Aspri, Andrea; Scherzer, Otmar Analysis of Generalized Iteratively Regularized Landweber Iterations driven by data. arXiv:2312.03337 Preprint, arXiv:2312.03337 [math.NA] (2023). MSC: 65J20 65J10 65J15 65J22 BibTeX Cite \textit{A. Aspri} and \textit{O. Scherzer}, ``Analysis of Generalized Iteratively Regularized Landweber Iterations driven by data'', Preprint, arXiv:2312.03337 [math.NA] (2023) Full Text: arXiv OA License
Boţ, Radu; Dong, Guozhi; Elbau, Peter; Scherzer, Otmar Convergence rates of first- and higher-order dynamics for solving linear ill-posed problems. (English) Zbl 07605400 Found. Comput. Math. 22, No. 5, 1567-1629 (2022). MSC: 47A52 47N10 65J20 PDFBibTeX XMLCite \textit{R. Boţ} et al., Found. Comput. Math. 22, No. 5, 1567--1629 (2022; Zbl 07605400) Full Text: DOI arXiv
Parzer, Fabian; Scherzer, Otmar On convergence rates of adaptive ensemble Kalman inversion for linear ill-posed problems. (English) Zbl 1504.47028 Numer. Math. 152, No. 2, 371-409 (2022). MSC: 47A52 65J20 65C05 PDFBibTeX XMLCite \textit{F. Parzer} and \textit{O. Scherzer}, Numer. Math. 152, No. 2, 371--409 (2022; Zbl 1504.47028) Full Text: DOI arXiv
Aspri, Andrea; Frischauf, Leon; Korolev, Yury; Scherzer, Otmar Data driven reconstruction using frames and Riesz bases. (English) Zbl 1523.65047 Jadamba, Baasansuren (ed.) et al., Deterministic and stochastic optimal control and inverse problems. Boca Raton, FL: CRC Press/Science Publishers. 303-318 (2022). MSC: 65J22 47A52 42C15 PDFBibTeX XMLCite \textit{A. Aspri} et al., in: Deterministic and stochastic optimal control and inverse problems. Boca Raton, FL: CRC Press/Science Publishers. 303--318 (2022; Zbl 1523.65047) Full Text: DOI arXiv
Frischauf, Leon; Melching, Melanie; Scherzer, Otmar Diffusion tensor regularization with metric double integrals. (English) Zbl 1502.47015 J. Inverse Ill-Posed Probl. 30, No. 2, 163-190 (2022). MSC: 47A52 65J20 PDFBibTeX XMLCite \textit{L. Frischauf} et al., J. Inverse Ill-Posed Probl. 30, No. 2, 163--190 (2022; Zbl 1502.47015) Full Text: DOI arXiv
Kirisits, Clemens; Quellmalz, Michael; Ritsch-Marte, Monika; Scherzer, Otmar; Setterqvist, Eric; Steidl, Gabriele Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations. (English) Zbl 1505.65125 Inverse Probl. 37, No. 11, Article ID 115002, 37 p. (2021). MSC: 65D18 65T50 65K10 78A46 92C55 42B10 PDFBibTeX XMLCite \textit{C. Kirisits} et al., Inverse Probl. 37, No. 11, Article ID 115002, 37 p. (2021; Zbl 1505.65125) Full Text: DOI arXiv
Kaltenbacher, Barbara; Nguyen, Tram Thi Ngoc; Scherzer, Otmar The tangential cone condition for some coefficient identification model problems in parabolic PDEs. (English) Zbl 1487.35343 Kaltenbacher, Barbara (ed.) et al., Time-dependent problems in imaging and parameter identification. Cham: Springer. 121-163 (2021). MSC: 35Q53 35Q56 35Q92 35Q60 65J20 65J22 78A46 92C55 74H75 35K58 35R30 PDFBibTeX XMLCite \textit{B. Kaltenbacher} et al., in: Time-dependent problems in imaging and parameter identification. Cham: Springer. 121--163 (2021; Zbl 1487.35343) Full Text: DOI arXiv
Melching, Melanie; Scherzer, Otmar Regularization with metric double integrals for vector tomography. (English) Zbl 1523.47024 J. Inverse Ill-Posed Probl. 28, No. 6, 857-875 (2020). MSC: 47A52 65J20 92C55 PDFBibTeX XMLCite \textit{M. Melching} and \textit{O. Scherzer}, J. Inverse Ill-Posed Probl. 28, No. 6, 857--875 (2020; Zbl 1523.47024) Full Text: DOI arXiv
Aspri, Andrea; Korolev, Yury; Scherzer, Otmar Data driven regularization by projection. (English) Zbl 1502.65030 Inverse Probl. 36, No. 12, Article ID 125009, 35 p. (2020). MSC: 65J22 PDFBibTeX XMLCite \textit{A. Aspri} et al., Inverse Probl. 36, No. 12, Article ID 125009, 35 p. (2020; Zbl 1502.65030) Full Text: DOI arXiv
Aspri, A.; Banert, S.; Öktem, O.; Scherzer, O. A data-driven iteratively regularized Landweber iteration. (English) Zbl 07241785 Numer. Funct. Anal. Optim. 41, No. 10, 1190-1227 (2020). MSC: 65J20 65J10 65J15 65J22 PDFBibTeX XMLCite \textit{A. Aspri} et al., Numer. Funct. Anal. Optim. 41, No. 10, 1190--1227 (2020; Zbl 07241785) Full Text: DOI arXiv
Ciak, René; Melching, Melanie; Scherzer, Otmar Regularization with metric double integrals of functions with values in a set of vectors. (English) Zbl 1451.49038 J. Math. Imaging Vis. 61, No. 6, 824-848 (2019). MSC: 49N45 46E35 PDFBibTeX XMLCite \textit{R. Ciak} et al., J. Math. Imaging Vis. 61, No. 6, 824--848 (2019; Zbl 1451.49038) Full Text: DOI arXiv
