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references.bib
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@book{AbsilMahonySepulchre:2008,
TITLE = {Optimization Algorithms on Matrix Manifolds},
AUTHOR = {Absil, P.-A. and Mahony, R. and Sepulchre, R.},
YEAR = {2008},
PUBLISHER = {Princeton University Press},
DOI = {10.1515/9781400830244},
NOTE = {[open access](http://press.princeton.edu/chapters/absil/)}
}
@article{Bacak:2014,
AUTHOR = {Bačák, M.},
DOI = {10.1137/140953393},
JOURNAL = {SIAM Journal on Optimization},
NUMBER = {3},
PAGES = {1542--1566},
TITLE = {Computing medians and means in Hadamard spaces},
VOLUME = {24},
YEAR = {2014}
}
@article{BacakBergmannSteidlWeinmann:2016,
AUTHOR = {Bačák, Miroslav and Bergmann, Ronny and Steidl, Gabriele and Weinmann, Andreas},
YEAR = {2016},
DOI = {10.1137/15M101988X},
JOURNAL = {SIAM Journal on Scientific Computing},
NUMBER = {1},
PAGES = {A567--A597},
TITLE = {A second order non-smooth variational model for restoring manifold-valued images},
VOLUME = {38}
NOTE = {arxiv: [1506.02409](https://arxiv.org/abs/1506.02409)}
}
@article{Bergmann:2022,
TITLE = {Manopt.Jl: Optimization on Manifolds in Julia},
AUTHOR = {Bergmann, Ronny},
YEAR = {2022},
JOURNAL = {Journal of Open Source Software},
VOLUME = {7},
NUMBER = {70},
PAGES = {3866},
PUBLISHER = {The Open Journal},
DOI = {10.21105/joss.03866}
}
@misc{Bergmann:2022zenodo,
TITLE = {Manopt.Jl},
AUTHOR = {Bergmann, Ronny},
YEAR = {2022},
DOI = {10.5281/zenodo.4290905},
COPYRIGHT = {MIT License},
HOWPUBLISHED = {Zenodo}
}
@article{BergmannGousenbourger:2018,
AUTHOR = {Bergmann, Ronny and Gousenbourger, Pierre-Yves},
YEAR = {2018},
DOI = {10.3389/fams.2018.00059},
JOURNAL = {Frontiers in Applied Mathematics and Statistics},
TITLE = {A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve},
VOLUME = {4},
NOTE = {arXiv: [1807.10090](https://arxiv.org/abs/1807.10090)}
}
@article{BergmannHerzogSilvaLouzeiroTenbrinckVidalNunez:2021,
AUTHOR = {Bergmann, Ronny and Herzog, Roland and Silva Louzeiro, Maurício and Tenbrinck, Daniel and Vidal-Núñez, José},
PUBLISHER = {Springer Science and Business Media LLC},
YEAR = {2021},
MONTH = jan,
DOI = {10.1007/s10208-020-09486-5},
JOURNAL = {Foundations of Computational Mathematics},
NUMBER = {6},
PAGES = {1465--1504},
TITLE = {Fenchel duality theory and a primal-dual algorithm on Riemannian manifolds},
VOLUME = {21},
NOTE = {arXiv: [1908.02022](http://arxiv.org/abs/1908.02022)}
}
@article{BergmannLausSteidlWeinmann:2014:1,
AUTHOR = {Bergmann, Ronny and Laus, Friederike and Steidl, Gabriele and Weinmann, Andreas},
DOI = {10.1137/140969993},
JOURNAL = {SIAM Journal on Imaging Sciences},
NUMBER = {4},
PAGES = {2916--2953},
TITLE = {Second order differences of cyclic data and applications in variational denoising},
VOLUME = {7},
YEAR = {2014},
NOTE = {arxiv: [1405.5349](https://arxiv.org/abs/1405.5349)}
}
@article{BergmannPerschSteidl:2016,
AUTHOR = {Bergmann, Ronny and Persch, Johannes and Steidl, Gabriele},
YEAR = {2016},
DOI = {10.1137/15M1052858},
JOURNAL = {SIAM Journal on Imaging Sciences},
NUMBER = {4},
PAGES = {901--937},
TITLE = {A parallel Douglas Rachford algorithm for minimizing ROF-like functionals on images with values in symmetric Hadamard manifolds},
