Jiang, Dandan; Azaiez, Mejdi; Miranville, Alain; Xu, Chuanju Nonlocal Cahn-Hilliard type model for image inpainting. (English) Zbl 07824622 Comput. Math. Appl. 159, 76-91 (2024). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{D. Jiang} et al., Comput. Math. Appl. 159, 76--91 (2024; Zbl 07824622) Full Text: DOI
Latz, Jonas Bayesian inverse problems are usually well-posed. (English) Zbl 07725072 SIAM Rev. 65, No. 3, 831-865 (2023). MSC: 62F15 49K40 65C60 65N21 68Q32 68T05 PDFBibTeX XMLCite \textit{J. Latz}, SIAM Rev. 65, No. 3, 831--865 (2023; Zbl 07725072) Full Text: DOI
Li, Lu On a Cahn-Hilliard-Oono model for image segmentation. (English) Zbl 1522.35527 Asymptotic Anal. 132, No. 3-4, 519-548 (2023). MSC: 35Q94 94A08 35A01 35A02 35B41 68U10 PDFBibTeX XMLCite \textit{L. Li}, Asymptotic Anal. 132, No. 3--4, 519--548 (2023; Zbl 1522.35527) Full Text: DOI
Barbu, Tudor Deep learning-based multiple moving vehicle detection and tracking using a nonlinear fourth-order reaction-diffusion based multi-scale video object analysis. (English) Zbl 07701126 Discrete Contin. Dyn. Syst., Ser. S 16, No. 1, 16-32 (2023). MSC: 68-XX 35Axx 68Txx 35A01 35A02 49K40 62H30 68T07 68U10 94A08 62M40 65D18 PDFBibTeX XMLCite \textit{T. Barbu}, Discrete Contin. Dyn. Syst., Ser. S 16, No. 1, 16--32 (2023; Zbl 07701126) Full Text: DOI
Yao, Changhui; Sun, Rong; Huang, Qiumei Global well-posedness and exponential stability for Maxwell’s equations under delayed boundary condition in metamaterials. (English) Zbl 1518.35584 J. Differ. Equations 365, 168-198 (2023). MSC: 35Q61 78A40 35A01 35A02 65D18 68U05 68U07 93B52 93D15 35R07 PDFBibTeX XMLCite \textit{C. Yao} et al., J. Differ. Equations 365, 168--198 (2023; Zbl 1518.35584) Full Text: DOI
Hsieh, Hsi-Wei; Charon, Nicolas Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric. (English) Zbl 1493.49043 Calc. Var. Partial Differ. Equ. 61, No. 5, Paper No. 165, 41 p. (2022). MSC: 49Q20 68T10 49J15 49K40 PDFBibTeX XMLCite \textit{H.-W. Hsieh} and \textit{N. Charon}, Calc. Var. Partial Differ. Equ. 61, No. 5, Paper No. 165, 41 p. (2022; Zbl 1493.49043) Full Text: DOI arXiv
Li, Yixin; Hu, Xianliang Artificial neural network approximations of Cauchy inverse problem for linear PDEs. (English) Zbl 1510.65230 Appl. Math. Comput. 414, Article ID 126678, 14 p. (2022). MSC: 65M32 35Q49 49N45 68T07 35R30 PDFBibTeX XMLCite \textit{Y. Li} and \textit{X. Hu}, Appl. Math. Comput. 414, Article ID 126678, 14 p. (2022; Zbl 1510.65230) Full Text: DOI
Christof, Constantin; Kowalczyk, Julia On the Omnipresence of Spurious Local Minima in Certain Neural Network Training Problems. arXiv:2202.12262 Preprint, arXiv:2202.12262 [cs.LG] (2022). MSC: 68T07 49K40 52A30 90C31 BibTeX Cite \textit{C. Christof} and \textit{J. Kowalczyk}, ``On the Omnipresence of Spurious Local Minima in Certain Neural Network Training Problems'', Preprint, arXiv:2202.12262 [cs.LG] (2022) Full Text: arXiv OA License
