Prof. Dr. Gitta Kutyniok

Chair of the Applied Functional Analysis Group

TU Berlin, Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
+49 (0) 30 314 25758
kutyniok@math.tu-berlin.de
Website


Research focus

Applied Harmonic Analysis
Compressed Sensing
Deep Learning
High-dimensional Data Analysis
Imaging Science
Inverse Problems
Numerical Analysis of Partial Differential Equations

Projects as a project leader

  • CH2

    Sparse compressed sensing based classifiers for -omics mass-data

    Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte
    Project members: Nada Cvetkovic / Martin Genzel
    Duration: -
    Status: completed
    Located at: Freie Universität Berlin / Technische Universität Berlin

    Description

    Tumor diseases rank among the most frequent causes of death in Western countries coinciding with an incomplete understanding of the underlying pathogenic mechanisms and a lack of individual treatment options. Hence, early diagnosis of the disease and early relapse monitoring are currently the best available options to improve patient survival. In this project, we aim for the identification of disease specific sets of biological signals that reliably indicate a disease outbreak (or status) in an individual. Such biological signals (e.g. proteomics or genomics data) are typically very large (millions of dimensions), which significantly increases the complexity of algorithms for analyzing the parameter space or makes them even infeasible. However, these types of data usually exhibit a very particular structure, and at the same time, the set of disease specific features is very small compared to the ambient dimension. Such a high-dimensional setting naturally calls for the application of the concept of sparse classifiers, which has been extensively studied in the fields of compressed sensing and statistical learning during the last decade. Our research focuses on both algorithmic improvements of available methods as well as theoretical results such as recovery guarantees for general data models.

    http://medicalbioinformatics.de/research/projects/ecmath-ch2
  • CH14

    Understanding cell trajectories with sparse similarity learning

    Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte
    Project members: -
    Duration: -
    Status: running
    Located at: Freie Universität Berlin / Technische Universität Berlin / Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    In living organisms, biological cells transition from one state to another. This happens during normal cell development (e.g. aging) or is triggered by events, such as diseases. The time-ordered set of state changes is called a trajectory. Identifying these cell trajectories is a crucial part in bio-medical research to understand changes on a gene and molecular level. It allows to derive biological insights such as disease mechanisms and can lead to new biomedical discoveries and to advances in health-care. With the advent of single cell experiments such as Drop-Seq or inDrop, individual gene expression profiles of thousands of cells can be measured in a single experiment. These large data-sets allow to determine a cell's state based on its gene activity (cell expression profiles, CEPs), which can be expressed as a large feature vector representing its location in some large state space. The main problem with these experiments is that the actual time-information is lost, and needs to be recovered. The state-of-the art solution is to introduce the concept of pseudo-time in which the cells are ordered by CEP similarity. To find robust and biological meaningful trajectories based on CEPs, two main tasks have to be performed: (1) A CEP-based metric has to be learned to define pair-wise distances between CEPs. (2) Given this metric, similar CEP groups and transition paths between those groups should be identified and analysed.

  • MI-AP18

    Discrete-Valued Sparse Signals - Theory, Algorithms and Applications

    Prof. Dr. Gitta Kutyniok

    Project heads: Prof. Dr. Gitta Kutyniok
    Project members: -
    Duration: 01.10.2014 - 30.09.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    Over the last decade, compressed sensing (CS) has gained enormous attention, both from a theoretical point of view and from its various applications. The key point in compressed sensing is to solve underdetermined systems of linear equations under the assumption that the unknown vector is sparse, i.e., a signal where only a few non-zero components are present. It is very attractive to use ideas and tools developed in compressed sensing in digital communications. Exemplary scenarios are transmitter-side signal optimization (e.g., peak-to-average power ratio reduction), multiple-access schemes with small duty cycles, source coding schemes, and radar applications. However, in these scenarios the vector/the signal to be recovered (from noisy measurements) may not only be sparse, but it is beneficial that its elements are taken from a discrete set. Hence, discrete sparse signals are extremely relevant in digital communication systems and signal processing. Unfortunately, such signals and the respective recovery algorithms are not yet studied adequately---if at all---in the literature. Consequently, this proposal addresses the application of compressed sensing methodology to the analysis of discrete-valued sparse signals. Effort has to be spent to fundamentally understand the problem from the mathematical side. To this end, we aim to develop a comprehensive theory for the recovery of discrete sparse signals, both from a geometric viewpoint and by adopting analytical results and tools. Moreover, we devise tailored recovery algorithms, thereby interpreting discrete compressed sensing as a link between classical compressed sensing and a multiple-input/multiple-output decoding task. Finally, the application of discrete sparse signals in communications, sensor networks, and for the identification of channel operators will be addressed.

