A. Denitiu (08/2012 – 12/2015): Compressed Sensing and 3D Tomography of Solid Objects
E. Bodnariuc (09/2013 – 01/2018): On Plane Wave Ultrasound Particle Image Velocimetry
R. Dalitz (since 10/2013 – 02/2017): Compressive Motion Sensing and Dynamic Tomo PIV
- J. Kuske (since 06/2016): Structured Cosparse Models for Discrete Tomography
- L. Kiefer (since 01/2017): Fast Algorithms for Free-Discontinuity Problems
1. Cosparse Tomographic Recovery from Few Projections
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, Stefania Petra
2. Compressed Motion Sensing for Tomo PIV and Echo PIV
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 (e.g. tomographic sensor or ultrasound transducer), 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, Stefania Petra
3. Structured Regularization for Multi-Spectral Signal Recovery
4. Geometry of Multiplicative Iterative Solvers
5. Graphical Model Parameter Learning by Inverse Linear Programming
6. Geometric Image Labeling