IPIS - Inverse Problems in the Imaging Sciences

Funded by the European Union - NextGenerationEU under the National Recovery and Resilience Plan (PNRR) - Mission 4 Education and research - Component 2 From research to business - Investment 1.1 Notice Prin 2022 - DD N. 104 del 2/2/2022

IPIS proposes to gather five research groups of applied mathematicians with two strategic objectives:

• In the short term, to push forward the state-of-the-art of imaging sciences, with specific focus on approaches inspired by inverse problems (IPs) theory.
• In the medium term, to make the IPIS network as a first embryo for a computational imaging center, diffused across Italy and open to contributions from all mathematicians interested in imaging applications.

IPIS conceptual starting point is the one of an Artificial Intelligence (AI) framework, in which the mathematical formulation of the data analysis methods is associated to the search for automatic procedures for their implementation. Therefore, the project will devote a methodological Work Package (WP) to the study of numerical methods in regularization theory, optimization, and numerical linear algebra crucial for the realization of automatic pipelines.

Mathematical approaches to imaging sciences are currently of two kinds: data-driven machine learning (ML) searches for hidden correlations among data, exploiting highly populated historical databases; model-driven inverse problems theory explicitly accounts for the mathematical model of signal formation and is particularly reliable in applications where large training sets are not available. IPIS aims at integrating these two paradigms by exploiting physical forward models to describe data generation, and prior models to identify data descriptors and decrease the conditioning of the numerical problem.

Besides representing a framework for the development of basic research in mathematical imaging, IPIS is also an application-oriented proposal, where the computational techniques of the methodological WPs will be mainstreamed into an application WP devoted to four imaging modalities: linear and non-linear tomographies, optical imaging, Fourier-based imaging, and parametric imaging. Further, two specific WPs will work at the implementation and validation of software tools, and at their showcasing across the  scientific community, via a dissemination campaign based on an open-source, open-data strategy.

IPIS will rely on the collaboration of five research units with a long-term experience in the formulation and applications of inversion and AI methods in imaging. The systematic connections of these groups with hospitals, space and ground telescope missions, and
high-tech companies will ease the validation of the numerical solutions developed within the project and will increase the impact of IPIS as a ToK setting at both a national and an international level.