Kirisits, Clemens; Scherzer, Otmar A range condition for polyconvex variational regularization. (English) Zbl 1401.49053 Numer. Funct. Anal. Optim. 39, No. 10, 1064-1076 (2018). MSC: 49N60 49N45 PDFBibTeX XMLCite \textit{C. Kirisits} and \textit{O. Scherzer}, Numer. Funct. Anal. Optim. 39, No. 10, 1064--1076 (2018; Zbl 1401.49053) Full Text: DOI arXiv
Iglesias, José A.; Mercier, Gwenael; Scherzer, Otmar A note on convergence of solutions of total variation regularized linear inverse problems. (English) Zbl 1516.35514 Inverse Probl. 34, No. 5, Article ID 055011, 28 p. (2018). MSC: 35R30 35A15 PDFBibTeX XMLCite \textit{J. A. Iglesias} et al., Inverse Probl. 34, No. 5, Article ID 055011, 28 p. (2018; Zbl 1516.35514) Full Text: DOI arXiv
Dong, Guozhi; Scherzer, Otmar Nonlinear flows for displacement correction and applications in tomography. (English) Zbl 1489.94010 Lauze, François (ed.) et al., Scale space and variational methods in computer vision. 6th international conference, SSVM 2017, Kolding, Denmark, June 4–8, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10302, 283-294 (2017). MSC: 94A08 68U10 90C90 PDFBibTeX XMLCite \textit{G. Dong} and \textit{O. Scherzer}, Lect. Notes Comput. Sci. 10302, 283--294 (2017; Zbl 1489.94010) Full Text: DOI arXiv
Elbau, Peter; Scherzer, Otmar; Shi, Cong Singular values of the attenuated photoacoustic imaging operator. (English) Zbl 1401.35329 J. Differ. Equations 263, No. 9, 5330-5376 (2017). Reviewer: Bernd Hofmann (Chemnitz) MSC: 35R25 47A52 PDFBibTeX XMLCite \textit{P. Elbau} et al., J. Differ. Equations 263, No. 9, 5330--5376 (2017; Zbl 1401.35329) Full Text: DOI arXiv
Kirisits, Clemens; Scherzer, Otmar Convergence rates for regularization functionals with polyconvex integrands. (English) Zbl 1376.49047 Inverse Probl. 33, No. 8, Article ID 085008, 16 p. (2017). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 49N45 65N21 65F22 PDFBibTeX XMLCite \textit{C. Kirisits} and \textit{O. Scherzer}, Inverse Probl. 33, No. 8, Article ID 085008, 16 p. (2017; Zbl 1376.49047) Full Text: DOI arXiv
Dong, Guozhi; Jüttler, Bert; Scherzer, Otmar; Takacs, Thomas Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces. (English) Zbl 1375.47002 Inverse Probl. Imaging 11, No. 2, 221-246 (2017). MSC: 47A52 65J20 53B20 46C99 65D07 PDFBibTeX XMLCite \textit{G. Dong} et al., Inverse Probl. Imaging 11, No. 2, 221--246 (2017; Zbl 1375.47002) Full Text: DOI arXiv
Belhachmi, Zakaria; Glatz, Thomas; Scherzer, Otmar Photoacoustic tomography with spatially varying compressibility and density. (English) Zbl 1355.65124 J. Inverse Ill-Posed Probl. 25, No. 1, 119-133 (2017). MSC: 65M32 65J22 35R30 PDFBibTeX XMLCite \textit{Z. Belhachmi} et al., J. Inverse Ill-Posed Probl. 25, No. 1, 119--133 (2017; Zbl 1355.65124) Full Text: DOI arXiv
Albani, V.; Elbau, P.; De Hoop, M. V.; Scherzer, O. Optimal convergence rates results for linear inverse problems in Hilbert spaces. (English) Zbl 1352.65146 Numer. Funct. Anal. Optim. 37, No. 5, 521-540 (2016). MSC: 65J20 47A52 49N45 PDFBibTeX XMLCite \textit{V. Albani} et al., Numer. Funct. Anal. Optim. 37, No. 5, 521--540 (2016; Zbl 1352.65146) Full Text: DOI arXiv
Belhachmi, Zakaria; Glatz, Thomas; Scherzer, Otmar A direct method for photoacoustic tomography with inhomogeneous sound speed. (English) Zbl 1382.65289 Inverse Probl. 32, No. 4, Article ID 045005, 25 p. (2016). MSC: 65M32 35L15 35R30 76Q05 94A08 PDFBibTeX XMLCite \textit{Z. Belhachmi} et al., Inverse Probl. 32, No. 4, Article ID 045005, 25 p. (2016; Zbl 1382.65289) Full Text: DOI arXiv
Andreev, Roman; Elbau, Peter; de Hoop, Maarten V.; Qiu, Lingyun; Scherzer, Otmar Generalized convergence rates results for linear inverse problems in Hilbert spaces. (English) Zbl 1378.65118 Numer. Funct. Anal. Optim. 36, No. 5, 549-566 (2015). MSC: 65J22 65J10 65R32 49N45 PDFBibTeX XMLCite \textit{R. Andreev} et al., Numer. Funct. Anal. Optim. 36, No. 5, 549--566 (2015; Zbl 1378.65118) Full Text: DOI arXiv
Kirisits, Clemens; Pöschl, Christiane; Resmerita, Elena; Scherzer, Otmar Finite-dimensional approximation of convex regularization via hexagonal pixel grids. (English) Zbl 1312.65089 Appl. Anal. 94, No. 3, 612-636 (2015). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 65J15 65J20 47J06 PDFBibTeX XMLCite \textit{C. Kirisits} et al., Appl. Anal. 94, No. 3, 612--636 (2015; Zbl 1312.65089) Full Text: DOI
de Hoop, Maarten V.; Qiu, Lingyun; Scherzer, Otmar An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints. (English) Zbl 1317.65133 Numer. Math. 129, No. 1, 127-148 (2015). Reviewer: Robert Plato (Siegen) MSC: 65J22 65J15 47J06 47J25 65J20 PDFBibTeX XMLCite \textit{M. V. de Hoop} et al., Numer. Math. 129, No. 1, 127--148 (2015; Zbl 1317.65133) Full Text: DOI arXiv
