.
Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18, 2419–2434 (2009)MathSciNetCrossRef
3.
Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation. Prentice Hall, Upper Saddle River (1989)MATH
4.
Carstensen, C.: Domain decomposition for a non-smooth convex minimization problems and its application to plasticity. Numer. Linear Algebra Appl. 4, 177–190 (1998)MathSciNetCrossRefMATH
5.
Combettes, P., Wajs, W.: Signal recovery by proximal forward–backward splitting. Multiscale Model. Simul. 4, 1168–1200 (2005)MathSciNetCrossRefMATH
6.
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120–145 (2011)MathSciNetCrossRefMATH
7.
8.
Chang, H., Tai, X.-C., Wang, L.-L., Yang, D.: Convergence rate of overlapping domain decomposition methods for the Rudin–Osher–Fatemi model based on a dual formulation. SIAM J. Imaging Sci. 8, 564–591 (2015)MathSciNetCrossRefMATH
9.
Esser, E.: Applications of Lagrangian-based alternating direction methods and connections to split Bregman. UCLA Cam Report, 9, 31 (2009)
10.
Friedman, J., Hastie, T., Höfling, H., Tibshirani, R.: Pathwise coordinate optimization. Ann. Appl. Stat. 1, 302–332 (2007)MathSciNetCrossRefMATH
11.
Fornasier, M.: Domain decomposition methods for linear inverse problems with sparsity constraints. Inverse Probl. 23, 2505–2526 (2007)MathSciNetCrossRefMATH
12.
Fornasier, M., Langer, A., Schönlieb, C.-B.: A convergent overlapping domain decomposition method for total variation minimization. Numer. Math. 116, 645–685 (2010)MathSciNetCrossRefMATH
13.
Fornasier, M., Schönlieb, C.-B.: Subspace correction methods for total variation and l1-minimization. SIAM J. Numer. Anal. 47, 3397–3428 (2009)MathSciNetCrossRefMATH
14.
15.
Hageman, L.A., Porsching, T.A.: Aspects of nonlinear block successive overrelaxation. SIAM J. Numer. Anal. 2, 316–335 (1975)MathSciNetCrossRefMATH
16.
He, B., Liao, L.Z., Han, D., Yang, H.: A new inexact alternating directions method for monotone variational inequalities. Math. Program. 92, 103–118 (2002)MathSciNetCrossRefMATH
17.
Hintermüller, M., Langer, A.: Subspace correction methods for a class of non-smooth and non-additive convex variational problems with mixed \(L^{1}/L^{2}\) data-fidelity in image processing. SIAM J. Imaging Sci. 6, 2134–2173 (2013)MathSciNetCrossRefMATH
18.
Hintermüller, M., Langer, A.: Non-overlapping domain decomposition methods for dual total variation based image denoising. J. Sci. Comp. 62, 456–481 (2015)
19.
Hintermüller, M., Langer, A.: Subspace correction methods for a class of non-smooth and non-additive convex variational problems with mixed \(L^1/L^2\) data-fidelity in image processing. SIAM J. Imaging Sci. 6, 2134–2173 (2013)MathSciNetCrossRefMATH
20.
Kang, M., Yun, S., Woo, H.: Two-level convex relaxed variational model for multiplicative denoising. SIAM J. Imaging Sci. 6, 875–903 (2013)MathSciNetCrossRefMATH
21.
Langer, A., Osher, S., Schönlieb, C.-B.: Bregmanized domain decomposition for image restoration. J. Sci. Comput. 54, 549–576 (2013)MathSciNetCrossRefMATH
22.
23.
Tseng, P.: Convergence of a block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109, 475–494 (2001)MathSciNetCrossRefMATH
24.
Tseng, P., Yun, S.: A coordinate gradient descent method for nonsmooth separable minimization. Math. Prog. (Ser. B) 117, 387–423 (2009)MathSciNetCrossRefMATH
25.
26.
Wen, Z., Yin, W., Zhang, Y.: Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Math. Program. Comput. 4, 333–361 (2012)MathSciNetCrossRefMATH
27.
Woo, H., Yun, S.: Proximal linearized alternating direction method for multiplicative denoising. SIAM J. Sci. Comput. 35, B336–B358 (2013)MathSciNetCrossRefMATH
28.
Wu, C., Tai, X.-C.: Augmented Lagrangian method, Dual methods and Split-Bregman Iterations for ROF, vectorial TV and higher order models. SIAM J. Imaging Sci. 3, 300–339 (2010)MathSciNetCrossRefMATH
29.
Xu, J., Tai, X.-C., Wang, L.-L.: A two-level domain decomposition method for image restoration. Inverse Probl. Imaging 4, 523–545 (2010)MathSciNetCrossRefMATH
30.
Yun, S., Woo, H.: Linearized proximal alternating minimization algorithm for motion deblurring by nonlocal regularization. Pattern Recognit. 44, 1312–1326 (2011)CrossRefMATH
31.
Zhang, X., Burger, M., Bresson, X., Osher, S.: Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM J. Imaging Sci. 3, 253–276 (2010)MathSciNetCrossRefMATH
32.
Zhang, X., Burger, M., Osher, S.: A unified primal-dual algorithm framework based on Bregman iteration. J. Sci. Comput. 46, 20–46 (2011)MathSciNetCrossRefMATH
33.
Zhu, M., Chan, T.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. UCLA CAM-report (2008)
Metadaten
Titel
Block Decomposition Methods for Total Variation by Primal–Dual Stitching
verfasst von
Chang-Ock Lee
Jong Ho Lee
Hyenkyun Woo
Sangwoon Yun
Publikationsdatum
21.11.2015
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-015-0138-9

Weitere Artikel der Ausgabe 1/2016

Journal of Scientific Computing 1/2016 Zur Ausgabe

OriginalPaper

Adaptive Finite Difference Methods for Nonlinear Elliptic and Parabolic Partial Differential Equations with Free Boundaries

OriginalPaper

A Hybridized Discontinuous Galerkin Method for the Nonlinear Korteweg–de Vries Equation

OriginalPaper

A 5-Wave Relaxation Solver for the Shallow Water MHD System

OriginalPaper

An Explicit High-Order Single-Stage Single-Step Positivity-Preserving Finite Difference WENO Method for the Compressible Euler Equations

OriginalPaper

$$C^0$$ C 0 IP Methods for the Transmission Eigenvalue Problem

OriginalPaper

Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem