MAJORIS

Majoration-Minimization algorithms for image processing

European Research Council

MAJORIS is a scientific project funded by the European Research Council under a Starting Grant (2020-2024) and coordinated by Emilie Chouzenoux at Inria Saclay, France.

Project abstract

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.

Examples of data and applications considered in the project

In-vivo multiphonic microscopy (Collaboration XLIM, CNRS)

In-vivo multiphonic microscopy

Mass spectrometry (Collaboration IFPEN)

Mass spectrometry

Brain MRI (Collaboration Institut Gustave Roussy)

Brain MRI

Latest news

New preprint about proximal gradient optimization under adjoint mismatch, available here

New preprint about MM algorithm for digital breast tomosynthesis reconstruction, available here

Members:

Andrès Contreras – Post-doctoral fellow

Jean-Baptiste Fest – PhD student

Paper about distributed MM algorithm accepted to ICIP 2020. [paper] [code]

Interview of the project PI available here.