Bal, Guillaume; Naetar, Wolf; Scherzer, Otmar; Schotland, John The Levenberg-Marquardt iteration for numerical inversion of the power density operator. (English) Zbl 1273.35307 J. Inverse Ill-Posed Probl. 21, No. 2, 265-280 (2013). MSC: 35R30 47J06 35J47 PDFBibTeX XMLCite \textit{G. Bal} et al., J. Inverse Ill-Posed Probl. 21, No. 2, 265--280 (2013; Zbl 1273.35307) Full Text: DOI arXiv
Abhau, Jochen; Aichholzer, Oswin; Colutto, Sebastian; Kornberger, Bernhard; Scherzer, Otmar Shape spaces via medial axis transforms for segmentation of complex geometry in 3D voxel data. (English) Zbl 06174325 Inverse Probl. Imaging 7, No. 1, 1-25 (2013). MSC: 65D18 65F22 68U10 94A08 PDFBibTeX XMLCite \textit{J. Abhau} et al., Inverse Probl. Imaging 7, No. 1, 1--25 (2013; Zbl 06174325) Full Text: DOI
Grasmair, M; Scherzer, O; Vanhems, A Nonparametric instrumental regression with non-convex constraints. (English) Zbl 1379.62033 Inverse Probl. 29, No. 3, 035006, 16 p. (2013). MSC: 62G08 PDFBibTeX XMLCite \textit{M Grasmair} et al., Inverse Probl. 29, No. 3, 035006, 16 p. (2013; Zbl 1379.62033) Full Text: DOI arXiv
Fidler, Thomas; Grasmair, Markus; Scherzer, Otmar Shape reconstruction with a priori knowledge based on integral invariants. (English) Zbl 1250.65152 SIAM J. Imaging Sci. 5, No. 2, 726-745 (2012). MSC: 65R10 65R30 65R32 44A12 65K10 49Q10 PDFBibTeX XMLCite \textit{T. Fidler} et al., SIAM J. Imaging Sci. 5, No. 2, 726--745 (2012; Zbl 1250.65152) Full Text: DOI Link
Pontow, Carsten; Scherzer, Otmar Analytical evaluations of double integral expressions related to total variation. (English) Zbl 1250.65045 Langer, Ulrich (ed.) et al., Numerical and symbolic scientific computing. Progress and prospects. New York, NY: Springer (ISBN 978-3-7091-0793-5/pbk; 978-3-7091-0794-2/ebook). Texts & Monographs in Symbolic Computation, 193-218 (2012). MSC: 65D32 41A55 41A63 68W30 65Y15 PDFBibTeX XMLCite \textit{C. Pontow} and \textit{O. Scherzer}, in: Numerical and symbolic scientific computing. Progress and prospects. New York, NY: Springer. 193--218 (2012; Zbl 1250.65045) Full Text: DOI arXiv
De Cezaro, A.; Scherzer, O.; Zubelli, J. P. Convex regularization of local volatility models from option prices: convergence analysis and rates. (English) Zbl 1263.47086 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2398-2415 (2012). Reviewer: Alexandra Rodkina (Kingston/Jamaica) MSC: 47N10 47A52 65M32 91B24 91G80 PDFBibTeX XMLCite \textit{A. De Cezaro} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2398--2415 (2012; Zbl 1263.47086) Full Text: DOI
Thorstensen, Nicolas; Scherzer, Otmar Convergence of variational regularization methods for imaging on Riemannian manifolds. (English) Zbl 1234.65023 Inverse Probl. 28, No. 1, Article ID 015007, 17 p. (2012). MSC: 65J10 65J22 65D19 65J20 47A52 58E50 PDFBibTeX XMLCite \textit{N. Thorstensen} and \textit{O. Scherzer}, Inverse Probl. 28, No. 1, Article ID 015007, 17 p. (2012; Zbl 1234.65023) Full Text: DOI arXiv
Grasmair, Markus; Haltmeier, Markus; Scherzer, Otmar The residual method for regularizing ill-posed problems. (English) Zbl 1247.65076 Appl. Math. Comput. 218, No. 6, 2693-2710 (2011). Reviewer: Ştefan M. Şoltuz (Westmount) MSC: 65J20 65J15 94A08 94A12 47J06 PDFBibTeX XMLCite \textit{M. Grasmair} et al., Appl. Math. Comput. 218, No. 6, 2693--2710 (2011; Zbl 1247.65076) Full Text: DOI arXiv
Grasmair, Markus; Scherzer, Otmar; Haltmeier, Markus Necessary and sufficient conditions for linear convergence of \(\ell^1\)-regularization. (English) Zbl 1217.65095 Commun. Pure Appl. Math. 64, No. 2, 161-182 (2011). Reviewer: Martín Argerami (Regina) MSC: 65J10 47A52 65J20 65J22 PDFBibTeX XMLCite \textit{M. Grasmair} et al., Commun. Pure Appl. Math. 64, No. 2, 161--182 (2011; Zbl 1217.65095) Full Text: DOI
Pöschl, Christiane; Resmerita, Elena; Scherzer, Otmar Discretization of variational regularization in Banach spaces. (English) Zbl 1200.47018 Inverse Probl. 26, No. 10, Article ID 105017, 18 p. (2010). MSC: 47A52 52A21 65F22 PDFBibTeX XMLCite \textit{C. Pöschl} et al., Inverse Probl. 26, No. 10, Article ID 105017, 18 p. (2010; Zbl 1200.47018) Full Text: DOI arXiv
Pöschl, Christiane; Modersitzki, Jan; Scherzer, Otmar A variational setting for volume constrained image registration. (English) Zbl 1204.68247 Inverse Probl. Imaging 4, No. 3, 505-522 (2010). MSC: 68U10 65N21 PDFBibTeX XMLCite \textit{C. Pöschl} et al., Inverse Probl. Imaging 4, No. 3, 505--522 (2010; Zbl 1204.68247) Full Text: DOI
