Mathematical optimization is the key to solving many problems in science, based on the observation that physical systems obey a general principle of least action. While some problems can be solved analytically, many more can only be solved via numerical algorithms. Research in this domain has proved essential over many years. In addition, science in general is changing. Increasingly, in biology, medicine, astronomy, chemistry, physics, large amounts of data are collected by constantly improving signal and image acquisition devices, that must be analyzed by sophisticated optimization tools. In this project, we consider handling optimization problems with large datasets. This means minimizing a cost function with a complex structure and many variables. The computational load for solving these problems is too heavy for even state-of-the-art algorithms. Thus, only relatively rudimentary data processing techniques are often employed, reducing the quality of the results and limiting the outcomes that can be achieved via these novel instruments. New algorithms must be designed with computational scalability, robustness, and versatility in mind.
In this context, Majorization-Minimization (MM) approaches have a crucial role to play. They consist of a class of efficient and effective optimization algorithms that benefit from solid theoretical foundations. The MAJORIS project aims at proposing a breakthrough in MM algorithms, so that they remain efficient when dealing with big data. Several challenging questions concerning algorithm design will be tackled. These include acceleration strategies, convergence analysis with complex costs and inexact schemes. Practical, massively parallel and distributed architecture implementations will be proposed.
In-vivo multiphonic microscopy (Collaboration XLIM, CNRS)
Mass spectrometry (Collaboration IFPEN)
Brain MRI (Collaboration Institut Gustave Roussy)
New preprint about proximal gradient optimization under adjoint mismatch, available here
New preprint about MM algorithm for digital breast tomosynthesis reconstruction, available here
Andrès Contreras – Post-doctoral fellow
Jean-Baptiste Fest – PhD student
Interview of the project PI available here.