Objective
This project will develop a mathematical theory of sample complexity, i.e. of finite measurements, for inverse problems in partial differential equations (PDE). Inverse problems are ubiquitous in science and engineering, and appear when a quantity has to be reconstructed from indirect measurements. Whenever physics plays a crucial role in the description of an inverse problem, the mathematical model is based on a PDE. Many imaging modalities belong to this category, including ultrasonography, electrical impedance tomography and photoacoustic tomography. Many different PDE appear, depending on the physical domain. Currently, there is a substantial gap between theory and practice: all theoretical results require infinitely many measurements, while in all applied studies and practical implementations, only a finite number of measurements are taken. We argue that this gap is crucial, since the number of measurements is usually not very large, and has important consequences, regarding the choice of measurements, the priors on the unknown and the reconstruction algorithms. Many safe and effective modalities have had very limited use due to low reconstruction quality. Within a multidisciplinary approach, by combining methods from PDE theory, numerical analysis, signal processing, compressed sensing and machine learning, we will bridge this gap by developing a theory of sample complexity for inverse problems in PDE. This will allow for the deriving of a new mathematical theory of inverse problems for PDE under realistic assumptions, which will impact the implementation of many modalities, guiding the choice of priors and measurements. Consequently, emerging imaging modalities will become closer to actual usage. As a by-product, we will also derive new compressed sensing results which are valid for a general class of problems, including nonlinear and ill-posed, and sparsity constraints. Collaborations with experts in the relevant fields will ensure the project’s success.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2021-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
16126 GENOVA
Italy
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.