In the sequel, we will discuss some of the applications, we are currently working on joint with collaborators from those application areas.
Electron Microscopy: This technology allows to
image materials at atom level. One problem is as in magnetic resonance
imaging the slow data acquisition process. One way to access the data
is by taking point samples, which in case of undersampling leads to
the inverse problem  of inpainting. We already designed
efficient approaches for inpainting, which now need to be suitably
adapted to the specific types of image data.
Image and Video Compression: Today a major
percentage of the data in internet traffic are images and videos.
Hence improving current compression algorithms is a crucial task to
prevent a collapse in the future. Our approach
to this problem is to use applied harmonic analysis  methods
specifically adapted to images of video sequences.
Magnetic Resonance Imaging: Magnetic resonance imaging is a widely used unharmful method for diagnoses of diseases which are often otherwise not detectable such as myocarditis. However, in particular for young patients the duration of the data acquisition process during which they are not allowed to move is painfully long, up to 1 hour for the upper torso. To speed up the data acquisition, leading to an ill-posed inverse problem , we utilize compressed sensing  type methods in combination with suitable systems from applied harmonic analysis  such as shearlets.
Massive MIMO: Massive MIMO, i.e., very large scale
multiuser multi-antenna technology, is widely expected to play a
fundamental role in meeting the target performance oft he future
generation of wireless/cellular networks, commonly indicated as 5G.
The key idea is that by scaling up the number of jointly processed
antennas at the infrastructure side (i.e., in the base stations), the
wireless channel, notoriously affected by random propagation effects,
converges to a deterministic limit in which the network behaves in a
predictable and very desirable manner, where intra-cell multiuser
interference can be nulled by precoding, and intra-cell interference
can be easily controlled. However, a major obstacle in the
implementation of Massive MIMO is represented by the very high
complexity of the signal acquisition, requiring to demodulate and
sample the output of hundreds of antennas, which we aim to attack by
using methods from compressed sensing  and sparse approximation
Proteomics: One key problem in medicine is early diagnosis of, for instance, cancer as one of the most serious diseases. One approach is to analyze so-called proteomics data which is extracted from blood samples of patients and provides information of the set of proteins contained in the blood at a specific time. Since diseases affect the proteins, one aims to find disease fingerprints in the proteomics data to be able to distinguished diseased patients from healthy ones, thereby also allowing very diagnosis at a very early stage of the disease. The approach we pursue is to use 1-bit compressed sensing  techniques as one main step to find a suitable (sparse) fingerprints for certain types of cancer.