AI Seminar: Enforcing necessary constraints for common diffusion MRI models using sum-of-squares programming
Tom Dela Haije, Postdoc in the Image Analysis, Computational Modelling and Geometry Section at Department of Computer Science, University of Copenhagen.
Diffusion-weighted magnetic resonance imaging (MRI) captures local micro-structural information by observing diffusing (water) molecules probing their surroundings at a microscopic scale. In order to analyze this type of data one can either estimate parameters that describe the diffusion itself, which provides a somewhat abstract but accurate description of the observed stochastics, or one can use a model of the ambient structure that re-expresses the observed diffusion in terms of more intuitive structural parameters. Both cases generally rely on optimization to reconstruct the descriptive parameters from diffusion-weighted images, and in this presentation I will introduce a specific set of basic constraints to improve such model reconstructions. These constraints are based on the non-negativity of the so-called ensemble average propagator or associated functions, but reformulated as the (relaxed) condition that these functions can be written as a sum of squared polynomials. For many commonly used models and basis expansions these constraints take the form of a positive-definiteness condition on a matrix that is linear in the model parameters, which can thus be enforced through the use of semidefinite programming or nonlinear optimization alternatives. In preliminary results I will show that the application of these constraints can be considered essential in many situations despite the associated computational costs.
This seminar is a part of the AI Seminar Series organised by SCIENCE AI Centre. The series highlights advances and challenges in research within Machine Learning, Data Science, and AI. Like the AI Centre itself, the seminar series has a broad scope, covering both new methodological contributions, ground-breaking applications, and impacts on society.