SPECT image reconstruction using PDE-constrained optimization

SPECT image reconstruction using PDE-constrained optimization

Akkerman, David (TU Delft Applied Sciences)

Lathouwers, D. (mentor)

Delft University of Technology

2021-01-08

SPECT is a nuclear medical imaging technique which measures the distribution of a radioactive agent in the human body. Because the scan data is available only on the boundary of the system, it is challenging to determine from which location a measured photon originated. In this research PDE-constrained optimization methods are used to determine the source reconstruction, incorporating the complete photon transport physics. A cost function is introduced such that the minimum of the cost function, constrained by the photon transport equation, yields the source reconstruction. To lift degeneracy and penalize erratic behaviour a regularization term is added to the cost function. An interior-point method is incorporated to impose a positivity constraint and a comparison is made between the reconstructions with and without this constraint. A proof of principle is presented for a two-dimensional model problem, indicating that the methods are a viable option to perform the source reconstruction, although the quality of the reconstruction is shown to vary significantly depending on the system parameters and the original source distribution. Because the linear system that is to be solved becomes too large to be solved directly, iterative solvers are used to obtain the solution, where the main focus is on the MINRES algorithm. Additionally, a number of preconditioners are introduced to reduce the computational cost of the iterative solver. Two preconditioners show to be promising when the problem is not constrained to yield only positive values, but they do no longer function properly when the positivity constraint is introduced.

http://resolver.tudelft.nl/uuid:857cda99-3902-4717-9c5e-011d00d93a20

2024-01-08

Student theses

master thesis

© 2021 David Akkerman