Chinneck, John W. Harvey Greenberg: analyzing infeasible mathematical programs. (English) Zbl 1514.00022 Holder, Allen (ed.), Harvey J. Greenberg. A legacy bridging operations research and computing. Cham: Springer. Int. Ser. Oper. Res. Manag. Sci. 295, 65-76 (2021). Reviewer: Torsten Bosse (Argonne) MSC: 00A71 65K05 68T20 49K40 90C05 90C06 90C46 90C51 PDFBibTeX XMLCite \textit{J. W. Chinneck}, Int. Ser. Oper. Res. Manag. Sci. 295, 65--76 (2021; Zbl 1514.00022) Full Text: DOI
Huo, Huixia; Xu, Houbao; Chen, Zhuoqian Modelling and dynamic behaviour analysis of the software rejuvenation system with periodic impulse. (English) Zbl 1487.68081 Math. Comput. Model. Dyn. Syst. 27, No. 1, 522-542 (2021). MSC: 68N99 34A37 34C60 93-10 PDFBibTeX XMLCite \textit{H. Huo} et al., Math. Comput. Model. Dyn. Syst. 27, No. 1, 522--542 (2021; Zbl 1487.68081) Full Text: DOI
Barbu, Tudor Mixed noise removal framework using a nonlinear fourth-order PDE-based model. (English) Zbl 1486.35252 Appl. Math. Optim. 84, Suppl. 2, 1865-1876 (2021). MSC: 35K35 35K59 60G35 65L12 65M06 68U10 68P30 94A08 PDFBibTeX XMLCite \textit{T. Barbu}, Appl. Math. Optim. 84, 1865--1876 (2021; Zbl 1486.35252) Full Text: DOI
Teo, Yong Siah; Sánchez-Soto, Luis L. Modern compressive tomography for quantum information science. (English) Zbl 1486.81027 Int. J. Quantum Inf. 19, No. 8, Article ID 2140003, 35 p. (2021). MSC: 81P18 49K40 68P30 81P15 81P45 81-01 PDFBibTeX XMLCite \textit{Y. S. Teo} and \textit{L. L. Sánchez-Soto}, Int. J. Quantum Inf. 19, No. 8, Article ID 2140003, 35 p. (2021; Zbl 1486.81027) Full Text: DOI arXiv
Zheng, Xiaojun; Huan, Zhongdan; Liu, Jun Well-posedness and convergence of the vector field regularization model in image registration. (Chinese. English summary) Zbl 1488.49047 Acta Math. Sin., Chin. Ser. 64, No. 3, 385-404 (2021). MSC: 49K40 49J45 68U10 94A08 PDFBibTeX XMLCite \textit{X. Zheng} et al., Acta Math. Sin., Chin. Ser. 64, No. 3, 385--404 (2021; Zbl 1488.49047)
Hühnerbein, Ruben; Savarino, Fabrizio; Petra, Stefania; Schnörr, Christoph Learning adaptive regularization for image labeling using geometric assignment. (English) Zbl 1516.68080 J. Math. Imaging Vis. 63, No. 2, 186-215 (2021). MSC: 68T05 49K40 62B11 65D18 65J22 90C31 PDFBibTeX XMLCite \textit{R. Hühnerbein} et al., J. Math. Imaging Vis. 63, No. 2, 186--215 (2021; Zbl 1516.68080) Full Text: DOI arXiv
Fakih, Hussein; Mghames, Ragheb; Nasreddine, Noura On the Cahn-Hilliard equation with mass source for biological applications. (English) Zbl 1460.35351 Commun. Pure Appl. Anal. 20, No. 2, 495-510 (2021). MSC: 35Q92 92C37 65M60 65M06 65N30 65M12 65M15 35B35 35J60 35A01 35A02 68U05 PDFBibTeX XMLCite \textit{H. Fakih} et al., Commun. Pure Appl. Anal. 20, No. 2, 495--510 (2021; Zbl 1460.35351) Full Text: DOI
