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All issues Volume 19 / No 1 (January-March 2013) ESAIM: COCV, 19 1 (2013) 190-218 References
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Issue
ESAIM: COCV
Volume 19, Number 1, January-March 2013
Page(s) 190 - 218
DOI https://doi.org/10.1051/cocv/2011205
Published online 27 March 2012
  1. R.A. Adams and J.J.F. Fournier, Sobolev spaces. Academic Press (2003). [Google Scholar]
  2. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press (2000). [Google Scholar]
  3. A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2 (2009) 183–202. [Google Scholar]
  4. T. Bonesky, K.S. Kazimierski, P. Maass, F. Schöpfer and T. Schuster, Minimization of Tikhonov functionals in Banach spaces. Abstr. Appl. Anal. (2008) 192679. [Google Scholar]
  5. K. Bredies and D.A. Lorenz, Iterated hard shrinkage for minimization problems with sparsity constraints. SIAM J. Sci. Comput. 30 (2008) 657–683. [CrossRef] [Google Scholar]
  6. K. Bredies and D.A. Lorenz, Linear convergence of iterative soft-thresholding. J. Fourier Anal. Appl. 14 (2008) 813–837. [CrossRef] [Google Scholar]
  7. K. Bredies, D.A. Lorenz and P. Maass, A generalized conditional gradient method and its connection to an iterative shrinkage method. Comput. Optim. Appl. 42 (2009) 173–193. [CrossRef] [Google Scholar]
  8. K. Bredies, T. Alexandrov, J. Decker, D.A. Lorenz and H. Thiele, Sparse deconvolution for peak picking and ion charge estimation in mass spectrometry, in Progress in Industrial Mathematics at ECMI 2008, edited by H.-G. Bock et al., Springer (2010) 287–292. [Google Scholar]
  9. M. Burger and S. Osher, Convergence rates of convex variational regularization. Inverse Prob. 20 (2004) 1411–1421. [CrossRef] [Google Scholar]
  10. E.J. Candès, J.K. Romberg and T. Tao, Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 (2006) 1207–1223. [CrossRef] [Google Scholar]
  11. C. Clason and K. Kunisch, A duality-based approach to elliptic control problems in non-reflexive Banach spaces. ESAIM : COCV 17 (2011) 243–266. [Google Scholar]
  12. P.L. Combettes and V.R. Wajs, Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4 (2005) 1168–1200. [CrossRef] [Google Scholar]
  13. J.B. Conway, A course in functional analysis. Springer (1990). [Google Scholar]
  14. I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Comm. Pure Appl. Math. 57 (2004) 1413–1457. [Google Scholar]
  15. D.L. Donoho, Compressed sensing. IEEE Trans. Inf. Theory 52 (2006) 1289–1306. [Google Scholar]
  16. D.L. Donoho, M. Elad and V.N. Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theory 52 (2006) 6–18. [Google Scholar]
  17. C. Dossal and S. Mallat, Sparse spike deconvolution with minimum scale, in Proc. of SPARS’05 (2005). [Google Scholar]
  18. N. Dunford and J.T. Schwartz, Linear Operators. I. General Theory. Interscience Publishers (1958). [Google Scholar]
  19. B. Efron, T. Hastie, I. Johnstone and R. Tibshirani, Least angle regression. Ann. Statist. 32 (2004) 407–499. [Google Scholar]
  20. I. Ekeland and R. Temam, Convex analysis and variational problems. North-Holland (1976). [Google Scholar]
  21. H.W. Engl and G. Landl, Convergence rates for maximum entropy regularization. SIAM J. Numer. Anal. 30 (1993) 1509–1536. [CrossRef] [MathSciNet] [Google Scholar]
  22. H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems. Kluwer Academic Publishers (1996). [Google Scholar]
  23. M.A.T. Figueiredo, R.D. Nowak and S.J. Wright, Gradient projection for sparse reconstruction : Application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1 (2007) 586–597. [CrossRef] [Google Scholar]
  24. I. Fonseca and G. Leoni, Modern methods in the calculus of variations : Lp spaces. Springer (2007). [Google Scholar]
  25. M. Fornasier and H. Rauhut, Recovery algorithms for vector valued data with joint sparsity constraints. SIAM J. Numer. Anal. 46 (2008) 577–613. [CrossRef] [MathSciNet] [Google Scholar]
  26. J.-J. Fuchs, On sparse representations in arbitrary redundant bases. IEEE Trans. Inf. Theory. 50 (2004) 1341–1344. [CrossRef] [Google Scholar]
