Checking date: 29/03/2023

Course: 2023/2024

Inverse Problems and Image Reconstruction
Máster Universitario en Matemática Industrial (RD 1393/2007) (Plan: 330 - Estudio: 258)

Coordinating teacher: TERRAGNI , FILIPPO

Department assigned to the subject: Mathematics Department

Type: Electives
ECTS Credits: 6.0 ECTS


Requirements (Subjects that are assumed to be known)
Partial Differential Equations. Numerical Analysis.
COMPETENCES and SKILLS - Acquiring theoretical knowledge that allows the student to develop original ideas, in a research context, knowing how to translate industrial needs into I+D+i projects in the Industrial Mathematics field. - Being able to explain the results, along with the acquired knowledge, to experts and non-experts. - Being able to get deeper into a subject in an autonomous way, which will be very useful to obtain a Ph.D. - Being able to get quantitative and qualitative information from experimental data using numerical techniques. - Knowing how to select the appropriate techniques to solve a specific problem.
Description of contents: programme
Introduction and Basic Notions - Direct and inverse problems - Well and ill-posed problems - Existence and uniqueness of the solution - Stability Least Squares - Motivation and general idea - Applications Regularization - Motivation and general idea - Tikhonov, Lardy and Landweber algorithms - Morozov's discrepancy principle Singular Value Decomposition - Theoretical background, meaning and properties - Noise filtering and data reconstruction - Linear systems and regularization - Extensions Computed Axial Tomography - Radon transform and sinogram - Methods: back-projection and algebraic reconstruction Topological Derivative - Theoretical background - Defects detection - Methods: multifrequency and iterative - Applications
Learning activities and methodology
Methodology: - In-person classes. - Homeworks and presentations. Tutorials: Students can ask questions via email and during the classes, or request an individual session.
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100
Calendar of Continuous assessment
Basic Bibliography
  • A. Kirsch. An Introduction to the Mathematical Theory of Inverse Problems. Springer-Verlag New York. 2011
  • Frank Natterer, Frank Wübbeling. Mathematical Methods in Image Reconstruction. SIAM. 2001
  • J. Mueller, S. Siltanen. Linear and Nonlinear Inverse Problems with Practical Applications. SIAM Computational Science and Engineering. 2012
  • M. Bertero, P. Boccacci. Introduction to Inverse Problems in Imaging. CRC Press. 1998

The course syllabus may change due academic events or other reasons.