Research Scientist
Mathematics and Signal Processing in Acoustics
Machine Learning

Tel. +43 1 51581-2529
Email: luis-daniel.abreu(at)oeaw.ac.at

Academic Background


Luis Daniel Abreu studied Mathematics at the University of Coimbra (Portugal), University of Gent (Belgium) and Arizona State University (USA). He finished his PhD thesis in 2003, in the field of Orthogonal Polynomials and Special Functions. From 2003-2012 he held an Assistant Professor position at the Department of Mathematics of the University of Coimbra.

While in Coimbra, he has teached several courses at undergraduated and post-graduated Level and mentored several undergraduated students in special programs of initiation to research.

In 2011/2012 he has worked at the University of Vienna at FWF project "Frames and Harmonic analysis". He ist currently a member of the research centers NUHAG (Vienna) and CMUC (Coimbra). In 2012 he joined the Acoustics Research Institute.

Current Research


His main current area of interest is Applied Harmonic Analysis (Frame Theory, Spectral Localization and Asymptotic Models) and applications in Physics and Acoustic Modelling. He is participating in the project FLAME (Frames and Linear operator for Acoustical Modeling and parameter Estimation).

Publications

Publications

  • N., Holighaus; Koliander, G.; Pruša, Z.; Abreu, L. D. (2019) Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm. IEEE Transactions on Signal Processing, Bd. 67, S. 3894-3908.
  • Speckbacher, M.; Abreu, L. D. (2019) Deterministic guarantees for L1-reconstruction: a large sieve approach with geometric flexibility., IEEE Proceedings SampTA 2019.
  • Tauböck, G.; Rajbamshi, S.; Balazs, P.; Abreu, D. (2019) Random Gabor Multipliers and Compressive Sensing., Proceedings of SampTA 2019 (13th International conference on Sampling Theory and Applications).
  • Abreu, L. D.; Gröchenig, K.; Romero, J. L. (2019) Harmonic analysis in phase space and finite Weyl–Heisenberg ensembles. Journal of Statistical Physics,, Bd. 174, S. 1104-1136.
  • Abreu, L. D.; Alvarez-Nodarse, R.; Cardoso, J. L. (2019) Uniform convergence of basic Fourier-Bessel series on a q-linear grid. in The Ramanujan Journal,, Bd. 49, S. 421-449.
  • Rajbamshi, S., Tauböck, G., Balazs, P., Abreu, L. D. (2019) Random Gabor Multipliers for Compressive Sensing: A Simulation Study., Proceedings of the EUSIPCO 2019.
  • Koliander, G.; Abreu, L. D.; Haimi, A.; Romero, J. L. (2019) Filtering the continuous wavelet transform using hyperbolic triangulations., Proc. Int. Conf. Samp. Theory and Appl. (SampTA-19); Bordeaux, France.
  • Abreu, L. D., Alvarez-Nodarse, R., Cardoso, J. L. (2018) Uniform convergence of basic Fourier-Bessel series on a q-linear grid. in The Ramanujan Journal, S. online.
  • Abreu, L. D. (2017) Superframes and polyanalytic wavelets. Journal of Fourier Analysis and its Applications, Bd. 23, S. 1-20.
  • Abreu, L. D.; Pereira, J. M.; Romero, J. L.; Torquato, S. (2017) The Weyl-Heisenberg ensemble: Statistical mechanics meets time-frequency analysis., Proceedings of the SampTA (2017); Tallinn, S. 199-202.
  • Abreu, L. D.; Romero, J. L. (2017) Multitaper spectral estimation and off-grid compressive sensing: MSE estimates., Proceedings of the SampTA (2017); Tallinn, S. 188-191.
  • Abreu, L. D.; Speckbacher, M. (2017) A planar large sieve and sparsity of time-frequency representations., Proceedings of the SampTA 2017; Tallinn, S. 283-287.
  • Abreu, L. D.; Pereira, J. M.; Romero, J.L.; Torquato, S. (2017) The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels. Journal of Statistical Mechanics: Theory and Experiment, Bd. 2017, S. 043103.
  • Abreu, L. D.; Romero, J. L. (2017) MSE estimates for multitaper spectral estimation and off-grid compressive sensing. IEEE Transactions on Information Theory, Bd. 63/12, S. 7770-7776.
  • Abreu, L. D.; Pereira, J. M.; Romero, J. L. (2017) Sharp rates of convergence for accumulated spectrograms. Inverse Problems, Bd. 33, S. 115008.
  • Abreu, L. D.; Romero, J. L. (2016) Performance bounds for multitaper estimators..
  • Abreu, L. D.; Pereira, J. M. (2015) Measures of localization and quantitative Nyquist densities. Applied and Computational Harmonic Analysis, Bd. 38, S. 524-534.
  • Abreu, L. D.; Balazs, P.; de Gosson, M.; Mouayn, Z. (2015) Discrete coherent states for higher Landau levels. Annals of Physics, Bd. 363, S. 337 -353.
  • Abreu, L. D.; Faustino, N. (2015) On Toeplitz operators and localization operators. Proceedings of the American Mathematical Society, Bd. 143, S. 4317-4323.
  • Abreu, L. D.; Feichtinger, H.G. (2014, online: 2013) Function spaces of polyanalytic function. In: Vasilev, A. (Hrsg.), Harmonic and Complex Analysis and its Applications; Heidelberg, New York, Dordrecht: Birkhäuser Verlag, S. 13881.