Pöschl, Christiane; Scherzer, Otmar Characterization of minimizers of convex regularization functionals. (English) Zbl 1163.47004 Larson, David R. (ed.) et al., Frames and operator theory in analysis and signal processing. AMS-SIAM special session, San Antonio, TX, USA, January 12–15, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4144-0/pbk). Contemporary Mathematics 451, 219-248 (2008). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 47A52 65F22 PDFBibTeX XMLCite \textit{C. Pöschl} and \textit{O. Scherzer}, Contemp. Math. 451, 219--248 (2008; Zbl 1163.47004)
Grasmair, Markus; Haltmeier, Markus; Scherzer, Otmar Sparse regularization with \(l^{q}\) penalty term. (English) Zbl 1157.65033 Inverse Probl. 24, No. 5, Article ID 055020, 13 p. (2008). Reviewer: Jiří Vaníček (Praha) MSC: 65J15 65J20 47J06 PDFBibTeX XMLCite \textit{M. Grasmair} et al., Inverse Probl. 24, No. 5, Article ID 055020, 13 p. (2008; Zbl 1157.65033) Full Text: DOI arXiv
Fuchs, Matthias; Scherzer, Otmar Regularized reconstruction of shapes with statistical a priori knowledge. (English) Zbl 1477.68470 Int. J. Comput. Vis. 79, No. 2, 119-135 (2008). MSC: 68U05 62H35 68U10 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{O. Scherzer}, Int. J. Comput. Vis. 79, No. 2, 119--135 (2008; Zbl 1477.68470) Full Text: DOI
De Cezaro, A.; Haltmeier, M.; Leitão, A.; Scherzer, O. On steepest-descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations. (English) Zbl 1157.65032 Appl. Math. Comput. 202, No. 2, 596-607 (2008). Reviewer: Werner H. Schmidt (Greifswald) MSC: 65J15 47J06 65J20 92C55 82D37 PDFBibTeX XMLCite \textit{A. De Cezaro} et al., Appl. Math. Comput. 202, No. 2, 596--607 (2008; Zbl 1157.65032) Full Text: DOI arXiv
Kaltenbacher, Barbara; Neubauer, Andreas; Scherzer, Otmar Iterative regularization methods for nonlinear ill-posed problems. (English) Zbl 1145.65037 Radon Series on Computational and Applied Mathematics 6. Berlin: de Gruyter (ISBN 978-3-11-020420-9/hbk). viii, 194 p. (2008). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 65J15 65J20 65J22 47J06 65-02 PDFBibTeX XMLCite \textit{B. Kaltenbacher} et al., Iterative regularization methods for nonlinear ill-posed problems. Berlin: de Gruyter (2008; Zbl 1145.65037) Full Text: DOI
Burger, M.; Frick, K.; Osher, S.; Scherzer, O. Inverse total variation flow. (English) Zbl 1147.49026 Multiscale Model. Simul. 6, No. 2, 366-395 (2007). MSC: 49N60 35K90 47A52 68U10 49J15 PDFBibTeX XMLCite \textit{M. Burger} et al., Multiscale Model. Simul. 6, No. 2, 366--395 (2007; Zbl 1147.49026) Full Text: DOI Link
Haltmeier, Markus; Kowar, Richard; Leitão, Antonio; Scherzer, Otmar Kaczmarz methods for regularizing nonlinear ill-posed equations. II: Applications. (English) Zbl 1135.65026 Inverse Probl. Imaging 1, No. 3, 507-523 (2007). Reviewer: Iulian Coroian (Baia Mare) MSC: 65J15 65J20 47J06 PDFBibTeX XMLCite \textit{M. Haltmeier} et al., Inverse Probl. Imaging 1, No. 3, 507--523 (2007; Zbl 1135.65026) Full Text: DOI arXiv
Haltmeier, Markus; Leitão, Antonio; Scherzer, Otmar Kaczmarz methods for regularizing nonlinear ill-posed equations. I: Convergence analysis. (English) Zbl 1123.65051 Inverse Probl. Imaging 1, No. 2, 289-298 (2007). Reviewer: Iulian Coroian (Baia Mare) MSC: 65J15 65J20 47J06 PDFBibTeX XMLCite \textit{M. Haltmeier} et al., Inverse Probl. Imaging 1, No. 2, 289--298 (2007; Zbl 1123.65051) Full Text: DOI arXiv
Hofmann, B.; Kaltenbacher, B.; Pöschl, C.; Scherzer, O. A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. (English) Zbl 1131.65046 Inverse Probl. 23, No. 3, 987-1010 (2007). Reviewer: Teresa Regińska (Warszawa) MSC: 65J15 65J20 47J06 91G60 PDFBibTeX XMLCite \textit{B. Hofmann} et al., Inverse Probl. 23, No. 3, 987--1010 (2007; Zbl 1131.65046) Full Text: DOI Link
Resmerita, Elena; Scherzer, Otmar Error estimates for nonquadratic regularization and the relation to enhancement. (English) Zbl 1103.65062 Inverse Probl. 22, No. 3, 801-814 (2006). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 65J15 65J20 47J06 PDFBibTeX XMLCite \textit{E. Resmerita} and \textit{O. Scherzer}, Inverse Probl. 22, No. 3, 801--814 (2006; Zbl 1103.65062) Full Text: DOI
Hinterberger, W.; Scherzer, O. Variational methods on the space of functions of bounded Hessian for convexification and denoising. (English) Zbl 1098.49022 Computing 76, No. 1-2, 109-133 (2006). Reviewer: Hans Benker (Merseburg) MSC: 49K20 49J25 65J20 49J40 65K10 PDFBibTeX XMLCite \textit{W. Hinterberger} and \textit{O. Scherzer}, Computing 76, No. 1--2, 109--133 (2006; Zbl 1098.49022) Full Text: DOI
Scherzer, Otmar; Yin, Wotao; Osher, Stanley Slope and \(G\)-set characterization of set-valued functions and applications to non-differentiable optimization problems. (English) Zbl 1094.65064 Commun. Math. Sci. 3, No. 4, 479-492 (2005). Reviewer: Efstratios Rappos (London) MSC: 65K10 49J52 49J53 PDFBibTeX XMLCite \textit{O. Scherzer} et al., Commun. Math. Sci. 3, No. 4, 479--492 (2005; Zbl 1094.65064) Full Text: DOI
