Free Access
Volume 19, Number 1, January-March 2013
Page(s) 190 - 218
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 q 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]

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.