  27. A.L. Gibbs and F.E. Su, On choosing and bounding probability metrics. Int. Stat. Rev. 70 (2002) 419–435. [Google Scholar]
  28. M. Grasmair, M. Haltmeier and O. Scherzer, Sparse regularization with ℓq penalty term. Inverse Prob. 24 (2008) 055020. [Google Scholar]
  29. R. Griesse and D.A. Lorenz, A semismooth Newton method for Tikhonov functionals with sparsity constraints. Inverse Prob. 24 (2008) 035007. [CrossRef] [Google Scholar]
  30. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Publishing Limited (1985). [Google Scholar]
  31. T. Hein, Tikhonov regularization in Banach spaces – improved convergence rates results. Inverse Prob. 25 (2009) 035002. [CrossRef] [Google Scholar]
  32. B. Hofmann, B. Kaltenbacher, C. Pöschl and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Inverse Prob. 23 (2007) 987–1010. [CrossRef] [Google Scholar]
  33. L. Hörmander, The Analysis of Linear Partial Differential Operators I. Springer-Verlag (1990). [Google Scholar]
  34. V.K. Ivanov, V.V. Vasin and V.P. Tanana, Theory of linear ill-posed problems and its applications, 2nd edition. Inverse and Ill-posed Problems Series, VSP, Utrecht (2002). [Google Scholar]
  35. H. Lee, A. Battle, R. Raina and A.Y. Ng, Efficient sparse coding algorithms, in Advances in Neural Information Processing Systems, edited by B. Schölkopf, J. Platt and T. Hoffman. MIT Press 19 (2007) 801–808. [Google Scholar]
  36. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces. Springer (1979). [Google Scholar]
  37. D.A. Lorenz, Convergence rates and source conditions for Tikhonov regularization with sparsity constraints. J. Inverse Ill-Posed Probl. 16 (2008) 463–478. [Google Scholar]
  38. D.A. Lorenz and D. Trede, Optimal convergence rates for Tikhonov regularization in Besov scales. Inverse Prob. 24 (2008) 055010. [CrossRef] [Google Scholar]
  39. D.A. Lorenz and D. Trede, Greedy deconvolution of point-like objects, in Proc. of SPARS’09 (2009). [Google Scholar]
  40. Y. Mao, B. Dong and S. Osher, A nonlinear PDE-based method for sparse deconvolution. Multiscale Model. Simul. 8 (2010) 965–976. [CrossRef] [Google Scholar]
  41. L.M. Mugnier, T. Fusco and J.-M. Conan, MISTRAL : a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images. J. Opt. Soc. Am. A 21 (2004) 1841–1854. [NASA ADS] [CrossRef] [Google Scholar]
  42. Y.E. Nesterov, A method of solving a convex programming problem with convergence rate O(1/k2). Soviet Math. Dokl. 27 (1983) 372–376. [Google Scholar]
  43. A. Neubauer, On enhanced convergence rates for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. Inverse Prob. 25 (2009) 065009. [CrossRef] [Google Scholar]
  44. E. Resmerita and O. Scherzer, Error estimates for non-quadratic regularization and the relation to enhancement. Inverse Prob. 22 (2006) 801–814. [CrossRef] [Google Scholar]
  45. O. Scherzer and B. Walch, Sparsity regularization for Radon measures, in Scale Space and Variational Methods in Computer Vision, edited by X.-C. Tai, K. Morken, M. Lysaker and K.-A. Lie. Springer-Verlag (2009) 452–463. [Google Scholar]
  46. G. Stadler, Elliptic optimal control problems with L1-control cost and applications for the placement of control devices. Comput. Optim. Appl. 44 (2009) 159–181. [Google Scholar]
  47. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965) 189–258. [CrossRef] [MathSciNet] [Google Scholar]
  48. A.S. Stern, D.L. Donoho and J.C. Hoch, NMR data processing using iterative thresholding and minimum l1-norm reconstruction. J. Magn. Reson. 188 (2007) 295–300. [CrossRef] [PubMed] [Google Scholar]
  49. A.N. Tikhonov, A.S. Leonov and A.G. Yagola, Nonlinear ill-posed problems 1. Chapman & Hall (1998). [Google Scholar]
  50. Z.B. Xu and G.F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces. J. Math. Anal. Appl. 157 (1991) 189–210. [CrossRef] [Google Scholar]
  51. C. Zălinescu, Convex analysis in general vector spaces. World Scientific (2002). [Google Scholar]
  52. E. Zeidler, Nonlinear Functional Analysis and its Applications III. Springer-Verlag (1985). [Google Scholar]

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