Grasmair, M.; Scherzer, O. Relaxation of nonlocal singular integrals. (English) Zbl 1094.47014 Numer. Funct. Anal. Optimization 26, No. 4-5, 481-506 (2005). Reviewer: John Schmeelk (Doha) MSC: 47A52 49J45 49J52 65R20 PDFBibTeX XMLCite \textit{M. Grasmair} and \textit{O. Scherzer}, Numer. Funct. Anal. Optim. 26, No. 4--5, 481--506 (2005; Zbl 1094.47014) Full Text: DOI
Grasmair, Markus; Lenzen, Frank; Obereder, Andreas; Scherzer, Otmar; Fuchs, Matthias A non-convex PDE scale space. (English) Zbl 1119.68475 Kimmel, Ron (ed.) et al., Scale space and PDE methods in computer vision. 5th international conference, Scale-Space 2005, Hofgeismar, Germany, April 7–9, 2005. Proceedings. Berlin: Springer (ISBN 3-540-25547-8/pbk). Lecture Notes in Computer Science 3459, 303-315 (2005). MSC: 68T45 68U10 PDFBibTeX XMLCite \textit{M. Grasmair} et al., Lect. Notes Comput. Sci. 3459, 303--315 (2005; Zbl 1119.68475) Full Text: DOI
Frühauf, F.; Scherzer, O.; Leitão, A. Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators. (English) Zbl 1092.65046 SIAM J. Numer. Anal. 43, No. 2, 767-786 (2005). Reviewer: Yuxia Guo (Beijing) MSC: 65J15 47J06 62J20 PDFBibTeX XMLCite \textit{F. Frühauf} et al., SIAM J. Numer. Anal. 43, No. 2, 767--786 (2005; Zbl 1092.65046) Full Text: DOI arXiv
Hinterberger, Walter; Hintermüller, Michael; Kunisch, Karl; von Oehsen, Markus; Scherzer, Otmar Tube methods for BV regularization. (English) Zbl 1101.68927 J. Math. Imaging Vis. 19, No. 3, 219-235 (2003). MSC: 68U10 PDFBibTeX XMLCite \textit{W. Hinterberger} et al., J. Math. Imaging Vis. 19, No. 3, 219--235 (2003; Zbl 1101.68927) Full Text: DOI
Leitão, A.; Scherzer, O. On the relation between constraint regularization, level sets, and shape optimization. (English) Zbl 1030.65062 Inverse Probl. 19, No. 1, L1-L11 (2003). MSC: 65J15 65J20 47J06 PDFBibTeX XMLCite \textit{A. Leitão} and \textit{O. Scherzer}, Inverse Probl. 19, No. 1, L1--L11 (2003; Zbl 1030.65062) Full Text: DOI arXiv
Kowar, R.; Scherzer, O. Convergence analysis of a Landweber-Kaczmarz method for solving nonlinear ill-posed problems. (English) Zbl 1048.65055 Romanov, V. G. (ed.) et al., Ill-posed and inverse problems. Dedicated to Academician Mikhail Mikhailovich Lavrentiev on the occasion of his 70th birthday. Utrecht: VSP (ISBN 90-6764-362-9/hbk). 253-270 (2002). MSC: 65J15 65J20 47J06 PDFBibTeX XMLCite \textit{R. Kowar} and \textit{O. Scherzer}, in: Ill-posed and inverse problems. Dedicated to Academician Mikhail Mikhailovich Lavrentiev on the occasion of his 70th birthday. Utrecht: VSP. 253--270 (2002; Zbl 1048.65055)
Scherzer, O. Explicit versus implicit relative error regularization on the space of functions of bounded variation. (English) Zbl 1028.65147 Nashed, M. Zuhair (ed.) et al., Inverse problems, image analysis, and medical imaging. AMS special session on interaction of inverse problems and image analysis, New Orleans, LA, USA, January 10-13, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 313, 171-198 (2002). MSC: 65R20 65R30 45G10 PDFBibTeX XMLCite \textit{O. Scherzer}, Contemp. Math. 313, 171--198 (2002; Zbl 1028.65147)
Groetsch, C. W.; Scherzer, O. Iterative stabilization and edge detection. (English) Zbl 1028.65056 Nashed, M. Zuhair (ed.) et al., Inverse problems, image analysis, and medical imaging. AMS special session on interaction of inverse problems and image analysis, New Orleans, LA, USA, January 10-13, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 313, 129-141 (2002). MSC: 65J10 65J20 65M12 47A52 PDFBibTeX XMLCite \textit{C. W. Groetsch} and \textit{O. Scherzer}, Contemp. Math. 313, 129--141 (2002; Zbl 1028.65056)
Kabanikhin, S. I.; Kowar, R.; Scherzer, O.; Vasin, V. V. Numerical comparison of iterative regularization methods for a parameter estimation problem in a hyperbolic PDE. (English) Zbl 1001.65103 J. Inverse Ill-Posed Probl. 9, No. 6, 615-626 (2001). MSC: 65M32 35R30 35L15 65M06 PDFBibTeX XMLCite \textit{S. I. Kabanikhin} et al., J. Inverse Ill-Posed Probl. 9, No. 6, 615--626 (2001; Zbl 1001.65103) Full Text: DOI
Burger, Martin; Scherzer, Otmar Regularization methods for blind deconvolution and blind source separation problems. (English) Zbl 1002.93060 Math. Control Signals Syst. 14, No. 4, 358-383 (2001). Reviewer: Christina Diakaki (Chania) MSC: 93E10 65F22 92B20 68U10 94A12 93E12 PDFBibTeX XMLCite \textit{M. Burger} and \textit{O. Scherzer}, Math. Control Signals Syst. 14, No. 4, 358--383 (2001; Zbl 1002.93060) Full Text: DOI
