Sparsity and compressed sensing in inverse problems

• Applicants: Professor Dr. Dirk A. Lorenz; Professor Dr. Gerd Teschke
• Subject Area: Mathematics
• Term: from 2008 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 79623291

This project is a continuation of the DFG project „Sparsity and Compressed Sensing in InverseProblems". The aim is to develop a thorough theory of Compressive Sampling (CS) techniquesand implementable recovery principles for inverse and ill-posed problems. Building on the success of the first project phase in developing CS techniques, recovery accuracy estimates and algorithms we aim to systematically continue with the development of in finite dimensional sensing models and sparse recovery algorithms for inverse problems in the second project phase. In particular, one objective is to design more general sensing frameworks and combine them with variational formulations the yield accuracy estimates and allows for an adaptive approximation of the solution. The development and application of adaptive solvers is of prime importance as we need to truly solve in finite dimensional sparse recovery problems. Finally, we plan to apply the developed concepts to three concrete applications: Ionospheric tomography, digital holography and the Radon transform on SO(3) in the context of crystallography.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1324: Extraction of Quantifiable Information from Complex Systems