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.

Recent LCAV publications in this area:

Relax and Recover: Guaranteed Range-Only Continuous Localization

M. Pacholska; F. Dümbgen; A. J. Scholefield 

IEEE Robotics and Automation Letters. 2020-04-01. Vol. 5, num. 2, p. 2248-2255. DOI : 10.1109/LRA.2020.2970952.

Sampling and Reconstruction of Bandlimited Signals with Multi-Channel Time Encoding

K. Adam; A. Scholefield; M. Vetterli 

IEEE Transactions on Signal Processing. 2020. Vol. 68, p. 1105-1119. DOI : 10.1109/TSP.2020.2967182.

Bound and Conquer: Improving Triangulation by Enforcing Consistency

A. J. Scholefield; A. Ghasemi; M. Vetterli 

IEEE Transactions on Pattern Analysis and Machine Intelligence. 2019-09-13. Vol. 42, num. 9, p. 2321-2326. DOI : 10.1109/TPAMI.2019.2939530.

Sampling at unknown locations: Uniqueness and reconstruction under constraints

G. Elhami; M. W. Pacholska; B. Bejar Haro; M. Vetterli; A. J. Scholefield 

IEEE Transactions on Signal Processing. 2018-11-15. Vol. 66, num. 22, p. 5862-5874. DOI : 10.1109/TSP.2018.2872019.

Super Resolution Phase Retrieval for Sparse Signals

G. Baechler; M. Krekovic; J. Ranieri; A. Chebira; M. L. Yue et al. 

IEEE Transactions On Signal Processing. 2018-08-06. Vol. 67, num. 18, p. 4839-4854. DOI : 10.1109/TSP.2019.2931169.

Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity

H. Pan; T. Blu; M. Vetterli 

IEEE Transactions on Signal Processing. 2018-07-20. Vol. 66, num. 17, p. 4642-4656. DOI : 10.1109/TSP.2018.2858213.

Towards Real-Time High-Resolution Interferometric Imaging with Bluebild

S. Kashani 

2017-08-01.

Sampling at unknown locations, with an application in surface retrieval

M. W. Pacholska; B. Bejar Haro; A. J. Scholefield; M. Vetterli 

2017. Sampling Theory and Applications, 12th International Conference, Tallinn, Estonia, July 3 – 7, 2017. p. 364-368. DOI : 10.1109/SAMPTA.2017.8024451.

Unlabeled Sensing: Reconstruction Algorithm and Theoretical Guarantees

G. Elhami; A. J. Scholefield; B. Bejar Haro; M. Vetterli 

2017. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, USA, March 5-9, 2017. p. 4566-4570. DOI : 10.1109/ICASSP.2017.7953021.

Sampling and Exact Reconstruction of Pulses with Variable Width

G. Baechler; A. J. Scholefield; L. Baboulaz; M. Vetterli 

IEEE Transactions on Signal Processing. 2017. Vol. 65, num. 10, p. 2629-2644. DOI : 10.1109/TSP.2017.2669900.

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

H. Pan; T. Blu; M. Vetterli 

IEEE Transactions on Signal Processing. 2017. Vol. 65, num. 4, p. 821-835. DOI : 10.1109/TSP.2016.2625274.

Accurate recovery of a specularity from a few samples of the reflectance function

G. Baechler; I. Dokmanic; L. Baboulaz; M. Vetterli 

2016. 41st IEEE International Conference on Acoustics Speech and Signal Processing, Shanghai, China, March 20-25, 2016. p. 1596-1600. DOI : 10.1109/ICASSP.2016.7471946.

Near-optimal Sensor Placement for Signals lying in a Union of Subspaces

D. El Badawy; J. Ranieri; M. Vetterli 

2014. 22nd European Signal Processing Conference (EUSIPCO 2014), Lisbon, Portugal, p. 880-884.

Near-Optimal Sensor Placement for Linear Inverse Problems

J. Ranieri; A. Chebira; M. Vetterli 

IEEE Transactions on Signal Processing. 2014. Vol. 62, num. 5, p. 1135-1146. DOI : 10.1109/Tsp.2014.2299518.

Sampling Curves with Finite Rate of Innovation

H. Pan; T. Blu; P. L. Dragotti 

IEEE Transactions on Signal Processing. 2014. Vol. 62, num. 2, p. 458-471. DOI : 10.1109/TSP.2013.2292033.

Sequences with Minimal Time-Frequency Spreads

R. Parhizkar; Y. Barbotin; M. Vetterli 

2013. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, 2013.

Sampling Curves with Finite Rate of Innovation

H. Pan; T. Blu; P. L. Dragotti 

2011. 9th International Conference on Sampling Theory and Applications, Singapore, May 2-6, 2011.

Sparse spectral factorization: Unicity and Reconstruction Algorithms

Y. Lu; M. Vetterli 

2011. International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 22-27, 2011. p. 5976-5979.

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