Scherzer, Otmar A posteriori error estimates for the solution of nonlinear ill-posed operator equations. (English) Zbl 0994.35122 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 45, No. 4, 459-481 (2001). Reviewer: Bernd Hofmann (Chemnitz) MSC: 35R30 47J06 65J22 PDFBibTeX XMLCite \textit{O. Scherzer}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 45, No. 4, 459--481 (2001; Zbl 0994.35122) Full Text: DOI
Engl, H. W.; Scherzer, O. Convergence rates results for iterative methods for solving nonlinear ill-posed problems. (English) Zbl 0998.65058 Colton, David (ed.) et al., Surveys on solution methods for inverse problems. Wien: Springer. 7-34 (2000). MSC: 65J15 65-02 65J20 47J25 47J06 PDFBibTeX XMLCite \textit{H. W. Engl} and \textit{O. Scherzer}, in: Surveys on solution methods for inverse problems. Wien: Springer. 7--34 (2000; Zbl 0998.65058)
Groetsch, C. W.; Scherzer, O. Non-stationary iterated Tikhonov-Morozov method and third-order differential equations for the evaluation of unbounded operators. (English) Zbl 0970.65059 Math. Methods Appl. Sci. 23, No. 15, 1287-1300 (2000). Reviewer: Teresa Regińska (Warszawa) MSC: 65J10 68U10 94A08 47A52 65J20 65D25 PDFBibTeX XMLCite \textit{C. W. Groetsch} and \textit{O. Scherzer}, Math. Methods Appl. Sci. 23, No. 15, 1287--1300 (2000; Zbl 0970.65059) Full Text: DOI
Scherzer, Otmar; Weickert, Joachim Relations between regularization and diffusion filtering. (English) Zbl 0945.68183 J. Math. Imaging Vis. 12, No. 1, 43-63 (2000). MSC: 68U10 PDFBibTeX XMLCite \textit{O. Scherzer} and \textit{J. Weickert}, J. Math. Imaging Vis. 12, No. 1, 43--63 (2000; Zbl 0945.68183) Full Text: DOI
Hanke, Martin; Scherzer, Otmar Error analysis of an equation error method for the identification of the diffusion coefficient in a quasi-linear parabolic differential equation. (English) Zbl 0928.35198 SIAM J. Appl. Math. 59, No. 3, 1012-1027 (1999). MSC: 35R30 65M30 65M15 35K55 PDFBibTeX XMLCite \textit{M. Hanke} and \textit{O. Scherzer}, SIAM J. Appl. Math. 59, No. 3, 1012--1027 (1999; Zbl 0928.35198) Full Text: DOI
Scherzer, O.; Gulliksson, M. Adaptive strategy for the damping parameters in an iteratively regularized Gauss-Newton method. (English) Zbl 0933.65062 J. Optimization Theory Appl. 100, No. 1, 161-180 (1999). Reviewer: R.Plato (Berlin) MSC: 65J15 65J20 47J25 65Y20 PDFBibTeX XMLCite \textit{O. Scherzer} and \textit{M. Gulliksson}, J. Optim. Theory Appl. 100, No. 1, 161--180 (1999; Zbl 0933.65062) Full Text: DOI
Nashed, M. Z.; Scherzer, O. Least squares and bounded variation regularization with nondifferentiable functionals. (English) Zbl 0914.65067 Numer. Funct. Anal. Optimization 19, No. 7-8, 873-901 (1998). Reviewer: K.Najzar (Praha) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{M. Z. Nashed} and \textit{O. Scherzer}, Numer. Funct. Anal. Optim. 19, No. 7--8, 873--901 (1998; Zbl 0914.65067) Full Text: DOI
Scherzer, Otmar An iterative multi level algorithm for solving nonlinear ill-posed problems. (English) Zbl 0918.65041 Numer. Math. 80, No. 4, 579-600 (1998). Reviewer: R.Plato (Berlin) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{O. Scherzer}, Numer. Math. 80, No. 4, 579--600 (1998; Zbl 0918.65041) Full Text: DOI
Hofmann, Bernd; Scherzer, Otmar Local ill-posedness and source conditions of operator equations in Hilbert spaces. (English) Zbl 0915.65052 Inverse Probl. 14, No. 5, 1189-1206 (1998). Reviewer: V.Berinde (Baia Mare) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{B. Hofmann} and \textit{O. Scherzer}, Inverse Probl. 14, No. 5, 1189--1206 (1998; Zbl 0915.65052) Full Text: DOI Link
Deuflhard, Peter; Engl, Heinz W.; Scherzer, Otmar A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions. (English) Zbl 0915.65053 Inverse Probl. 14, No. 5, 1081-1106 (1998). Reviewer: W.C.Rheinboldt (Pittsburgh) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{P. Deuflhard} et al., Inverse Probl. 14, No. 5, 1081--1106 (1998; Zbl 0915.65053) Full Text: DOI
Neubauer, Andreas; Scherzer, Otmar Regularization for curve representations: Uniform convergence for discontinuous solutions of ill-posed problems. (English) Zbl 0916.65128 SIAM J. Appl. Math. 58, No. 6, 1891-1900 (1998). Reviewer: R.Lepp (Tallinn) MSC: 65R20 45B05 65R30 PDFBibTeX XMLCite \textit{A. Neubauer} and \textit{O. Scherzer}, SIAM J. Appl. Math. 58, No. 6, 1891--1900 (1998; Zbl 0916.65128) Full Text: DOI
