"Spherical t-design curves for beneficial data representations."Karner, ClemensSpherical t-design curves have the special property that path integrals along them integrate algebraic polynomials of total degree t exactly on the sphere. In classical t-design theory, which is based on point evaluations, a multitude of constructed t-design point configurations is known. In contrast, only few t-design curves have been discovered. We present a novel approach to find such spherical t-design curves based on geodesic chains with applications in the development of dimension reduction techniques to serve visualization and aid information extraction tasks. Furthermore, we optimize the curve as well as along the curve provides to obtain beneficial data representations for visualization and for subsequent downstream tasks, e.g. in medical imaging. Such a curve of projections applied to data as a low-dimensional data can be interpreted as a “movie”, which we claim to be a useful tool for data visualization. In the applied setting, we are especially interested in discrete curves for the sampling of spatial frequencies, called k-space, with applications to Magnetic resonance imaging (MRI). |
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