Spatio-temporal Structure Tensor Resampling and Transformation

Research group
Hans Knutsson	Professor	Medical Informatics
Mats Andersson	Ass. Prof.	Medical Informatics
Matts Karlsson	Professor	Biomedical Modelling and Simulation

A problem of considerable theoretical depth has surfaced in the work concerning estimation of motion and flow in ultrasonic images of the heart. It turns out that there exists no applicable theory for how to transform the tensors describing local structure and motion in the original polar ultrasound data to corresponding tensors in the geometrically correct image.

The objective of the project is to investigate how local spatio-temporal structure tensors should be transformed when data are interpolated and re-sampled. The intention is to perform an in depth theoretical analysis establishing the appropriate rules for tensor transformations induced by changes in space-time geometry. The investigation will be done in a signal theoretic setting allowing analysis of optimality as well as tests on simulated data for various classes of signals and noise.

Apart from being of direct consequence for the ultrasound project, the results will also be of high potential value where anisotropic sampling of multidimensional signals are used, e.g MR and CT data. In general the project will contribute to the growth of competence within NiMed. The techniques developed in the project are of general nature and can prove useful within other NiMed projects, and results and ideas originating from other NiMed projects may prove useful within the present project.