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All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 92 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 92
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2025078
Published online 17 November 2025
  1. S.S. Chen, D.L. Donoho and M.A. Saunders, Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20 (1998) 33–61. [CrossRef] [MathSciNet] [Google Scholar]
  2. V. Duval and G. Peyré, Exact support recovery for sparse spikes deconvolution. Found. Comput. Math. 15 (2015) 1315–1355. [Google Scholar]
  3. M. Carioni and L. Del Grande, A general theory for exact sparse representation recovery in convex optimization. Preprint arXiv:2311.08072 [math.OC] (2023). [Google Scholar]
  4. C. Boyer, A. Chambolle, Y. De Castro, V. Duval, F. De Gournay and P. Weiss, On representer theorems and convex regularization. SIAM J. Optim. 29 (2019) 1260–1281. [Google Scholar]
  5. K. Bredies and M. Carioni, Sparsity of solutions for variational inverse problems with finite-dimensional data. Calc. Var. Part. Diff. Equ. 59 (2020) 1–26. [Google Scholar]
  6. K. Bredies, M. Carioni, S. Fanzon and D. Walter, Asymptotic linear convergence of fully-corrective generalized conditional gradient methods. Math. Program. 205 (2024) 135–202. [Google Scholar]
  7. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. Oxford University Press, New York (2000). [Google Scholar]
  8. A. Chambolle, V. Caselles, D. Cremers, M. Novaga and T. Pock, An introduction to total variation for image analysis, in Theoretical Foundations and Numerical Methods for Sparse Recovery, Vol. 9 of Radon Ser. Comput. Appl. Math.. Walter de Gruyter, Berlin (2010) 263-340. [Google Scholar]
  9. B. Goldluecke, E. Strekalovskiy and D. Cremers, The natural vectorial total variation which arises from geometric measure theory. SIAM J. Imaging Sci. 5 (2012) 537–564. [Google Scholar]
  10. J.-F. Babadjian and F. Iurlano, Piecewise rank-one approximation of vector fields with measure derivatives. Bull. London Math. Soc. 57 (2025) 181–202. [Google Scholar]
  11. K. Bredies, K. Kunisch and T. Pock, Total generalized variation. SIAM J. Imaging Sci. 3 (2010) 492–526. [Google Scholar]
  12. R. Temam, Problèmes mathématiques en plasticité, Vol. 12 of Méthodes Mathématiques de l’Informatique. Gauthier-Villars, Montrouge (1983). [Google Scholar]
  13. R. Temam and G. Strang. Functions of bounded deformation. Arch. Rational Mech. Anal., 75 (1980/81) 7-21. [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Ambrosio, C. Brena and S. Conti, Functions with bounded Hessian–Schatten variation: density, variational and extremality properties. Arch. Ration. Mech. Anal. 247 (2023) 111. [Google Scholar]
  15. P. Trautmann and D. Walter, A fast primal-dual-active-jump method for minimization in BV ((0, T); ℝd). Optimization 73 (2024) 1851–1895. [Google Scholar]
  16. J.A. Iglesias and D. Walter, Extremal points of total generalized variation balls in 1D: characterization and applications. J. Convex Anal. 29 (2022) 1251–1290. [Google Scholar]
  17. Y. De Castro, V. Duval and R. Petit, Towards off-the-grid algorithms for total variation regularized inverse problems. J. Math. Imaging Vis. 65 (2023) 53–81. [Google Scholar]
  18. G. Cristinelli, J.A. Iglesias and D. Walter, Conditional gradients for total variation regularization with PDE constraints: a graph cuts approach. Comput. Optim. Appl. (2025) doi: 10.1007/s10589-025-00699-4. [Google Scholar]
  19. J.A. Iglesias, G. Mercier, E. Chaparian and I.A. Frigaard, Computing the yield limit in three-dimensional flows of a yield stress fluid about a settling particle. J. Non-Newton. Fluid Mech. 284 (2020) 104374. [Google Scholar]