VOLUME = {9},
NOTE = {arxiv: [1512.02814](https://arxiv.org/abs/1512.02814)}
}
@book{Boumal:2023,
TITLE = {An Introduction to Optimization on Smooth Manifolds},
AUTHOR = {Boumal, Nicolas},
YEAR = {2023},
MONTH = mar,
EDITION = {First},
PUBLISHER = {Cambridge University Press},
DOI = {10.1017/9781009166164},
URLDATE = {2023-07-13},
ABSTRACT = {Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.},
ISBN = {978-1-00-916616-4}
}
@book{doCarmo:1992,
TITLE = {Riemannian Geometry},
AUTHOR = {do Carmo, Manfredo Perdigão},
YEAR = {1992},
SERIES = {Mathematics: Theory & Applications},
PAGES = {xiv+300},
PUBLISHER = {Birkhäuser Boston, Inc., Boston, MA},
DOI = {10.1007/978-1-4757-2201-7},
ISBN = {0-8176-3490-8}
}
@techreport{deCasteljau:1959,
AUTHOR = {de Casteljau, Paul},
institution = {Enveloppe Soleau 40.040, Institute National de la Propriété Industrielle, Paris.},
TITLE = {Outillage methodes calcul},
YEAR = {1959}
}
@techreport{deCasteljau:1963,
AUTHOR = {de Casteljau, Paul},
institution = {Microfiche P 4147-1, Institute National de la Propriété Industrielle, Paris.},
TITLE = {Courbes et surfaces à pôles},
YEAR = {1963}
}
@article{ChambollePock:2011,
AUTHOR = {Chambolle, Antonin and Pock, Thomas},
YEAR = {2011},
DOI = {10.1007/s10851-010-0251-1},
JOURNAL = {Journal of Mathematical Imaging and Vision},
NUMBER = {1},
PAGES = {120--145},
TITLE = {A first-order primal-dual algorithm for convex problems with applications to imaging},
VOLUME = {40}
}
@article{DuranMoelleSbertCremers:2016,
AUTHOR = {Duran, J. and Moeller, M. and Sbert, C. and Cremers, D.},
TITLE = {Collaborative Total Variation: A General Framework for Vectorial TV Models},
JOURNAL = {SIAM Journal on Imaging Sciences},
VOLUME = {9},
NUMBER = {1},
PAGES = {116-151},
YEAR = {2016},
DOI = {10.1137/15M102873X},
NOTE = {arxiv: [1508.01308](https://arxiv.org/abs/1508.01308)}
}
@article{Karcher:1977,
AUTHOR = {Karcher, H.},
DOI = {10.1002/cpa.3160300502},
JOURNAL = {Communications on Pure and Applied Mathematics},
NUMBER = {5},
PAGES = {509--541},
TITLE = {Riemannian center of mass and mollifier smoothing},
VOLUME = {30},
YEAR = {1977}
}
@article{LausNikolovaPerschSteidl:2017,
AUTHOR = {Laus, F. and Nikolova, M. and Persch, J. and Steidl, G.},
YEAR = {2017},
DOI = {10.1137/16M1087114},
JOURNAL = {SIAM Journal on Imaging Sciences},
NUMBER = {1},
PAGES = {416--448},
TITLE = {A nonlocal denoising algorithm for manifold-valued images using second order statistics},
VOLUME = {10}
}
@article{LiuBoumal:2019,
AUTHOR = {Liu, Changshuo and Boumal, Nicolas},
PUBLISHER = {Springer Science and Business Media LLC},
YEAR = {2019},
MONTH = mar,
DOI = {10.1007/s00245-019-09564-3},
JOURNAL = {Applied Mathematics & Optimization},
TITLE = {Simple algorithms for optimization on Riemannian manifolds with constraints},
URL = {https://arxiv.org/abs/1901.10000}
}
@article{PopielNoakes:2007,
DOI = {10.1016/j.jat.2007.03.002},
YEAR = {2007},
MONTH = oct,
PUBLISHER = {Elsevier},
VOLUME = {148},
NUMBER = {2},
PAGES = {111--127},
AUTHOR = {Tomasz Popiel and Lyle Noakes},
TITLE = {Bézier curves and $C^2$ interpolation in Riemannian manifolds},
JOURNAL = {Journal of Approximation Theory}
}