We are developing novel signal processing frameworks for signals (or data) indexed by power sets (aka set functions), signals indexed by meet/joint lattices, and signals on hypergraphs. This means that we derive suitable notions of shift, convolutions, and Fourier transforms to these domains. With the theory in place signal processing methods can be imported to yield novel methods for data analysis and learning in these domains.

Our work builds on and extends the algebraic signal processing theory, an axiomatic theory and constructive approach to deriving novel signal processing frameworks.

References

  1. Bastian Seifert, Chris Wendler, Markus Püschel
    A Causal Shift and Fourier Transform for Directed Acyclic Graphs
    submitted for publication

  2. Vedran Mihal, Bastian Seifert, Markus Püschel
    Porting Signal Processing from Undirected to Directed Graphs: Case Study Signal Denoising with Unrolling Networks
    submitted for publication

  3. Bastian Seifert, Chris Wendler, Markus Püschel
    Wiener Filter on Meet/Join Lattices
    Proc. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2021

  4. Markus Püschel, Bastian Seifert, Chris Wendler
    Discrete Signal Processing on Meet/Join Lattices
    IEEE Transactions on Signal Processing, 2021

  5. Chris Wendler, Andisheh Amrollahi, Bastian Seifert, Andreas Krause, Markus Püschel
    Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases
    Proc. AAAI Conference on Artificial Intelligence, 2021

  6. Jakob Weissteiner, Chris Wendler, Sven Seuken, Ben Lubin, Markus Püschel
    Fourier Analysis-based Iterative Combinatorial Auctions
    submitted for publication

  7. Bastian Seifert, Markus Püschel
    Digraph Signal Processing with Generalized Boundary Conditions
    IEEE Transactions on Signal Processing, 2021

  8. Markus Püschel, Chris Wendler
    Discrete Signal Processing with Set Functions
    IEEE Transactions on Signal Processing, 2021

  9. Panagiotis Misiakos, Chris Wendler, Markus Püschel
    Diagonalizable Shift and Filters for Directed Graphs Based on the Jordan-Chevalley Decomposition
    Proc. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2020

  10. Chris Wendler, Dan Alistarh and Markus Püschel
    Powerset Convolutional Neural Networks
    Proc. Neural Information Processing Systems (NeurIPS), 2019

  11. Chris Wendler and Markus Püschel
    Sampling Signals on Meet/Join Lattices
    Proc. Global Conference on Signal and Information Processing (GlobalSIP), 2019

  12. Markus Püschel
    A Discrete Signal Processing Framework for Meet/Join Lattices with Applications to Hypergraphs and Trees
    Proc. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2019

  13. Markus Püschel
    A Discrete Signal Processing Framework for Set Functions
    Proc. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2018