Professor Unser, Head of CIBM Signal Processing EPFL Mathematical Imaging Section and Head of the Biomedical Imaging Group in the School of Engineering at EPFL received the European Research Council (ERC) Advanced Grant for his FunLearn proposal (Functional Learning: From Theory to Application in Bioimaging).
The ERC Advanced Grants are given each year to established, leading principal investigators to fund long-term funding for “ground-breaking, high-risk” research projects in any field.
How does your third ERC Advanced Grant funded project relate to CIBM?
Professor Unser: We started applying machine learning tools—in particular, deep convolutional nets (CNN)—in the context of our collaborations in CIBM for improving the quality of medical image reconstruction, which, incidentally, also led to a Best Paper Award (IEEE SPS 2019).
CNN-based algorithms are extremely promising and generally outperform the standard techniques. However, there is increasing evidence that they have a stability/reproducibility problem, meaning that they sometimes (fortunately rarely) output inconsistent/flawed results, in a way that is still poorly understood.
The recently approved FunLearn research program (Oct 2021- Oct 2026) aims at correcting these weaknesses by developing novel algorithms that combine the best features of classical image reconstruction and CNN-based techniques. As suggested by the title, we shall rely on FUNctional optimisation to design a new brand of “stable” neural networks (the LEARNing components) that are based on splines; that is, continuous, piecewise-linear functions.
The FUN part too is that this uses elegant mathematics (functional analysis in non-reflexive Banach spaces), which I have LEARNed and progressively built up during the course of my scientific career. See for instance A Unifying Representer Theorem for Inverse Problems and Machine Learning
My role with CIBM as a Section Head greatly facilitates the launching of collaborations. The present FunLearn grant includes an important subproject on the development of novel methods for dynamic MRI in collaboration with Prof. Stuber, Head CIBM MRI CHUV-UNIL.
The ERC advanced grant will provide CIBM with better image reconstruction methods, which should pave the way to faster and higher-resolution medical imaging. We also plan to make our image reconstruction software available publicly for greater impact.
Who are the partners involved in this project?
Professor Unser: Partners involved in the project include Prof. Stuber (CHUV-UNIL), and various imaging scientists at the EPFL; e.g. Prof Henning Stahlberg, Head of the new Dubochet Center for Imaging cryo-electron microscopy. On the international side, we are also collaborating with mathematicians, including Prof. Costanza Conti (Univ Florence) and Prof. Luigi Ambrosio (Scuola Normale Superiore, Pisa).
As this is your third ERC grant, what is your advice to those aiming to write their first ERC grant?
Professor Unser: This is my third ERC grant and the advice I would offer those aiming to write their research proposal is that it needs to be ground breaking and high-risk. Look at the summaries of recently accepted (ERC) proposals within the panel you plan to apply in order to get some idea of what gets funded. Have a clear, high-level story where all the parts of the project (including former achievements) reinforce each other.
Invest the effort to make it perfect, because it is super competitive—but it is worth it: a stimulating intellectual exercise that will shape your research agenda for the coming years (even if you don’t get the grant).
Finally, make it known to the authorities/public that it is an immense benefit for Switzerland to be part of the EU research program. So far, the grants received by Swiss scientists have outweighed the financial contribution of Switzerland to the program, because the evaluation of ERC is based on scientific merit alone.
The ERC program is a widely recognised instrument for assessing and promoting scientific excellence. It is very competitive with a most comprehensive review process: It is not uncommon that projects get evaluated by as many as 10 independent/anonymous reviewers (scientific peers). These reviews are precious feedback that is communicated to the applicants. Getting kicked out of this program, as a result of the failing of the bilateral agreements with the EU, would be a huge loss for the Swiss research community.
Abstract FunLearn project
Professor Michaël Unser, EPFL School of Engineering
Functional Learning: From Theory to Application in Bioimaging
This research program is motivated by the remarkable ability of deep neural networks to improve the quality of biomedical image reconstruction. While the results reported so far are extremely encouraging, serious reservations have been voiced pertaining to the stability of these tools and the extent to which we can trust their output. The main concern is that it is very difficult to control the Lipschitz constant of the current neural architectures. This means that a small perturbation of the input can result in a huge deviation of the output, which can have devastating effects in the context of image reconstruction.
We believe that the remedy lies in the use of much shallower networks, which are easier to control. However, a reduction in the number of layers will degrade the performance, unless we augment the sophistication of the primary modules; in particular, the nonlinear ones. By drawing on our career-long experience with splines, we therefore propose to rely on the powerful tools of functional optimization to improve learning architectures. This will allow us to develop two novel approaches to learning: sparse simplicial splines, and hierarchical spline networks—an extension of the popular deep ReLU neural networks.
In parallel, we shall develop specific neural networks to solve two outstanding problems in biomedical imaging:
- A “best-of-both-worlds” approach to biomedical image reconstruction, involving the stable integration of state-of-the-art physics-based solvers with the new tools of machine learning;
- The 3D reconstruction of the entire manifold of configurations of a biomolecule from a large collection of very low-dose cryo-electron tomograms. This goal, which may be viewed as the Graal of structural biology, has remained elusive so far and calls for an entirely new paradigm for single-particle analysis.