Latz, Jonas On the well-posedness of Bayesian inverse problems. (English) Zbl 1437.49050 SIAM/ASA J. Uncertain. Quantif. 8, 451-482 (2020). MSC: 49N45 49K40 62F15 65N21 68Q32 68T05 PDFBibTeX XMLCite \textit{J. Latz}, SIAM/ASA J. Uncertain. Quantif. 8, 451--482 (2020; Zbl 1437.49050) Full Text: DOI arXiv
Zhang, Linan; Schaeffer, Hayden Forward stability of ResNet and its variants. (English) Zbl 1434.68528 J. Math. Imaging Vis. 62, No. 3, 328-351 (2020). MSC: 68T07 34A60 49K40 PDFBibTeX XMLCite \textit{L. Zhang} and \textit{H. Schaeffer}, J. Math. Imaging Vis. 62, No. 3, 328--351 (2020; Zbl 1434.68528) Full Text: DOI arXiv
Giacomelli, Lorenzo; Łasica, Michał; Moll, Salvador Regular 1-harmonic flow. (English) Zbl 1436.35229 Calc. Var. Partial Differ. Equ. 58, No. 2, Paper No. 82, 24 p. (2019). Reviewer: Vincenzo Vespri (Firenze) MSC: 35K51 35A01 35A02 35K59 35B40 35D35 35K92 35R01 53C21 68U10 PDFBibTeX XMLCite \textit{L. Giacomelli} et al., Calc. Var. Partial Differ. Equ. 58, No. 2, Paper No. 82, 24 p. (2019; Zbl 1436.35229) Full Text: DOI arXiv
Hintermüller, Michael; Rautenberg, Carlos N.; Wu, Tao; Langer, Andreas Optimal selection of the regularization function in a weighted total variation model. II: Algorithm, its analysis and numerical tests. (English) Zbl 1382.94016 J. Math. Imaging Vis. 59, No. 3, 515-533 (2017). MSC: 94A08 68U10 49K20 49K30 49K40 49M37 65K15 PDFBibTeX XMLCite \textit{M. Hintermüller} et al., J. Math. Imaging Vis. 59, No. 3, 515--533 (2017; Zbl 1382.94016) Full Text: DOI
Hintermüller, Michael; Rautenberg, Carlos N. Optimal selection of the regularization function in a weighted total variation model. I: Modelling and theory. (English) Zbl 1382.94015 J. Math. Imaging Vis. 59, No. 3, 498-514 (2017). MSC: 94A08 68U10 49K20 49K30 49K40 49M37 65K15 PDFBibTeX XMLCite \textit{M. Hintermüller} and \textit{C. N. Rautenberg}, J. Math. Imaging Vis. 59, No. 3, 498--514 (2017; Zbl 1382.94015) Full Text: DOI
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain A complex version of the Cahn-Hilliard equation for grayscale image inpainting. (English) Zbl 1377.35143 Multiscale Model. Simul. 15, No. 1, 575-605 (2017). MSC: 35K55 35B45 35B40 68U10 PDFBibTeX XMLCite \textit{L. Cherfils} et al., Multiscale Model. Simul. 15, No. 1, 575--605 (2017; Zbl 1377.35143) Full Text: DOI
Souopgui, Innocent; Ngodock, Hans E.; Vidard, Arthur; Le Dimet, François-Xavier Incremental projection approach of regularization for inverse problems. (English) Zbl 1358.49023 Appl. Math. Optim. 74, No. 2, 303-324 (2016). MSC: 49K40 49M05 68U10 PDFBibTeX XMLCite \textit{I. Souopgui} et al., Appl. Math. Optim. 74, No. 2, 303--324 (2016; Zbl 1358.49023) Full Text: DOI
