A. Denitiu (08/2012 – 12/2015): Compressed Sensing and 3D Tomography of Solid Objects
E. Bodnariuc (since 09/2013): Compressive Motion Sensing and Dynamic Echo PIV
R. Dalitz (since 10/2013): Compressive Motion Sensing and Dynamic Tomography
- J. Kuske (since 06/2016): Structured Cosparse Models for Discrete Tomography
1. Cosparse Tomographic Recovery
Sampling patterns as used in industrial tomographical set-ups with limited numbers of projections fall short of the common assumptions (e.g.~restricted isometry property) underlying compressed sensing. In this project, we investigate the relation between the number of sufficient tomographic projections and the co-/sparsity of volume functions for unique recovery of these functions from given projection data. We also investigate approaches to efficiently solve the corresponding large numerical optimization problem in the 3D case.
Researchers: Andreea Denitiu, Jan Kuske, Lukas Kiefer, Christoph Schnörr (IPA), Stefania Petra
2. Compressed Motion Sensing
We consider the problem of sparse signal recovery in dynamic sensing scenarios. Specifically, we study the recovery of a sparse time-varying signal from linear measurements of a single static sensor, that are taken at two different points of time. This set-up can be modelled as observing a single signal using two different sensors – a real one and a virtual one induced by signal motion, and we examine the recovery properties of the resulting combined sensor. We specify a condition of sufficient change of the signal, besides the usual sparsity assumption, under which not only the signal can be uniquely recovered with overwhelming probability by linear programming, but also the correspondence of signal values (signal motion) can be established between the two points of time.
Researchers: Robert Dalitz, Ecaterina Bodnariuc, Christoph Schnörr (IPA), Stefania Petra
3. Tomographical Particle Image Reconstruction
4. Motion Estimation in Ultrasound Imaging
5. Geometry of Multiplicative Iterative Solvers
6. Graphical Model Parameter Learning by Inverse Linear Programming