Scherzer, Otmar; Strohmer, Thomas A multi-level algorithm for the solution of moment problems. (English) Zbl 0908.65127 Numer. Funct. Anal. Optimization 19, No. 3-4, 353-375 (1998). Reviewer: R.S.Dahiya (Ames) MSC: 65R10 44A60 65J10 65J20 94A12 65T40 42A15 PDFBibTeX XMLCite \textit{O. Scherzer} and \textit{T. Strohmer}, Numer. Funct. Anal. Optim. 19, No. 3--4, 353--375 (1998; Zbl 0908.65127) Full Text: DOI arXiv
Scherzer, O. A modified Landweber iteration for solving parameter estimation problems. (English) Zbl 0915.65054 Appl. Math. Optimization 38, No. 1, 45-68 (1998). Reviewer: Gabriel Dimitriu (Iaşi) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{O. Scherzer}, Appl. Math. Optim. 38, No. 1, 45--68 (1998; Zbl 0915.65054) Full Text: DOI
Scherzer, O. Denoising with higher order derivatives of bounded variation and an application to parameter estimation. (English) Zbl 0891.65103 Computing 60, No. 1, 1-27 (1998). Reviewer: T.Semerdjiev (Sofia) MSC: 65M30 35R30 35K05 PDFBibTeX XMLCite \textit{O. Scherzer}, Computing 60, No. 1, 1--27 (1998; Zbl 0891.65103) Full Text: DOI
Hettlich, Frank; Morgan, Jeff; Scherzer, Otmar On the estimation of interfaces from boundary measurements. (English) Zbl 0867.73022 Engl, Heinz W. (ed.) et al., Inverse problems in geophysical applications. Proceedings of the GAMM-SIAM conference held in Yosemite, CA, USA, December 16–19, 1995. Philadelphia, PA: SIAM. 163-178 (1997). MSC: 74J25 86A15 PDFBibTeX XMLCite \textit{F. Hettlich} et al., in: Inverse problems in geophysical applications. Proceedings of the GAMM-SIAM conference held in Yosemite, CA, USA, December 16--19, 1995. Philadelphia, PA: SIAM. 163--178 (1997; Zbl 0867.73022)
Nashed, M. Zuhair; Scherzer, Otmar Stable approximations of a minimal surface problem with variational inequalities. (English) Zbl 0937.49020 Abstr. Appl. Anal. 2, No. 1-2, 137-161 (1997). MSC: 49Q05 49J40 49N60 49J45 65K10 26A45 65J15 65J20 PDFBibTeX XMLCite \textit{M. Z. Nashed} and \textit{O. Scherzer}, Abstr. Appl. Anal. 2, No. 1--2, 137--161 (1997; Zbl 0937.49020) Full Text: DOI EuDML Link
Scherzer, Otmar Stable evaluation of differential operators and linear and nonlinear multi-scale filtering. (English) Zbl 0891.65075 Electron. J. Differ. Equ. 1997, Paper 15, 12 p. (1997). Reviewer: V.Arnăutu (Iaşi) MSC: 65K10 49J52 49J40 65J10 65J15 PDFBibTeX XMLCite \textit{O. Scherzer}, Electron. J. Differ. Equ. 1997, Paper 15, 12 p. (1997; Zbl 0891.65075) Full Text: EuDML EMIS
Blaschke, Barbara; Neubauer, Andreas; Scherzer, Otmar On convergence rates for the iteratively regularized Gauss-Newton method. (English) Zbl 0881.65050 IMA J. Numer. Anal. 17, No. 3, 421-436 (1997). Reviewer: V.Berinde (Baia Mare) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{B. Blaschke} et al., IMA J. Numer. Anal. 17, No. 3, 421--436 (1997; Zbl 0881.65050) Full Text: DOI
Frigaard, I. A.; Scherzer, O. Spraying the perfect billet. (English) Zbl 0876.47045 SIAM J. Appl. Math. 57, No. 3, 649-682 (1997). MSC: 47J25 65J20 65J15 82D99 PDFBibTeX XMLCite \textit{I. A. Frigaard} and \textit{O. Scherzer}, SIAM J. Appl. Math. 57, No. 3, 649--682 (1997; Zbl 0876.47045) Full Text: DOI
Nashed, M. Zuhair; Scherzer, Otmar Stable approximation of nondifferentiable optimization problems with variational inequalities. (English) Zbl 0868.49008 Censor, Yair (ed.) et al., Recent developments in optimization theory and nonlinear analysis. AMS/IMU special session on optimization and nonlinear analysis, May 24–26, 1995, Jerusalem, Israel. Providence, RI: American Mathematical Society. Contemp. Math. 204, 155-170 (1997). MSC: 49J40 49Q05 65K10 49N60 PDFBibTeX XMLCite \textit{M. Z. Nashed} and \textit{O. Scherzer}, Contemp. Math. 204, 155--170 (1997; Zbl 0868.49008)
Binder, A.; Hanke, M.; Scherzer, O. On the Landweber iteration for nonlinear ill-posed problems. (English) Zbl 0879.65037 J. Inverse Ill-Posed Probl. 4, No. 5, 381-389 (1996). Reviewer: G.Dimitriu (Iaşi) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{A. Binder} et al., J. Inverse Ill-Posed Probl. 4, No. 5, 381--389 (1996; Zbl 0879.65037) Full Text: DOI
Dobson, David; Scherzer, Otmar Analysis of regularized total variation penalty methods for denoising. (English) Zbl 0866.65041 Inverse Probl. 12, No. 5, 601-617 (1996). Reviewer: Yu Wenhuan (Tianjin) MSC: 65K10 49J22 49M15 49M30 PDFBibTeX XMLCite \textit{D. Dobson} and \textit{O. Scherzer}, Inverse Probl. 12, No. 5, 601--617 (1996; Zbl 0866.65041) Full Text: DOI Link
Scherzer, Otmar A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems. (English) Zbl 0852.65048 Numer. Funct. Anal. Optimization 17, No. 1-2, 197-214 (1996). Reviewer: Simeon Reich (Haifa) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{O. Scherzer}, Numer. Funct. Anal. Optim. 17, No. 1--2, 197--214 (1996; Zbl 0852.65048) Full Text: DOI
