Scientific Computing for X-Ray Computed Tomography

• Describe the underlying physics of a CT scanner.
• Formulate the corresponding mathematical model and the Radon transform.
• Formulate the inverse Radon transform and the Filtered Back Projection algorithm.
• Discretize the Radon transform to obtain a system of linear equations.
• Use the singular value decomposition (SVD) to analyze the reconstruction problem.
• Formulate and use algebraic iterative methods that include simple constraints.
• Formulate the convergence behavior of these methods.
• Use the software package Core Imaging Library (CIL) for large-scale problems.
• Formulate variational problems based on Bayesian noise modeling.
• Formulate and use Tikhonov regularization and Total Variation regularization.
• Use modern numerical methods from convex optimization for CT reconstruction.

Introduction to CT and some of its applications. The CT-scanner. The Radon transform and its inverse, Filtered Back Projection. Discretization of the CT problem. The Singular Value Decomposition (SVD) and its use for studying the CT problem. Stability and the need for filtering; truncated SVD.
Algebraic iterative reconstruction algorithms – foundations and convergence properties. Their behavior for noisy data; semi-convergence and stopping rules. The use of GPU computing. The software package Core Imaging Library (CIL) and its algebraic reconstruction algorithms.
Noise models, priors and regularization. Variational formulations and Bayesian modeling. Cases: Total Variation and Tikhonov regularization. Introduction to convex optimization and numerical optimization algorithms. Artifacts in reconstructions and model calibration.

Experience with Matlab programming (e.g, 02631/33) and numerical computations (e.g., 02601).

Seminars and small reports on the computer projects.

Minimum: 5.

Please be aware that this course will only be held if the required minimum number of participants is met. You will be informed 8 days before the start of the course, whether the course will be held.