Superresolution mehrskaliger Bilder aus den Materialwissenschaften unter Ausnutzung geometrischer Kenngrößen
Zusammenfassung der Projektergebnisse
Recent and ongoing developments in imaging techniques and computational analysis deeply modify the way materials sciences and engineering consider their objects of research. Our project contributed to this direction of research by developing new superresolution methods guided by high-resolution local subimages of D materials data. In cooperation with our colleagues from Bordeaux we tackled the problem by combining variational approaches with generalized mixture models. Then we extended the original focus of the project by including modern techniques from machine learning, in particular so-called normalizing ows, and from optimal transport, in particular Wasserstein gradient ows, into our models. This required a careful analysis of the models in terms of convergence, stability and expressiveness. Our work was very successful and we published our results in highly ranked journals and at top conferences in machine learning.
Projektbezogene Publikationen (Auswahl)
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Convolutional proximal neural networks and Plug-and-Play algorithms. Linear Algebra and its Applications, 631, 203-234.
Hertrich, Johannes; Neumayer, Sebastian & Steidl, Gabriele
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Inertial stochastic PALM and applications in machine learning. Sampling Theory, Signal Processing, and Data Analysis, 20(1).
Hertrich, Johannes & Steidl, Gabriele
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PCA reduced Gaussian mixture models with applications in superresolution. Inverse Problems & Imaging, 16(2), 341.
Hertrich, Johannes; Nguyen, Dang-Phuong-Lan; Aujol, Jean-Francois; Bernard, Dominique; Berthoumieu, Yannick; Saadaldin, Abdellatif & Steidl, Gabriele
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Stochastic Normalizing Flows for Inverse Problems: A Markov Chains Viewpoint. SIAM/ASA Journal on Uncertainty Quantification, 10(3), 1162-1190.
Hagemann, Paul; Hertrich, Johannes & Steidl, Gabriele
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Wasserstein Patch Prior for Image Superresolution. IEEE Transactions on Computational Imaging, 8, 693-704.
Hertrich, Johannes; Houdard, Antoine & Redenbach, Claudia
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Image super-resolution with PCA reduced generalized Gaussian mixture models in materials science. Inverse Problems and Imaging, 17(6), 1165-1192.
Nguyen, Dang-Phuong-Lan; Hertrich, Johannes; Aujol, Jean-Francois & Berthoumieu, Yannick
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PatchNR: learning from very few images by patch normalizing flow regularization. Inverse Problems, 39(6), 064006.
Altekrüger, Fabian; Denker, Alexander; Hagemann, Paul; Hertrich, Johannes; Maass, Peter & Steidl, Gabriele
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WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution. SIAM Journal on Imaging Sciences, 16(3), 1033-1067.
Altekrüger, Fabian & Hertrich, Johannes
