Introduction to variational image-processing models and applications

References

• Barendt , S. and Modersitzki , J. 2013 . A variational model for SPECT reconstruction with a nonlinearly transformed attenuation prototype . Int. J. Comput. Math. , 90 ( 1 ) : 82 – 91 .
   Web of Science ®Google Scholar
• Bonettini , S. , Landi , G. , Loli Piccolomini , E. and Zanni , L. 2013 . Scaling techniques for gradient projection-type methods in astronomical image deblurring . Int. J. Comput. Math. , 90 ( 1 ) : 9 – 29 .
   Web of Science ®Google Scholar
• Bredies , K. , Dong , Y. and Hintermüller , M. 2013 . Spatially dependent regularization parameter selection in total generalized variation models for image restoration . Int. J. Comput. Math. , 90 ( 1 ) : 109 – 123 .
   Web of Science ®Google Scholar
• Brito , C. and Chen , K. 2010 . Multigrid algorithm for high order denoising . SIAM J. Imaging Sci. , 3 ( 3 ) : 363 – 389 . (doi:10.1137/080737903)
   Google Scholar
• Brito-Loeza , C. and Chen , K. 2013 . Fast iterative algorithms for solving the minimization of curvature-related functionals in surface fairing . Int. J. Comput. Math. , 90 ( 1 ) : 92 – 108 .
   Web of Science ®Google Scholar
• Chan , T. F. and Shen , J. H. 2005 . Image Processing and Analysis – Variational, PDE, Wavelet, and Stochastic Methods , Philadelphia : SIAM Publications .
   Google Scholar
• Chen , K. 2005 . Matrix Preconditioning Techniques and Applications , Cambridge : Cambridge University Press .
   Google Scholar
• Chumchob , N. , Chen , K. and Brito-Loeza , C. 2013 . A new variational model for removal of combined additive and multiplicative noise and a fast algorithm for its numerical approximation . Int. J. Comput. Math. , 90 ( 1 ) : 140 – 161 .
   Web of Science ®Google Scholar
• Droske , M. and Rumpf , M. 2004 . A level set formulation for Willmore flow . Interfaces Free Bound. , 6 ( 3 ) : 361 – 378 . (doi:10.4171/IFB/105)
   Web of Science ®Google Scholar
• Elsey , M. and Esedōglu , S. 2009 . Analogue of the total variation denoising model in the context of geometry processing . Multiscale Model. Simul. , 7 ( 4 ) : 1549 – 1573 . (doi:10.1137/080736612)
   Web of Science ®Google Scholar
• Hansen , P. C. , Nagy , J. G. and O'Leary , D. P. 2006 . Deblurring Images: Matrices, Spectra, and Filtering , Philadelphia : SIAM Publications .
   Google Scholar
• Häuser , S. and Steidl , G. 2013 . Convex multiclass segmentation with shearlet regularization . Int. J. Comput. Math. , 90 ( 1 ) : 62 – 81 .
   Web of Science ®Google Scholar
• Lysaker , M. , Osher , S. and Tai , X. C. 2004 . Noise removal using smoothed normals and surface fitting . IEEE Trans. Image Proc. , 13 ( 10 ) : 345 – 1457 . (doi:10.1109/TIP.2004.834662)
   Google Scholar
• Modersitzki , J. 2009 . FAIR: Flexible Algorithms for Image Registration – Software and Applications , Philadelphia : SIAM Publications .
   Google Scholar
• Mumford , D. and Shah , J. 1989 . Optimal approximation by piecewise smooth functions and associated variational problems . Commun. Pure Appl. Math. , 42 : 577 – 685 . (doi:10.1002/cpa.3160420503)
   Web of Science ®Google Scholar
• Osher , S. and Fedkiw , R. 2003 . Level Set Methods and Dynamic Implicit Surfaces , Berlin : Springer .
   Google Scholar
• Perona , P. and Malik , J. 1990 . Scale-space and edge detection using anisotropic diffusion . IEEE Trans. Pattern Anal. Mach. Intell. , 12 ( 7 ) : 629 – 639 . (doi:10.1109/34.56205)
   Web of Science ®Google Scholar
• Rudin , L. , Osher , S. and Fatemi , E. 1992 . Nonlinear total variation based noise removal algorithms . Physica D , 60 : 259 – 268 . (doi:10.1016/0167-2789(92)90242-F)
   Web of Science ®Google Scholar
• Sapiro , G. 2001 . Geometric Partial Differential Equations and Image Analysis , Cambridge : Cambridge University Press .
   Google Scholar
• Sethian , J. A. 1999 . Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science , Cambridge : Cambridge University Press .
   Google Scholar
• Scherzer , O. , Grasmair , M. , Grossauer , H. , Haltmeier , M. and Lenzen , F. 2009 . Variational Methods in Imaging , Berlin : Springer .
   Google Scholar
• Tai , X. C. , Morkken , K. , Lysaker , M. and Lie , K. A. 2009 . Scale Space and Variational Methods in Computer Vision , Edited by: Tai , X. C. , Morkken , K. , Lysaker , M. and Lie , K. A. Vol. 5567 , Berlin : Springer . Lecture Notes in Computer Science
   Google Scholar
• Tasdizen , T. , Whitaker , R. , Burchard , P. and Osher , S. 2003 . Geometric surface processing via normal maps . ACM Trans. Graph. , 22 ( 4 ) : 1012 – 1033 . (doi:10.1145/944020.944024)
   Web of Science ®Google Scholar
• Vese , L. A. 2012 . Variational Methods in Image Processing , Boca Raton, FL : Chapman & Hall, CRC Press .
   Google Scholar
• Vogel , C. R. 2002 . Computational Methods for Inverse Problems , Philadelphia : SIAM Publications .
   Google Scholar
• Wang , F. and Ng , M. K. 2013 . A fast minimization method for blur and multiplicative noise removal . Int. J. Comput. Math. , 90 ( 1 ) : 48 – 61 .
   Web of Science ®Google Scholar
• Yan , M. 2013 . Convergence analysis of SART: Optimization and statistics . Int. J. Comput. Math. , 90 ( 1 ) : 30 – 47 .
   Web of Science ®Google Scholar
• Zhu , W. and Chan , T. F. 2012 . Image denoising using mean curvature . SIAM J. Imaging Sci. , 5 : 1 – 32 . (doi:10.1137/110822268)
   Web of Science ®Google Scholar
• Zhu , W. , Kang , S. H. and Biros , G. 2013 . A geodesic-active-contour-based variational model for short-axis cardiac MR image segmentation . Int. J. Comput. Math. , 90 ( 1 ) : 124 – 139 .
   Web of Science ®Google Scholar