HIERARCHICAL DECOMPOSITIONS

A collection of selected references on

Hierarchical decompositions with applications in image processing and PDEs.
  • E. Tadmor, S. Nezzar and L. Vese
    A multiscale image representation using hierarchical (BV,L2) decompositions
    Multiscale Modeling and Simulations 2(4) (2004) 554-579.

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  • D. Paquin, D. Levy, E. Schreibmann and L. Xing,
    Multiscale Image Registration
    Mathematical Biosciences and Engineering 3(2) (2006) 389-418.

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  • N. Kruglyak
    The K-functional and Calderon-Zygmund type decompositions
    in "Interpolation Theory and Applications", Contemporary Mathematics Series, Proceedings of the conference in honor of Professor M. Cwikel held in Miami, Florida in 2006, Vol. 445 (Laura De Carli and Mario Milman, eds.), Amer. Math. Society (2007) 183-194..

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  • D. Paquin, D. Levy and L. Xing
    Hybrid multiscale landmark and deformable image registration
    Mathematical Biosciences and Engineering 4 (2007) 711-737.

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  • Björn Jawerth and Mario Milman
    Lectures on optimization, image processing, and interpolation theory
    in "Function Spaces, Inequalities and Interpolation", Lectures on Optimization, Image Processing and Interpolation Theory, Spring School on Analysis held at Paseky nad Jizerou, chalet in the Krkonose Mountains in 2007 (2007).

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  • Dana Paquin, Doron Levy and Lei Xing
    Multiscale deformable registration of noisy medical images
    Mathematical Bio-sciences and Engineering 5(1) (2008) 125-144.

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  • E. Tadmor, S. Nezzar and L. Vese
    Multiscale hierarchical decomposition of images with applications to deblurring, denoising and segmentation
    Communications in Mathematical Sciences 6(2) (2008) 281-307.

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  • E. Tadmor and P. Athavale
    Multiscale image representation using integro-differential equations
    Inverse Problems and Imaging 3(4) (2009) 693-710.

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  • P. Athavale and E. Tadmor
    Novel integro-differential equations in image processing and its applications
    in "Computational Imaging VIII", Proceedings of SPIE meeting held in San Jose in 2010, Vol. 7533 (C. A. Bouman, I. Pollak, P. J. Wolfe eds.) (2010) 75330S..

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  • Michael Hintermüller and M Monserrat Rincon-Camacho
    Expected absolute value estimators for a spatially adapted regularization parameter choice rule in L1-TV-based image restoration
    Inverse Problems 26(8) (2010).

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  • Moncef Hidane, Olivier Lézoray, Vinh-Thong Ta and Abderrahim Elmoataz
    Nonlocal multiscale hierarchical decomposition on graphs
    in "ECCV2010", Proceeding of 11th European Conference on Computer Vision held in Heraklion, Crete in 2010, Vol. LNCS 6314 (Part IV) (K.Daniilidis, P.Maragos and N.Paragios eds.), Springer-Verlag (2010) 638-650..

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  • Yiqiu Dong, Michael Hintermüller and M. Monserrat Rincon-Camacho
    Automated regularization parameter selection in multi-scale total variation models for image restoration
    Journal of Mathematical Imaging and Vision 40(1) (2010) 82-104.

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  • P. Athavale and E. Tadmor
    Integro-differential equations based on (BV, L1) image decomposition
    SIAM journal on Imaging Sciences 4(1) (2011) 300-312.

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  • E. Tadmor and C. Tan
    Hierarchical construction of bounded solutions of div U=F in critical regularity spaces
    in "Nonlinear Partial Differential Equations", Proceedings of the 2010 Abel Symposium held in 2010, Vol. 7 - Abel Symposia (H. Holden & K. Karlsen eds.), Springer, Oslo (2012) 255-269..

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  • Jerome Gilles
    Multiscale texture separation
    Multiscale Modeling & Simulation 10(4) (2012) 1409–1427.

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  • Moncef Hidane, Olivier Lézoray and Abderrahim Elmoataz
    Nonlinear multilayered representation of graph-signals
    Journal of Mathematical Imaging and Vision 45(2) (2013) 114-137.

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  • P. Athavale., R. Xu, P. Radau., A. Nachman and G. Wright
    Multiscale TV flow with applications to fast denoising and registration
    in "SPIE Medical Imaging: image processing", Proceedings of SPIE meeting held in Lake Buena Vista, Florida in 2013, Vol. 8669 86692K-1 (S. Ourselin, D. R. Haynor eds.) (2013).

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  • Liming Tang and Chuanjiang He
    Multiscale Texture Extraction with Hierarchical (BV,Gp,L2) Decomposition
    Journal of Mathematical Imaging and Vision 45(2) (2013) 148-163.

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  • Xiaohui Wang
    Multiscale decompositions and optimization
    (2013).

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  • Prashant Athavale, Robert Xu, Perry Radau, Graham Wright and Adrian Nachman
    Multiscale properties of weighted total variation flow with applications to denoising and registration
    IEEE Transactions in Medical Imaging 11(4) (2013) 1-12.

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  • Liming Tang and Chuanjiang He
    Multiscale image representation and texture extraction using hierarchical variational decomposition
    Journal of Applied Mathematics 107120 (2013).

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  • Juan Carlos Moreno, Surya Prasath, Dmitry Vorotnikov and Hugo Proença
    Adaptive diffusion constrained Total Variation scheme with application to cartoon+texture+edge image decomposition.

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  • E. Tadmor
    Hierarchical construction of bounded solutions in critical regularity spaces
    Communications on Pure and Applied Mathematics 69(6) (2016) 1087-1109.

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  • Prashant Athavale, Robert L. Jerrard, Matteo Novaga and Giandomenico Orlandi
    Weighted TV minimization and applications to vortex density models
    Journal of Convex Analysis 24(4) (2017) 1051-1084.

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  • Klas Modin, Adrian Nachman and Luca Rondi
    A multiscale theory for image registration and nonlinear inverse problems
    Advances in Mathematics 346 (2019) 1009-1066.

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