Mathematical signal processing

Mathematical methods for signal processing have grown more sophisticated over the last decades. After the introduction of wavelet methods as an effective tool for time-frequency analysis, new signal representations have been introduced for classes of non bandlimited signals. These allow in particular to extend the applicability of the sampling theorem. The key insights have been:

  • An exploration of new sampling techniques for sparse signals.
  • A new understanding of the interaction of continuous-time and discrete-time signal processing.
  • The construction of new orthonormal, biorthogonal and frame bases.
  • A full exploration of linear time-frequency analysis methods, which include short-time Fourier transforms and wavelets as particular cases, as well as multidimensional extensions.
  • The understanding of the approximation power of certain bases, and their application to compression and denoising, both for piecewise smooth signals and for more general signals.

The work of our group has covered all of these areas over time, leading to a number of PhD theses over the years, as well as a graduate textbook.

Please select an item from the menu on the right for an detailed presentation of our current efforts in this research domain. You can also consult our archives for a list of past projects.

  

Recent LCAV publications in this area

G. Elhami; M. W. Pacholska; B. Bejar Haro; M. Vetterli; A. J. Scholefield : Sampling at unknown locations: Uniqueness and reconstruction under constraints; IEEE Transactions on Signal Processing. 2018-11-15. DOI : 10.1109/TSP.2018.2872019.
G. Baechler; M. Krekovic; J. Ranieri; A. Chebira; M. L. Yue et al. : Super Resolution Phase Retrieval for Sparse Signals. 2018-08-06.
H. Pan; T. Blu; M. Vetterli : Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity; IEEE Transactions on Signal Processing. 2018-07-20. DOI : 10.1109/TSP.2018.2858213.
M. W. Pacholska; B. Bejar Haro; A. J. Scholefield; M. Vetterli : Sampling at unknown locations, with an application in surface retrieval. 2017. Sampling Theory and Applications, 12th International Conference, Tallinn, Estonia, July 3 – 7, 2017,. p. 364-368. DOI : 10.1109/SAMPTA.2017.8024451.
G. Baechler; A. J. Scholefield; L. Baboulaz; M. Vetterli : Sampling and Exact Reconstruction of Pulses with Variable Width; IEEE Transactions on Signal Processing. 2017. DOI : 10.1109/TSP.2017.2669900.
H. Pan; T. Blu; M. Vetterli : Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy; IEEE Transactions on Signal Processing. 2017. DOI : 10.1109/TSP.2016.2625274.
G. Baechler; I. Dokmanic; L. Baboulaz; M. Vetterli : Accurate recovery of a specularity from a few samples of the reflectance function. 2016. 41st IEEE International Conference on Acoustics Speech and Signal Processing, Shanghai, China, March 20-25, 2016.
D. El Badawy; J. Ranieri; M. Vetterli : Near-optimal Sensor Placement for Signals lying in a Union of Subspaces. 2014. 22nd European Signal Processing Conference (EUSIPCO 2014), Lisbon, Portugal. p. 880-884.
J. Ranieri; A. Chebira; M. Vetterli : Near-Optimal Sensor Placement for Linear Inverse Problems; IEEE Transactions on Signal Processing. 2014. DOI : 10.1109/Tsp.2014.2299518.
H. Pan; T. Blu; P. L. Dragotti : Sampling Curves with Finite Rate of Innovation; IEEE Transactions on Signal Processing. 2014. DOI : 10.1109/TSP.2013.2292033.
R. Parhizkar; Y. Barbotin; M. Vetterli : Sequences with Minimal Time-Frequency Spreads. 2013. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, 2013.
H. Pan; T. Blu; P. L. Dragotti : Sampling Curves with Finite Rate of Innovation. 2011. 9th International Conference on Sampling Theory and Applications, Singapore, May 2-6, 2011.
Y. Lu; M. Vetterli : Sparse spectral factorization: Unicity and Reconstruction Algorithms. 2011. International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 22-27, 2011. p. 5976-5979.

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