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain A Cahn-Hilliard system with a fidelity term for color image inpainting. (English) Zbl 1381.94014 J. Math. Imaging Vis. 54, No. 1, 117-131 (2016). MSC: 94A08 35B30 68M07 35B40 35B41 35K55 PDFBibTeX XMLCite \textit{L. Cherfils} et al., J. Math. Imaging Vis. 54, No. 1, 117--131 (2016; Zbl 1381.94014) Full Text: DOI
März, Thomas A well-posedness framework for inpainting based on coherence transport. (English) Zbl 1336.35351 Found. Comput. Math. 15, No. 4, 973-1033 (2015). Reviewer: Wiesław Kotarski (Sosnowiec) MSC: 35R10 68U10 35F15 35A30 35D30 47H10 65D18 35-04 35Q68 PDFBibTeX XMLCite \textit{T. März}, Found. Comput. Math. 15, No. 4, 973--1033 (2015; Zbl 1336.35351) Full Text: DOI Link
Mecca, Roberto; Wetzler, Aaron; Bruckstein, Alfred M.; Kimmel, Ron Near field photometric stereo with point light sources. (English) Zbl 1319.68222 SIAM J. Imaging Sci. 7, No. 4, 2732-2770 (2014). MSC: 68T45 35A02 35B30 35D30 35F30 35Q68 65N12 65N21 68U10 94A08 PDFBibTeX XMLCite \textit{R. Mecca} et al., SIAM J. Imaging Sci. 7, No. 4, 2732--2770 (2014; Zbl 1319.68222) Full Text: DOI
Iagar, Razvan Gabriel; Moll, Salvador Rotationally symmetric \(p\)-harmonic flows from \(D^2\) to \(S^2\): local well-posedness and finite time blow-up. (English) Zbl 1304.35386 J. Math. Anal. Appl. 416, No. 1, 229-257 (2014). MSC: 35K92 35K51 82D40 68U10 35K59 76A15 PDFBibTeX XMLCite \textit{R. G. Iagar} and \textit{S. Moll}, J. Math. Anal. Appl. 416, No. 1, 229--257 (2014; Zbl 1304.35386) Full Text: DOI arXiv
Wunderli, Thomas Total variation time flow with quantile regression for image restoration. (English) Zbl 1282.49002 J. Math. Anal. Appl. 403, No. 1, 272-282 (2013). MSC: 49J10 49K40 62G08 94A08 68U10 PDFBibTeX XMLCite \textit{T. Wunderli}, J. Math. Anal. Appl. 403, No. 1, 272--282 (2013; Zbl 1282.49002) Full Text: DOI
Li, Jing; Yin, Jingxue; Sun, Jiebao; Guo, Zhichang A weighted dual porous medium equation applied to image restoration. (English) Zbl 1288.35316 Math. Methods Appl. Sci. 36, No. 16, 2117-2127 (2013). Reviewer: Vladimir N. Grebenev (Darmstadt) MSC: 35K65 35K55 68U10 35K20 PDFBibTeX XMLCite \textit{J. Li} et al., Math. Methods Appl. Sci. 36, No. 16, 2117--2127 (2013; Zbl 1288.35316) Full Text: DOI
Fornasier, Massimo; March, Riccardo; Solombrino, Francesco Existence of minimizers of the Mumford-Shah functional with singular operators and unbounded data. (English) Zbl 1266.49071 Ann. Mat. Pura Appl. (4) 192, No. 3, 361-391 (2013). MSC: 49N60 49J99 49K40 35J70 65J22 68U10 PDFBibTeX XMLCite \textit{M. Fornasier} et al., Ann. Mat. Pura Appl. (4) 192, No. 3, 361--391 (2013; Zbl 1266.49071) Full Text: DOI
Abdukerim, Haji; Bilikiz, Yunus Stability analysis of a repairable computer system. (Chinese. English summary) Zbl 1289.68001 Acta Math. Appl. Sin. 35, No. 6, 1003-1017 (2012). MSC: 68M07 68M15 47D60 PDFBibTeX XMLCite \textit{H. Abdukerim} and \textit{Y. Bilikiz}, Acta Math. Appl. Sin. 35, No. 6, 1003--1017 (2012; Zbl 1289.68001)
