NoMADS - Nonlocal Methods for Arbitrary Data Sources

NoMADS is an international research project consisting of 16 universities and 7 industrial partners. The project is funded by the European Commission within the Marie Skłodowska-Curie Research and Innovation Staff Exchange action (MSCA-RISE).

The main goal of this project is to build a large multidisciplinary network of universities and companies to fill the current gaps between theory and applications of nonlocal methods. Our consortium brings together a strong international group of leading researchers from mathematics (applied and computational analysis, statistics, and optimisation), computer vision, and data mining. We aim to significantly increase the understanding and applicability of nonlocal methods in a wide range of applications. Our long-term vision is to discover fundamental mathematical principles for the characterization of nonlocal operators, the development of new robust and efficient algorithms, and the implementation of those in high quality software products for real-world applications.

Motivation

Our world is inundated with data – the internet, mobile telephony, medical imaging, satellite navigation, social networks are ubiquitous in our daily life. We are surrounded by technology that collects, transmits, and manipulates information of an order of magnitude that is hard to comprehend. At present the typical uses of these vast amounts of data are seriously underpowered if not to say unsophisticated. On the other hand the ever more sophisticated theories and techniques that are developed by mathematics, computer science, and engineering do not readily apply to real-world applications. Examples in imaging and structured data processing, remote sensing for earth conservation, agriculture and exploration, as well as biomedical data science have demonstrated the
enormous potential of next-generation algorithms.

In the last years, the trend in data sciences was shifting from model-driven towards data-driven methods. While the former explains data based on assumptions often deduced from physical principles, like diffusion of information, the latter aims to directly exploit ephemeral patterns hidden in the data. A number of recent data-driven methods make use of self-similarity of patterns within the data by relating information that is not necessarily in a close proximity. These methods are termed as ‘nonlocal methods’ and constitute a rather new field of mathematical research. Nonlocal algorithms ideally incorporate information from all available data. This property has motivated their study in the context of partial differential equations (PDEs) for the modeling of several physical phenomena, game theory and their application to a wide range of image processing applications, e.g., for image denoising, inpainting and segmentation. However, the use of nonlocal methods is o still restricted to academic toy projects. There is still a large gap between the academic theories for nonlocal methods and their practical application to real-world problems: the reason why those methods work so well in practice is far from being fully understood.

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 777826. The project duration for NoMADS is from March 2018 to February 2022.