    http://gepris.dfg.de/gepris/projekt/257184199?language=en
  • MI-AP19

    Compressive Sensing Algorithms for Structured Massive MIMO

    Prof. Dr. Gitta Kutyniok

    Project heads: Prof. Dr. Gitta Kutyniok
    Project members: -
    Duration: 01.10.2015 - 31.03.2018
    Status: running
    Located at: Technische Universität Berlin

    Description

    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. Massive MIMO has been widely analyzed under simple independent and identically distributed channel statistics, and under the naive assumption that the precoding/beamforming operations can be implemented by standard baseband signal processing (fully digital domain). 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. In this project, we propose to exploit the fine structure oft he wireless scattering channel in the asymptotic regime of a large number of antennas, in order to develop a low-complexity structured approach to Massive MIMO. The key observation is that the channel (random) vectors are spatially correlated, and therefore they are sparse in the domain of their Karhunen-Loeve basis. Hence, ideas and techniques from sparse signal processing (sensing and reconstruction) become instrumental to devise new tranceivers architectures, which eventually make Massive MIMO implementable in practice. The central questions that we propose to investigate include: finding universal sparsifying bases or frames to represent general channel spatial correlations; consider wideband channels with sparsity in both the angular and delay domain; understand the tradeoffs and the methods of treating sparsity in the continuous rather than in the discretized domain; understanding the tradeoff, in terms of stable reconstruction of sampling rate versus quantization resolution; consider sparse signal separation in multiuser environments with multiple sparse interferers in the angle-delay and time domain; developing dimensionality reduction techniques that make Massive MIMO affordable also for Frequency-Division Duplexing systems. The proposed research spans across Communications, Information Theory, Signal Processing and Mathematics. The PI team is highly qualified, involving two PIs in the EECS Department and one PI in the Mathematics Department of TU-Berlin. Two PhD students (full time) and two MS/BS students (part-time) will be jointly supervised and collaborate in the research project.

    https://www.ti.rwth-aachen.de/SPP1798/CSMIMO.html
  • SE4

    Mathematical modeling, analysis and novel numerical concepts for anisotropic nanostructured materials

    Dr. Christiane Kraus / Prof. Dr. Gitta Kutyniok / Prof. Dr. Barbara Wagner

    Project heads: Dr. Christiane Kraus / Prof. Dr. Gitta Kutyniok / Prof. Dr. Barbara Wagner
    Project members: Esteban Meca Álvarez / Dr. Arne Roggensack
    Duration: -
    Status: completed
    Located at: Technische Universität Berlin / Weierstraß-Institut

    Description

    The project SE4 aims to develop and study mathematical models in order to understand, functionalize and optimize modern nanostructured materials. Such materials are fundamental for the design of next generation thin-film solar cells as well as batteries for the production and storage of sustainable energy, respectively. Besides the mathematical modeling, the main goals of this research project are the analysis of the developed phase field systems and the construction of numerical algorithms that efficiently capture the material properties and, in particular, their anisotropic nature. More information...

    http://www.wias-berlin.de/people/roggensa/se4/
  • GV-AP3

    Riemannian manifold learning via shearlet approximation

    Prof. Dr. Gitta Kutyniok

    Project heads: Prof. Dr. Gitta Kutyniok
    Project members: -
    Duration: 01.01.2013 - 30.06.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    Applied harmonic analysis provides powerful methodologies to approximate geometric objects, which might be given as a Riemannian manifold itself or as an approximating point cloud. The main tools are specifically designed representation systems such as shearlets. These systems are of a multiscale type, thus an approximation process provides different resolution levels. One might ask: "Which resolution level allows detection of which geometric properties, such as curvature or torsion?" Project A10 aims to analyze such relations between approximations and learning of geometrical properties.

    http://www.discretization.de/en/projects/A10/
  • GV-AP13

    Low-Dimensional Models for Complex Structured Data

    Prof. Dr. Gitta Kutyniok

    Project heads: Prof. Dr. Gitta Kutyniok
    Project members: -
    Duration: 01.10.2015 - 30.09.2018
    Status: running
    Located at: Technische Universität Berlin

    Description

    DEDALE is an interdisciplinary project that intends to develop the next generation of data analysis methods for the new era of big data in astrophysics and compressed sensing. Novel data analysis methods in machine learning allow for a better preservation of the intrinsic physical properties of real data that generally live on intricate spaces, such as signal manifolds.

    Our project have three main scientific directions:
    • Introduce new models and methods to analyse and restore complex, multivariate, manifold-based signals.
    • Exploit the current knowledge in optimisation and operations research to build efficient numerical data processing algorithms in the large-scale settings.
    • Show the reliability of the proposed methods in two different applications: one in cosmology and one in remote sensing.


    http://dedale.cosmostat.org/