Scherzer, Otmar Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems. (English) Zbl 0842.65036 J. Math. Anal. Appl. 194, No. 3, 911-933 (1995). Reviewer: Yu Wenhuan (Tianjin) MSC: 65J15 34A55 47J25 65J20 PDFBibTeX XMLCite \textit{O. Scherzer}, J. Math. Anal. Appl. 194, No. 3, 911--933 (1995; Zbl 0842.65036) Full Text: DOI
Hanke, Martin; Neubauer, Andreas; Scherzer, Otmar A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. (English) Zbl 0840.65049 Numer. Math. 72, No. 1, 21-37 (1995). Reviewer: G.Vainikko (Espoo) MSC: 65J20 65J15 45G10 65R30 47J25 PDFBibTeX XMLCite \textit{M. Hanke} et al., Numer. Math. 72, No. 1, 21--37 (1995; Zbl 0840.65049) Full Text: DOI
Neubauer, A.; Scherzer, O. A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems. (English) Zbl 0826.65053 Z. Anal. Anwend. 14, No. 2, 369-377 (1995). Reviewer: V.Berinde (Baia Mare) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{A. Neubauer} and \textit{O. Scherzer}, Z. Anal. Anwend. 14, No. 2, 369--377 (1995; Zbl 0826.65053) Full Text: DOI
Binder, Andreas; Engl, Heinz W.; Groetsch, Charles W.; Neubauer, Andreas; Scherzer, Otmar Weakly closed nonlinear operators and parameter identification in parabolic equations by Tikhonov regularization. (English) Zbl 0835.65078 Appl. Anal. 55, No. 3-4, 215-234 (1994). MSC: 65J15 47J25 65M30 65J20 35K55 35R30 PDFBibTeX XMLCite \textit{A. Binder} et al., Appl. Anal. 55, No. 3--4, 215--234 (1994; Zbl 0835.65078) Full Text: DOI
Hofmann, Bernd; Scherzer, Otmar Factors influencing the ill-posedness of nonlinear problems. (English) Zbl 0809.35157 Inverse Probl. 10, No. 6, 1277-1297 (1994). MSC: 35R30 65J20 47J05 PDFBibTeX XMLCite \textit{B. Hofmann} and \textit{O. Scherzer}, Inverse Probl. 10, No. 6, 1277--1297 (1994; Zbl 0809.35157) Full Text: DOI
Scherzer, O. Convergence rates of iterated Tikhonov regularized solutions of nonlinear ill-posed problems. (English) Zbl 0791.65040 Numer. Math. 66, No. 2, 259-279 (1993). Reviewer: O.Scherzer (Linz) MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{O. Scherzer}, Numer. Math. 66, No. 2, 259--279 (1993; Zbl 0791.65040) Full Text: DOI EuDML
Scherzer, Otmar A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates. (English) Zbl 0797.65048 Appl. Math., Praha 38, No. 6, 479-487 (1993). Reviewer: V.Berinde (Baia Mare) MSC: 65J15 65J20 65M30 35R30 47J25 PDFBibTeX XMLCite \textit{O. Scherzer}, Appl. Math., Praha 38, No. 6, 479--487 (1993; Zbl 0797.65048) Full Text: EuDML
Scherzer, O.; Engl, H. W.; Kunisch, K. Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems. (English) Zbl 0799.65060 SIAM J. Numer. Anal. 30, No. 6, 1796-1838 (1993). Reviewer: G.Vainikko (Tartu) MSC: 65J15 65J20 47J05 PDFBibTeX XMLCite \textit{O. Scherzer} et al., SIAM J. Numer. Anal. 30, No. 6, 1796--1838 (1993; Zbl 0799.65060) Full Text: DOI
Scherzer, O. The use of Morozov’s discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems. (English) Zbl 0801.65053 Computing 51, No. 1, 45-60 (1993). MSC: 65J15 65J20 47J25 PDFBibTeX XMLCite \textit{O. Scherzer}, Computing 51, No. 1, 45--60 (1993; Zbl 0801.65053) Full Text: DOI
Scherzer, O.; Engl, H. W.; Anderssen, R. S. Parameter identification from boundary measurements in a parabolic equation arising from geophysics. (English) Zbl 0776.35083 Nonlinear Anal., Theory Methods Appl. 20, No. 2, 127-156 (1993). Reviewer: B.Hofmann (Chemnitz) MSC: 35R30 65M30 86A22 PDFBibTeX XMLCite \textit{O. Scherzer} et al., Nonlinear Anal., Theory Methods Appl. 20, No. 2, 127--156 (1993; Zbl 0776.35083) Full Text: DOI
Scherzer, Otmar Tikhonov regularization of non-linear ill-posed problems with applications to parameter identification in partial differential equations. (English) Zbl 0741.65100 Dissertationen der Johannes Kepler-Universiät Linz 86. Wien: Verband der Wissenschaftlichen Gesellschaften Österreichs (VWGÖ) (ISBN 3-85369-827-1). 117 p. (1991). Reviewer: F.Natterer MSC: 65Z05 65M30 35R25 35R30 PDFBibTeX XMLCite \textit{O. Scherzer}, Tikhonov regularization of non-linear ill-posed problems with applications to parameter identification in partial differential equations. Wien: Verband der Wissenschaftlichen Gesellschaften Österreichs (VWGÖ) (1991; Zbl 0741.65100)
Neubauer, Andreas; Scherzer, Otmar Finite-dimensional approximation of Tikhonov regularized solutions of nonlinear ill-posed problems. (English) Zbl 0691.65050 Numer. Funct. Anal. Optimization 11, No. 1-2, 85-99 (1990). Reviewer: A.Neubauer MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{A. Neubauer} and \textit{O. Scherzer}, Numer. Funct. Anal. Optim. 11, No. 1--2, 85--99 (1990; Zbl 0691.65050) Full Text: DOI