As LiDAR sensors for depth acquisition advance to solid-state technologies, new capabilities raise new theoretical and technological challenges. In particular, we investigate benefits afforded by controlling and changing in real time the sampling scheme (adaptive sampling). We use neural-network to predict the optimal sampling scheme per scene, given a fixed sampling budget. We found that for a given RMSE, the sampling budget can be reduced by a factor of about 4 on average. Various strategies and algorithms are examined.
We investigate analytic and numerical solutions of nonlinear gradient flows. We examine the flows as nonlinear PDE’s and use tools from nonlinear spectral theory. We have recently revealed relations between Dynamic mode decomposition (DMD), a common tool for fluid dynamics, and nonlinear eigenfunctions related to homogeneous flows. We are investigating through this lens gradient descent algorithms of complex systems.
We examine how to define systems and signals through nonlinear eigenvalue analysis. For example – we developed an image representation based on the total-variation transform. We also examine neural-networks through eigen-analysis and design algorithms to reveal their (nonlinear) eigenfunctions.