Alt, Tobias; Schrader, Karl; Augustin, Matthias; Peter, Pascal; Weickert, Joachim Connections between numerical algorithms for PDEs and neural networks. (English) Zbl 07694853 J. Math. Imaging Vis. 65, No. 1, 185-208 (2023). MSC: 68-XX 94-XX PDFBibTeX XMLCite \textit{T. Alt} et al., J. Math. Imaging Vis. 65, No. 1, 185--208 (2023; Zbl 07694853) Full Text: DOI arXiv
Alt, Tobias; Schrader, Karl; Weickert, Joachim; Peter, Pascal; Augustin, Matthias Designing rotationally invariant neural networks from PDEs and variational methods. (English) Zbl 07576604 Res. Math. Sci. 9, No. 3, Paper No. 52, 23 p. (2022). MSC: 68-XX 92-XX PDFBibTeX XMLCite \textit{T. Alt} et al., Res. Math. Sci. 9, No. 3, Paper No. 52, 23 p. (2022; Zbl 07576604) Full Text: DOI arXiv
Daropoulos, Viktor; Augustin, Matthias; Weickert, Joachim Sparse inpainting with smoothed particle hydrodynamics. (English) Zbl 1474.94013 SIAM J. Imaging Sci. 14, No. 4, 1669-1705 (2021). MSC: 94A08 65D18 68U10 76M28 PDFBibTeX XMLCite \textit{V. Daropoulos} et al., SIAM J. Imaging Sci. 14, No. 4, 1669--1705 (2021; Zbl 1474.94013) Full Text: DOI arXiv
Welk, Martin; Weickert, Joachim PDE evolutions for M-smoothers in one, two, and three dimensions. (English) Zbl 1517.94021 J. Math. Imaging Vis. 63, No. 2, 157-185 (2021). MSC: 94A08 68U10 35Q94 PDFBibTeX XMLCite \textit{M. Welk} and \textit{J. Weickert}, J. Math. Imaging Vis. 63, No. 2, 157--185 (2021; Zbl 1517.94021) Full Text: DOI arXiv
Bildhauer, M.; Fuchs, M.; Weickert, J. An alternative approach towards the higher order denoising of images. analytical aspects. (English) Zbl 1384.35019 J. Math. Sci., New York 224, No. 3, 414-441 (2017) and Zap. Nauchn. Semin. POMI 444, 47-88 (2016). Reviewer: Guy Jumarie (Montréal) MSC: 35J20 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., J. Math. Sci., New York 224, No. 3, 414--441 (2017; Zbl 1384.35019) Full Text: DOI
Bildhauer, M.; Fuchs, M.; Weickert, J. Denoising and inpainting of images using TV-type energies: theoretical and computational aspects. (English. Russian original) Zbl 1381.94011 J. Math. Sci., New York 219, No. 6, 899-910 (2016); translation from Probl. Mat. Anal. 87, 69-78 (2016). MSC: 94A08 49J10 68U10 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., J. Math. Sci., New York 219, No. 6, 899--910 (2016; Zbl 1381.94011); translation from Probl. Mat. Anal. 87, 69--78 (2016) Full Text: DOI
Pizarro, Luis; Mrázek, Pavel; Didas, Stephan; Grewenig, Sven; Weickert, Joachim Generalised nonlocal image smoothing. (English) Zbl 1477.94020 Int. J. Comput. Vis. 90, No. 1, 62-87 (2010). MSC: 94A08 PDFBibTeX XMLCite \textit{L. Pizarro} et al., Int. J. Comput. Vis. 90, No. 1, 62--87 (2010; Zbl 1477.94020) Full Text: DOI
Bae, Egil; Weickert, Joachim Partial differential equations for interpolation and compression of surfaces. (English) Zbl 1274.65025 Dæhlen, Morten (ed.) et al., Mathematical methods for curves and surfaces. 7th international conference, MMCS 2008, Tønsberg, Norway, June 26–July 1, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-642-11619-3/pbk). Lecture Notes in Computer Science 5862, 1-14 (2010). MSC: 65D17 65D05 65M60 68P30 94A08 PDFBibTeX XMLCite \textit{E. Bae} and \textit{J. Weickert}, Lect. Notes Comput. Sci. 5862, 1--14 (2010; Zbl 1274.65025) Full Text: DOI
Galić, Irena; Weickert, Joachim; Welk, Martin; Bruhn, Andrés; Belyaev, Alexander; Seidel, Hans-Peter Image compression with anisotropic diffusion. (English) Zbl 1448.94012 J. Math. Imaging Vis. 31, No. 2-3, 255-269 (2008). MSC: 94A08 PDFBibTeX XMLCite \textit{I. Galić} et al., J. Math. Imaging Vis. 31, No. 2--3, 255--269 (2008; Zbl 1448.94012) Full Text: DOI
Welk, Martin; Steidl, Gabriele; Weickert, Joachim Locally analytic schemes: a link between diffusion filtering and wavelet shrinkage. (English) Zbl 1161.68831 Appl. Comput. Harmon. Anal. 24, No. 2, 195-224 (2008). MSC: 68U10 68T05 65T60 60J70 60G35 PDFBibTeX XMLCite \textit{M. Welk} et al., Appl. Comput. Harmon. Anal. 24, No. 2, 195--224 (2008; Zbl 1161.68831) Full Text: DOI Link
Breuß, Michael; Bürgel, Andrea; Brox, Thomas; Sonar, Thomas; Weickert, Joachim Numerical aspects of TV flow. (English) Zbl 1116.65099 Numer. Algorithms 41, No. 1, 79-101 (2006). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65M06 35K55 65M12 PDFBibTeX XMLCite \textit{M. Breuß} et al., Numer. Algorithms 41, No. 1, 79--101 (2006; Zbl 1116.65099) Full Text: DOI