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Inverse problems and Imaging

02624
Mathematics and Statistics

About this course

The aim of the course is to give a systematic, mathematical introduction to inverse problems in science and engineering. Such problems arise, e.g., in connection with medical imaging, tomography, seismic exploration, and deblurring og images. The course gives the mathematical background for inverse problems and their solution. The theory is illustrated by computational exercises that gives hands-on experience with some common techniques and paradigms.

Learning outcomes

At the end of the course the learner will be able to: Formulate and identify simple models in the technical sciences, in the form of inverse problems Understand the inherent difficulties of inverse problems Discretize and solve first-kind Fredholm integral equations Understand the mechanisms of regularization for the solution to an inverse problem Implement and use computational tools for the analysis and solution of inverse problems by means of regularization Use different methods for choosing the regularization parameter Implement and use iterative methods for large-scale problems Understand, analyze and solve selected inverse problems in differential euqations Formulate inverse problems in imaging, computerized tomography and electrical impedance tomography Identify nonlinear inverse problems and solve them Explain and utilize the Bayesian approach to inverse problems.

Enrolment details

NB! This course is open for enrolment from May 14 – July 29, 2024. In case no ‘Apply now’ information is shown in the right-hand side, please check enrolment information under ‘Help’ – ‘How do I register’ for your institution.

Examination

Oral examination and reports

Course requirements

Experience with advanced engineering mathematics (e.g. 01035) and numerical computations.

Activities

Lectures and exercises with theory and computations.

Additional information

  • Credits
    ECTS 5
  • Level
    Master
  • Contact hours per week
    4
  • Instructors
    Kim Knudsen
  • Mode of instruction
    Hybrid
If anything remains unclear, please check the FAQ of DTU (Denmark).

Offering(s)

  • Start date

    4 September 2024

    • Ends
      6 December 2024
    • Term *
      unknown
    • Location
      Online
    • Instruction language
    • Register between
      14 May - 29 Jul 2024
    Only 8 days to enrol
    Apply now
These offerings are valid for students of L'X (France)