Methods for finding sparse solutions to ill-posed inverse problems

Mathematical models are used in numerous applications to describe some real world problem settings. In many cases there is a need to find unknown quantities in these models given some measurements. These problems are called inverse problems and are often ill-posed, i.e., the solution is very sensitive to errors in the measurements. Moreover, the solution may also be sparse which means that it consists of only a few non-zero elements. I this project we analyse and develop methods for finding sparse solutions to ill-posed inverse problems.