Esedoḡlu, Selim; Santosa, Fadil Error estimates for a bar code reconstruction method. (English) Zbl 1247.68311 Discrete Contin. Dyn. Syst., Ser. B 17, No. 6, 1889-1902 (2012). MSC: 68U10 65R20 65R32 49K40 49N45 PDFBibTeX XMLCite \textit{S. Esedoḡlu} and \textit{F. Santosa}, Discrete Contin. Dyn. Syst., Ser. B 17, No. 6, 1889--1902 (2012; Zbl 1247.68311) Full Text: DOI
Villa, S.; Rosasco, L.; Mosci, S.; Verri, A. Consistency of learning algorithms using Attouch-Wets convergence. (English) Zbl 1236.93157 Optimization 61, No. 1-3, 287-305 (2012). MSC: 93E35 68T05 49K40 65J20 68Q32 PDFBibTeX XMLCite \textit{S. Villa} et al., Optimization 61, No. 1--3, 287--305 (2012; Zbl 1236.93157) Full Text: DOI
Wunderli, Thomas On time flows of minimizers of general convex functionals of linear growth with variable exponent in BV space and stability of pseudosolutions. (English) Zbl 1183.49024 J. Math. Anal. Appl. 364, No. 2, 591-598 (2010). MSC: 49K40 49J20 68U10 94A08 PDFBibTeX XMLCite \textit{T. Wunderli}, J. Math. Anal. Appl. 364, No. 2, 591--598 (2010; Zbl 1183.49024) Full Text: DOI
Cao, Yang; Yin, Jingxue; Liu, Qiang; Li, Meihui A class of nonlinear parabolic-hyperbolic equations applied to image restoration. (English) Zbl 1180.35378 Nonlinear Anal., Real World Appl. 11, No. 1, 253-261 (2010). MSC: 35M13 94A08 35L72 68U10 PDFBibTeX XMLCite \textit{Y. Cao} et al., Nonlinear Anal., Real World Appl. 11, No. 1, 253--261 (2010; Zbl 1180.35378) Full Text: DOI
Wu, Hui-Ling; Ye, Ping-Kai Theoretical analysis of a nonlinear parabolic equation with time-delay based on image processing. (English) Zbl 1180.35307 Far East J. Math. Sci. (FJMS) 35, No. 2, 199-210 (2009). MSC: 35K65 35K59 35R10 35K20 68U10 PDFBibTeX XMLCite \textit{H.-L. Wu} and \textit{P.-K. Ye}, Far East J. Math. Sci. (FJMS) 35, No. 2, 199--210 (2009; Zbl 1180.35307) Full Text: Link
Guidotti, Patrick A new nonlocal nonlinear diffusion of image processing. (English) Zbl 1170.35450 J. Differ. Equations 246, No. 12, 4731-4742 (2009). MSC: 35K55 35K60 35B10 68U10 PDFBibTeX XMLCite \textit{P. Guidotti}, J. Differ. Equations 246, No. 12, 4731--4742 (2009; Zbl 1170.35450) Full Text: DOI
Aubert, G.; El Hamidi, A.; Ghannam, C.; Ménard, M. On a class of ill-posed minimization problems in image processing. (English) Zbl 1158.49027 J. Math. Anal. Appl. 352, No. 1, 380-399 (2009). MSC: 49K40 68U10 94A08 49M30 PDFBibTeX XMLCite \textit{G. Aubert} et al., J. Math. Anal. Appl. 352, No. 1, 380--399 (2009; Zbl 1158.49027) Full Text: DOI
Dal Passo, Roberta; Giacomelli, Lorenzo; Moll, Salvador Rotationally symmetric 1-harmonic maps from \(D^{2}\) to \(S^{2}\). (English) Zbl 1147.58015 Calc. Var. Partial Differ. Equ. 32, No. 4, 533-554 (2008). MSC: 58E20 49J05 49J45 49K05 49K40 49N60 34B16 76A15 82D40 68U10 PDFBibTeX XMLCite \textit{R. Dal Passo} et al., Calc. Var. Partial Differ. Equ. 32, No. 4, 533--554 (2008; Zbl 1147.58015) Full Text: DOI
