Free Access
Issue
ESAIM: COCV
Volume 25, 2019
Article Number 83
Number of page(s) 19
DOI https://doi.org/10.1051/cocv/2018009
Published online 19 December 2019
  1. B. Adcock and A.C. Hansen, A generalized sampling theorem for stable reconstructions in arbitrary bases. J. Fourier Anal. Appl. 18 (2012) 685–716. [Google Scholar]
  2. B. Adcock and A.C. Hansen, Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon. Appl. Comput. Harmon. Anal. 32 (2012) 357–388. [Google Scholar]
  3. B. Adcock, A.C. Hansen and C. Poon, On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate. Appl. Comput. Harmon. Anal. 36 (2014) 387–415. [Google Scholar]
  4. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Science Publications (2000). [Google Scholar]
  5. M. Bergounioux, K. Ito and K. Kunisch, Primal-dual strategy for optimal control problems. SIAM J. Control Optim. 37 (1999) 1176–1194. [Google Scholar]
  6. J. Bochnak, M. Coste and M.F. Roy, Real Algebraic geometry. Springer (1998). [CrossRef] [Google Scholar]
  7. K. Bredies, Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty. Lecture Notes Comput. Sci. 8293 (2014) 44–77. [CrossRef] [Google Scholar]
  8. K. Bredies and T. Valkonen, Inverse problems with second-order total generalized variation constraints. In Proceedings of SampTA 2011 – 9th International Conference on Sampling Theory and Applications. Singapore (2011). [Google Scholar]
  9. K. Bredies and M. Holler, Regularization of linear inverse problems with Total Generalized Variation. J. Inverse Ill-posed Probl. 22 (2014) 871–913. [CrossRef] [Google Scholar]
  10. K. Bredies, K. Kunisch and T. Pock, Total Generalized Variation. SIAM J. Imag. Sci. 3 (2010) 492–526. [CrossRef] [Google Scholar]
  11. K. Bredies, C. Langkammer and D. Vicente, TGV-based single-step QSM reconstruction with coil combination. In 4th International Workshop on MRI Phase Constrast and Quantitative Susceptibility Mapping. Medical University of Graz (2016). [Google Scholar]
  12. E.J. Candès and C. Fernandez-Granda, Towards a mathematical theory of super-resolution. Commun. Pure Appl. Math. 67 (2014) 906–956. [Google Scholar]
  13. E.J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52 (2006) 489–509. [Google Scholar]
  14. V. Caselles, A. Chambolle and M. Novaga, The discontinuity set of solutions of the TV denoising problem and some extensions. Multiscale Modeling Simul. 6 (2007) 879–894. [CrossRef] [Google Scholar]
  15. A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imag. Vision 40 (2011) 120–145. [CrossRef] [Google Scholar]
  16. A. Chambolle, V. Duval, G. Peyré and C. Poon, Geometric properties of solutions to the total variation denoising problem. Inverse Probl. 33 (2016) 015002. [Google Scholar]
  17. I. Chatnuntawech, P. McDaniel, S.F. Cauley, B.A. Gagoski, C. Langkammer, A. Martin, P.E. Grant, L.L. Wald, K. Setsompop, E. Adalsteinsson and B. Bilgic, Single-step quantitative susceptibility mapping with variational penalties. NMR Biomed. (2016). [Google Scholar]
  18. J.K. Choi, H.S. Park, S. Wang and J.K. Seo, Inverse problem in quantitative susceptibility mapping. SIAM J. Imag. Sci. 7 (2014) 1669–1689. [CrossRef] [Google Scholar]
  19. L. de Rochefort, R. Brown, M. Prince and Y. Wang, Quantitative MR susceptibility mapping using piecewise constant regularized inversion of the magnetic field. Magn. Res. Med. 60 (2008) 1003–1009. [CrossRef] [Google Scholar]
  20. G. De Philippis and F. Rindler, On the structure of 𝒜-free measures and applications. Ann. Math. 184 (2016) 1017–1039. [Google Scholar]
  21. V. Duvaland G. Peyré, Exact support recovery for sparse spikes deconvolution. Found. Comput. Math. 15 (2015) 1315–1355. [CrossRef] [Google Scholar]
  22. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics (1992). [Google Scholar]
  23. T. Goldstein and S. Osher, The split Bregman method for L1-regularized problems. SIAM J. Imag. Sci. 2 (2009) 323–343. [CrossRef] [Google Scholar]
  24. E.M. Haacke, R.W. Brown, M.R. Thompson and R. Venkatesan, Magnetic Resonance Imaging: Physical Principles and Sequence Design. John Wiley and Sons, New York (1999). [Google Scholar]
  25. E.M. Haacke, N.Y. Cheng, M.J. House, Q. Liu, J. Neelavalli, R.J. Ogg, A. Khan, M. Ayaz, W. Kirsch and A. Obenaus, Imaging iron stores in the brain using magnetic resonance imaging. Magn. Res. Imag. 23 (2005) 1–25. [CrossRef] [Google Scholar]
  26. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13 (2006) 865–888. [Google Scholar]
  27. L. Hörmander, The Analysis of Linear Partial Differential Operators I. Distribution Theory and Fourier Analysis, 2nd edition. Springer Verlag, Berlin (1990). [Google Scholar]
  28. C. Langkammer, K. Bredies, B.A. Poser, M. Barth, G. Reishofer, A.P. Fan, B. Bilgic, F. Fazekas, C. Mainero and S. Ropele, Fast Quantitative Susceptibility Mapping using 3D EPI and Total Generalized Variation. NeuroImage 111 (2015) 622–630. [CrossRef] [PubMed] [Google Scholar]
  29. C. Li, W. Yin and Y. Zhang, TVAL3: TV minimization by Augmented Lagrangian and ALternating direction ALgorithms. Available at: http://www.caam.rice.edu/~optimization/L1/TVAL3/ (2019). [Google Scholar]
  30. C. Meyer, A. Rösch and F. Tröltzsch, Optimal control problems of PDEs with regularized pointwise state constraints. Comput. Optim. Appl. 33 (2006) 209–228. [Google Scholar]
  31. W. Rossmann, Lie groups: an introduction through linear groups. Oxford University Press (2002). [Google Scholar]
  32. L.I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259–268. [Google Scholar]
  33. F. Schweser, S.D. Robinson, L. de Rochefort, W. Li and K. Bredies, An illustrated comparison of processing methods for phase MRI and QSM: removal of background field contributions from sources outside the region of interest. NMR Biomed. 30 (2017). [Google Scholar]
  34. F. Tröltzsch, Optimal control of partial differential equations. Americal Mathematical Society (2010). [Google Scholar]
  35. Y. Wang and T. Liu, Quantitative Susceptibility Mapping (QSM): Decoding MRI data for a tissue magnetic biomarker. Magn. Res. Med. 73 (2015) 82–101. [CrossRef] [Google Scholar]
  36. Y. Zhang, W. Deng, J. Yang and W. Yin, YALL1: Your ALgorithms for L1. Available at: http://yall1.blogs.rice.edu/ (2019). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.