Many machine-learning and signal-processing algorithms rely on regularization. Amplitude-equivariant regularizers are characterized by a symmetric star-shaped unit ball. Given samples of such a regularizer on the unit sphere, the goal of this project is to approximate its star-shaped contour using piecewise-linear splines.

The candidate will develop the underlying functional framework and implement software for computing optimal spline approximations, with the objective of minimizing the number of breakpoints required to achieve a prescribed accuracy. The project will focus first on the two-dimensional case and may subsequently be extended to three dimensions using suitable triangulations of the sphere.