Optimization with Partial Differential Equation Constraints for Bio-imaging Applications

Abstract

Molecular transport and interaction are of funda- mental importance in biology and medicine. The spatiotemporal diffusion map can reflect the regulation of molecular interactions and their intracellular functions. To construct subcellular diffusion maps based on bio-imaging data, we explore a general optimization framework with diffusion equation constraints (OPT-PDE). For the solution of the spatially piecewise constant and anisotropic diffusion.