CIBM SP EPFL SECTION

Mathematical Imaging

Section Head: Prof. Michaël Unser (EPFL)

The CIBM Signal Processing EPFL  Mathematical Imaging Section develops mathematical frameworks and advanced algorithms for the reconstruction of biomedical images.
In particular, we focus on designing reliable machine-learning-based methods that come with mathematical guarantees of convergence and stability. We also explore the use of generative models and efficient Bayesian sampling techniques to reduce and quantify uncertainty.

RESEARCH TOPICS

GlobalBioIm - A unifying library for imaging inverse problems

Description: Our work in imaging inverse problems ranges from the theoretical exploration of the fundamentals of variational problems[1],  to making them accessible to all engineers across imaging modalities[2, 3 & 4]. GlobalBioIm is a software library that integrates all our advances in this field and makes them easily available to the community. Imaging scientists in any biomedical imaging modality no longer need to reinvent and reimplement the forward models and optimisation algorithms at the core of the state-of-the-art reconstruction methods. This project is funded by the H2020 Advanced ERC Grant No 692726 (2016-2021). 

Investigator: Michaël Unser (EPFL)

Collaborators: Shayan Aziznejad, Thomas Debarre, Laurène Donati, Julien Fageot, Harshit Gupta, Kyong Jin, Thanh-An Pham, Emmanuel Soubies, Ferréol Soulez, Luc Zeng, in direct collaboration with Michael T. McCann and Pol del Aguila Pla, funded by the CIBM.

References: [1] Michaël Unser  ; Julien Fageot ; Harshit Gupta, Representer Theorems for Sparsity-Promoting ℓ1 Regularization, IEEE Transactions on Information Theory (Volume: 62 , Issue: 9 , Sept. 2016)

[2] Michael T. McCann and Michaël Unser, Biomedical Image Reconstruction: From the Foundations to Deep Neural Networks, Foundations and Trends in Signal Processing (Vol. 13: No. 3, pp 283-359, December 2019)

[3] Emmanuel Soubies, Ferréol Soulez, Michael T McCann, Thanh-an Pham, Laurène Donati, Thomas Debarre, Daniel Sage and Michaël Unser, Pocket guide to solve inverse problems with GlobalBioIm, Inverse Problems (Volume 35, Number 10, September 2019), Special Issue on Variational Methods and Effective Algorithms for Imaging and Vision

[4] Michaël Unser, Emmanuel Soubies, Ferréol Soulez, Michael McCann, and Laurène Donati, GlobalBioIm: A Unifying Computational Framework for Solving Inverse Problems, Optical Society of America (Paper CTu1B.1, 2017)

Deep learning for image reconstruction

Description: Deep learning has pushed performance boundaries in countless imaging applications. Nonetheless, biomedical imaging reconstruction presents unique challenges. On the medical side, robustness and predictability of image artifacts are key for informing diagnosis. On the biological side, major improvements by deep learning have only recently started to appear. Our work in this field covers the effort to provide novel foundations[1], the thorough review of the field[2 & 3], and the construction of specific architectures for practical problems[4].

Investigator: Michaël Unser (EPFL)

Collaborators: Kyong Hwan Jin, in direct collaboration with Michael T. McCann, funded by the CIBM.

References: [1] Michaël Unser, A Representer Theorem for Deep Neural Networks, Journal of Machine Learning Research (20, 1-30, 2019)

[2] Michael T. McCann  ; Kyong Hwan Jin ; Michaël Unser, Convolutional Neural Networks for Inverse Problems in Imaging: A Review, IEEE Signal Processing Magazine ( Volume: 34 , Issue: 6 , Nov. 2017)

[3] Michael T. McCann and Michaël Unser, Biomedical Image Reconstruction: From the Foundations to Deep Neural Networks, Foundations and Trends in Signal Processing (Vol. 13: No. 3, pp 283-359, December 2019)

[4] Kyong Hwan Jin  ; Michael T. McCann  ; Emmanuel Froustey ; Michaël Unser, Deep Convolutional Neural Network for Inverse Problems in Imaging, IEEE Transactions on Image Processing ( Volume: 26 , Issue: 9 , Sept. 2017)