Recently, very remarkable results on the stable recovery of signals and data from incomplete measurements have been proven that are of enormous practical importance and that meanwhile already spread into industrial applications. The core problem that has to be solved is to find a sparsest solution, i.e., minimizing the number of nonzeros, of an overcomplete linear equation system. This is an NP-hard problem, but under certain conditions on the system one can find such a solution by solving a linear program.
In this project we investigate whether these ideas can be exploited in the context of solving differential equations, where the function to be sparsely represented is unknown but implicitly given via the differential equation.
11/2006 - 04/2008