MACHINE LEARNING FOR INVERSE PROBLEMS
Abstract
This project will develop a mathematical theory of machine learning (ML) for inverse problems (IP). IP are ubiquitous in science and engineering, and appear whenever a physical quantity has to be reconstructed from indirect measurements. The range of applications is very wide. They are especially known for medical imaging (computed tomography, magnetic resonance imaging, etc.) and detection systems (lidar, radar, sonar, etc.), but IP are present in many other areas, including nondestructive testing, geophysics, astrophysics, signal processing and computer vision. Hence, advancements in this field will have an enormous impact. The ill-posedness of IP is classically mitigated by the use of regularization. Despite the great advancements in the last decades, these techniques suffer from several drawbacks: slow computations, high sensitivity to modeling errors and very low spatial resolution. In recent years, data-driven methods based on ML, and especially deep-learning, have become very popular for solving many IP. The results are often impressive, however, very few theoretical results are available. The understanding and reliability of these approaches are still very low. The goal of our research is to use and develop methods from learning theory for solving IP. In particular, we shall study how ML can be a valuable tool for dealing with imperfect measurements and choosing priors. A new rigorous theory of data-driven methods for IP will be possible by combining regularization theory, statistical learning, computational harmonic analysis and abstract and numerical IP. The algorithms developed in this project will improve the recovery methods of IP, in particular regarding reconstruction quality and speed. This will enhance the established modalities and bring many emerging imaging modalities closer to actual usage. The main case study will be scattering problems, the mathematical model of many detection systems used in defense (e.g., radar and sonar).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 11, 2021
- Source ID
- FA86552017027
Entities
People
- Matteo Santacesaria
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Genoa