Ong, Y. S.; Lum, K. Y.; Nair, P. B. Hybrid evolutionary algorithm with Hermite radial basis function interpolants for computationally expensive adjoint solvers. (English) Zbl 1147.49301 Comput. Optim. Appl. 39, No. 1, 97-119 (2008). MSC: 49K10 49K40 65D05 68T05 92D15 PDFBibTeX XMLCite \textit{Y. S. Ong} et al., Comput. Optim. Appl. 39, No. 1, 97--119 (2008; Zbl 1147.49301) Full Text: DOI Link
Durand, Sylvain; Nikolova, Mila Denoising of frame coefficients using \(\ell^1\) data-fidelity term and edge-preserving regularization. (English) Zbl 1147.49025 Multiscale Model. Simul. 6, No. 2, 547-576 (2007). MSC: 49N45 68U10 94A08 49K40 PDFBibTeX XMLCite \textit{S. Durand} and \textit{M. Nikolova}, Multiscale Model. Simul. 6, No. 2, 547--576 (2007; Zbl 1147.49025) Full Text: DOI
Elliott, C. M.; Smitheman, S. A. Analysis of the TV regularization and \(H^{-1}\) fidelity model for decomposing an image into cartoon plus texture. (English) Zbl 1148.35329 Commun. Pure Appl. Anal. 6, No. 4, 917-936 (2007). MSC: 35K35 35K55 35K30 68U10 35K85 35D05 PDFBibTeX XMLCite \textit{C. M. Elliott} and \textit{S. A. Smitheman}, Commun. Pure Appl. Anal. 6, No. 4, 917--936 (2007; Zbl 1148.35329) Full Text: DOI
Amadori, A. L.; Vázquez, J. L. Singular free boundary problem from image processing. (English) Zbl 1081.35054 Math. Models Methods Appl. Sci. 15, No. 5, 689-715 (2005). Reviewer: Pavol Quittner (Bratislava) MSC: 35K65 35K55 68U10 35R35 PDFBibTeX XMLCite \textit{A. L. Amadori} and \textit{J. L. Vázquez}, Math. Models Methods Appl. Sci. 15, No. 5, 689--715 (2005; Zbl 1081.35054) Full Text: DOI
van der Schaft, Arjan; Schumacher, Hans An introduction to hybrid dynamical systems. (English) Zbl 0940.93004 Lecture Notes in Control and Information Sciences. 251. London: Springer. xi, 174 p. (2000). Reviewer: Lubomír Bakule (Praha) MSC: 93-02 93B12 93B03 93D15 93B51 37N35 70G60 68U20 90C90 93B52 PDFBibTeX XMLCite \textit{A. van der Schaft} and \textit{H. Schumacher}, An introduction to hybrid dynamical systems. London: Springer (2000; Zbl 0940.93004)
Chancelier, J. P.; Gomez, C.; Quadrat, J. P.; Sulem, A. Automatic study in stochastic control. (English) Zbl 0648.93070 Stochastic differential systems, stochastic control theory and applications, Proc. Workshop Minneapolis/Minn. 1986, IMA Vol. Math. Appl. 10, 79-86 (1988). MSC: 93E20 65Yxx 93E25 68W99 PDFBibTeX XML
Kirichenko, N. F.; Slabospitsky, A. S. Simultaneous estimation of states and parameters in control systems with incomplete data. (English) Zbl 0589.93013 Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 657-668 (1986). MSC: 93B30 49K40 93C15 68T10 93D05 PDFBibTeX XML