References
- Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Vol. 375, Mathematics and its application. Dordrecht: Kluwer Academic; 1996.
- Acar R, Vogel CR. Analysis of bounded variation penalty methods for ill-posed problems. Inverse Prob. 1994;10:1217–1229.
- Chambolle A, Lions PL. Image recovery via total variational minimization and related problems. Numer. Math. 1997;76:167–188.
- Meyer Y. Oscillating patterns in image processing and nonlinear evolution equations. Providence (RI): AMS; 2001.
- Rudin LI, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Phys. D. 1992;60:259–268.
- Daubechies I, Defrise M, DeMol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 2004;51:1413–1441.
- Ramlau R, Teschke G. A Tikhonov-based projection iteration for non-linear ill-posed problems with sparsity constraints. Numer. Math. 2006;104:177–203.
- Ramlau R. Regularization properties of Tikhonov regularization with sparsity constraints. Electron. Trans. Numer. Anal. 2008;30:54–74.
- Scherzer O, Grasmair M, Grossauer H, Haltmeier M, Lenzen F. Variational methods in imaging. New York (NY): Springer-Verlag; 2009.
- Schuster T, Kaltenbacher B, Hofmann B, Kazimierski KS. Regularization methods in Banach spaces. Vol. 10, Radon series on computational and applied mathematics. Berlin: Walter de Gruyter; 2012.
- Anzengruber SW, Hofmann B, Mathé P. Regularization properties of the discrepancy principle for Tikhonov regularization in Banach spaces. Appl. Anal. 2014;93:1382–1400.
- Anzengruber SW, Ramlau R. Morozov’s discrepancy principle for Tikhonov-type functionals with nonlinear operators. Inverse Prob. 2010;26:025001.
- Anzengruber SW, Ramlau R. Convergence rates for Morozov’s discrepancy principle using variational inequalities. Inverse Prob. 2011;27:105007.
- Burger M, Osher S. Convergence rates of convex variational regularization. Inverse Prob. 2004;20:1411–1421.
- Grasmair M, Haltmeier M, Scherzer O. Sparse regularization with lq penalty term. Inverse Prob. 2008;24:1–13.
- Hofmann B, Kaltenbacher B, Poeschl C, Scherzer O. A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Inverse Prob. 2007;23:987–1010.
- Hofmann B, Mathé P. Parameter choice in Banach space regularization under variational inequalities. Inverse Prob. 2012;28:104006.
- Resmerita E, Scherzer O. Error estimates for non-quadratic regularization and the relation to enhancement. Inverse Prob. 2006;22:801–814.
- Ramlau R. A steepest descent algorithm for the global minimization of the Tikhonov functional. Inverse Prob. 2002;18:381–405.
- Ramlau R. TIGRA – an iterative algorithm for regularizing nonlinear ill-posed problems. Inverse Prob. 2003;19:433–465.
- Kokurin MY. Convexity of the Tikhonov functional and iteratively regularized methods for solving irregular nonlinear operator equations. Comput. Math. Math. Phys. 2010;50:620–632.
- Kokurin MY. The global search in the Tikhonov scheme. Russ. Math. 2010;54:17–26.
- Kokurin MY. On sequential minimization of Tikhonov functionals in ill-posed problems with a priori information on solutions. J. Inverse Ill-Posed Prob. 2011;18:1031–1050.
- Kaltenbacher B. Towards global convergence for strongly nonlinear ill-posed problems via a regularizing multilevel method. Numer. Funct. Anal. Optimiz. 2006;27:637–665.
- Kaltenbacher B. Convergence rates of a multilevel method for the regularization of nonlinear ill-posed problems. J. Integr. Equ. Appl. 2008;20:201–228.
- de Hoop MV, Qiu L, Scherzer O. An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints. Numerische Mathematik. 2012. doi:10.1007/s00211-014-0629-x
- Bonesky T, Kazimierski KS, Maass P, Schöpfer F, Schuster T. Minimization of Tikhonov functionals in Banach spaces Abstr. Appl. Anal. 2008;2008:192679.
- Xu ZB, Roach GF. Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces. J. Math. Anal. Appl. 1991;157:189–210.
- Butnariu D, Iusem AN. Totally convex functions for fixed point computation and infinite dimensional optimization. Vol. 40, Applied optimization. Dordrecht: Kluwer Academic; 2000.
- Lorenz DA. Convergence rates and source conditions for Tikhonov regularization with sparsity constraints. J. Inverse Ill-Posed Prob. 2008;16:463–478.
- Ramlau R, Resmerita E. Convergence rates for regularization with sparsity constraints. Electron. Trans. Numer. Anal. 2010;37:87–104.
- Hein T, Hofmann B. Approximate source conditions for nonlinear ill-posed problems – chances and limitations. Inverse Prob. 2009;25:035003.
- Scherzer O. A modified Landweber iteration for solving parameter estimation problems. Appl. Math. Optim. 1998;38:45–68.
- Gorenflo R, Hofmann B. On autoconvolution and regularization. Inverse Prob. 1994;10:353–373.
- Bürger S, Hofmann B. About a deficit in low order convergence rates on the example of autoconvolution. Appl. Anal. 2014. Available from: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-130630.