  20. I.A. Frigaard, J.A. Iglesias, G. Mercier, C. Pöschl and O. Scherzer, Critical yield numbers of rigid particles settling in Bingham fluids and Cheeger sets. SIAM J. Appl. Math. 77 (2017) 638–663. [Google Scholar]
  21. J.A. Iglesias, G. Mercier and O. Scherzer, Critical yield numbers and limiting yield surfaces of particle arrays settling in a Bingham fluid. Appl. Math. Optim. 82 (2020) 399–432. [Google Scholar]
  22. J. Diestel and J.J. Uhl Jr., Vector Measures. Mathematical Surveys, No. 15. American Mathematical Society, Providence, RI (1977). [Google Scholar]
  23. F. Maggi, Sets of finite perimeter and geometric variational problems, Vol. 135 of Cambridge Studies in Advanced Mathematics. Cambridge University Press (2012). [Google Scholar]
  24. M. Amar and G. Bellettini, A notion of total variation depending on a metric with discontinuous coefficients. Ann. Inst. H. Poincaré C Anal. Non Linéaire 11 (1994) 91–133. [Google Scholar]
  25. K. Jalalzai, Regularization of Inverse Problems in Image Processing. PhD thesis, École Polytechnique X, Palaiseau (2012). [Google Scholar]
  26. F. Demengel and R. Temam, Convex functions of a measure and applications. Indiana Univ. Math. J. 33 (1984) 673–709. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Parhi and R.D. Nowak, What kinds of functions do deep neural networks learn? Insights from variational spline theory. SIAM J. Math. Data Sci. 4 (2022) 464–489. [Google Scholar]
  28. G. Ongie, R. Willett, D. Soudry and N. Srebro, A function space view of bounded norm infinite width ReLU nets: The multivariate case, in 8th International Conference on Learning Representations, ICLR 2020 (2020). [Google Scholar]
  29. R. Parhi and R.D. Nowak, Banach space representer theorems for neural networks and ridge splines. J. Mach. Learn. Res. 22 (2021) 1–40. [Google Scholar]
  30. J. Saunderson, P.A. Parrilo and A.S. Willsky, Semidefinite descriptions of the convex hull of rotation matrices. SIAM J. Optim. 25 (2015) 1314–1343. [Google Scholar]
  31. L. Ambrosio, S. Aziznejad, C. Brena and M. Unser, Linear inverse problems with Hessian-Schatten total variation. Calc. Var. Part. Diff. Equ. 63 (2024) Paper No. 9. [Google Scholar]
  32. G. Dal Maso and R. Toader, A new space of generalised functions with bounded variation motivated by fracture mechanics. Nonlinear Diff. Equ. Appl. 29 (2022) Paper No. 63. [Google Scholar]
  33. L. Ambrosio, A. Coscia and G. Dal Maso, Fine properties of functions with bounded deformation. Arch. Rational Mech. Anal. 139 (1997) 201–238. [CrossRef] [MathSciNet] [Google Scholar]
  34. A. Chambolle, A. Giacomini and M. Ponsiglione, Piecewise rigidity. J. Funct. Anal. 244 (2007) 134–153. [Google Scholar]
  35. G. Dolzmann and S. Müller, Microstructures with finite surface energy: the two-well problem. Arch. Rational Mech. Anal. 132 (1995) 101–141. [Google Scholar]
  36. L. Ambrosio, V. Caselles, S. Masnou and J.-M. Morel, Connected components of sets of finite perimeter and applications to image processing. J. Eur. Math. Soc. 3 (2001) 39–92. [Google Scholar]
  37. M. Carioni, J.A. Iglesias and D. Walter, Extremal points and sparse optimization for generalized Kantorovich–Rubinstein norms. Found. Comput. Math. 25 (2025) 103–144. [Google Scholar]
  38. W.P. Ziemer, Weakly Differentiable Functions, Vol. 120 of Graduate Texts in Mathematics. Springer-Verlag, New York (1989). [Google Scholar]
  39. L.E. Blumenson, A derivation of n-dimensional spherical coordinates. Amer. Math. Monthly 67 (1960) 63–66. [Google Scholar]

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