Superiorized Iterative Methods for Reconstruction of CT Images

Computed tomography (CT) is a medical imaging modality in which X-ray data acquired from around a patient is used to mathematically reconstruct a three-dimensional image of patient anatomy. An iterative method begins with an initial estimate of the image, and then repeatedly corrects it by comparing its forward projection with the measured X-ray data. Conventional iterative methods may fail to provide accurate images under less-than-ideal circumstances. This includes cases where the X-ray data are noisy, where some data are missing, or where the object being imaged contains metal objects. Superiorization is a promising new approach for dealing with these situations. A superiorized algorithm incorporates a secondary objective into the iterative reconstruction (for example, that the image should be fairly smooth). By choosing an appropriate objective, one may significantly improve image quality. The goal of this project is to investigate and validate superiorization techniques for improving image quality in a variety of situations.

Student Outcomes

Gain an understanding of the mathematical and computational aspects of CT image reconstruction and material decomposition. Develop scientific programming skills. Gain experience with reading scientific papers and reviewing the literature. Develop scientific writing skills.

Student Qualifications

This project is suitable for junior or senior-level students with a background in mathematics, computer science, or engineering. Prospective students should:

• Have experience and be comfortable programming in MATLAB or a similar language.
• Have taken linear algebra (STMATH 308). Numerical analysis and scientific computing experience (STMATH 405 or CSS 455) are assets.
• Be able to commit to at least 10 hours a week (2 credits) for at least one quarter starting in Winter. (Two quarters preferred).

Student Responsibilities

• Meet weekly with the supervisor to develop ideas and discuss progress.
• Review current literature in the field to develop knowledge of existing techniques.
• Implement existing or new iterative reconstruction techniques in MATLAB.
• Validate techniques with simulated CT data.
• Present work at UW Undergraduate Research Symposium in May.
• Prepare a report on their work for the supervisor.

Time Commitment

Be able to commit to at least 10 hours a week (2 credits) for at least one quarter (two quarters preferred).