ANR-DFG - Appel à projets générique 2018 - DFG

Superresolution of multiscale images from materials sciences using geometrical features – SUPREMATIM

SUPREMATIM

SUPerREsolution of 3d MATerials IMages

3D image superresolution

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 will contribute to this direction of research by developing new super-resolution methods guided by high-resolution local sub-images of 3D materials data.

The mathematical methods of choice will be based on local and global Generalized Gaussian Mixture Models as well as Student-t Mixture Models in conjunction with variational methods. Appropriate geometrical features related to the engineering topics have to be established to provide an evaluation platform for the super-resolution images, and to be directly involved into the Bayesian and variational models. The mathematical models will be developed, analyzed and appropriate efficient algorithms will be derived, including an examination of their convergence behavior.
The models will be extended to multimodal images, where due to the size of the structures of interest, the high resolution image are taken by serial sectioning (FIB-SEM) tomography and the low resolution images by micro computed tomography. This requires to take the special acquisition of FIB-SEM tomographic images, in particular curtaining effects and the anisotropy with respect to the third dimension into account.
A numerical evaluation of the relevance and the benefit of the developed super-resolution methods will be performed by comparing the effective properties computed for reactive flow in porous media.

The main one is Publication #8 which is a joint publication by almost all the participants of the project. It corresponds to the first main point of the project: using GMM based models for image super-resolution for 3D images. To cope with the large dimension of the data, the model incorporates a PCA step which enables us to deal with the curse of dimension. The results obtained both on synthetic and real data are promising.
The other publications are related either to image super-resolution, or to estimation problems related to super-resolution.

The next steps are now to extend the approach of Publication #8 to more general distributions than GMM, and to introduce in the modeling a measure based on the specificity of the data.
The consortium of the project has the required expertise to do so.

1. F. Laus, G. Steidl, Multivariate myriad filters based on parameter estimation of Student-t distributions, SIAM Journal on Imaging Sciences, 2019.
2. M. Hasanasab, J. Hertrich, F. Laus and G. Steidl. Alternatives of the EM algorithm for estimating the parameters of the Student-t distribution, Numerical algorithms, 2020.
3. M. Hasanasab, J. Hertrich, F. Laus and G. Steidl, Parseval proximal neuralnetworks, The Journal of Fourier Analysis, 2020.
4. A. Gastineau, J-F. Aujol, Y. Berthoumieu, and C. Germain, A residual dense generative adversarial network for pansharpening with geometrical constraints, ICIP 2020.
5. J. Hertrich, G. Steidl, Inertial Stochastic PALM and its Application for Learning Student-t Mixture Models, 2020.
6. J. Hertrich, Superresolution via Student-t Mixture Models, SIAM Conference on Imaging Science 2020.
7. A. Gastineau, J-F. Aujol, Y. Berthoumieu, and C. Germain, Multi-Discriminator with Spectral and Spatial Constraints Adversarial Network for Pansharpening, 2020, in IEEE Transaction on Geoscience and Remote Sensing (TGRS).
8. J. Hertrich, L. Nguyen, J-F. Aujol, D. Bernard, Y. Berthoumieu, A. Saadaldin and G. Steidl, PCA Reduced Gaussian Mixture Models with Applications in Superresolution, 2020, in Inverse Problem.
9. Y. Traonmilin, J-F. Aujol, and A. Leclaire, The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension

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 will contribute to this direction of research by developing
new superresolution methods guided by high-resolution local subimages of 3D materials data.

The mathematical methods of choice will be based on local and global Generalized Gaussian Mixture Models as well as
Student-t Mixture Models in conjuction with variational methods.
Appropriate geometrical features related to the engineering topics
have to be established to provide an evaluation platform for the SR images,
and to be directly involved into the Bayesian and variational models.
The mathematical models will be developed, analyzed and appropriate efficient algorithms will be derived,
including an examination of their convergence behavior.

The models will be enlarged to multimodal images,
where due to the size of the structures of interest, the HR image are taken by FIB-SEM tomography and the LR images by CT.
This requires to take the special acquisition of FIB-SEM tomographic images, in particular
curtaining effects and the anisotropy with respect to the third dimension into account.
A numerical evaluation of the relevance and the benefit of the developed super resolution methods will be performed by comparing the effectives properties computed for reactive flow in porous media using these methods and classical mesh refinement strategies.

Project coordinator

Monsieur Jean-François Aujol (Institut de mathématiques de Bordeaux)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

IMS Laboratoire d'intégration du matériau au système
ICMCB INSTITUT DE CHIMIE DE LA MATIERE CONDENSEE DE BORDEAUX
Technische Universität Kaiserslautern
IMB Institut de mathématiques de Bordeaux

Help of the ANR 184,680 euros
Beginning and duration of the scientific project: February 2019 - 36 Months

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