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:
Towards Real-Time High-Resolution Interferometric Imaging with Bluebild2017-08-01.
Near-optimal Sensor Placement for Signals lying in a Union of Subspaces2014. 22nd European Signal Processing Conference (EUSIPCO 2014), Lisbon, Portugal, p. 880-884.
Sequences with Minimal Time-Frequency Spreads2013. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, 2013.
Sampling Curves with Finite Rate of Innovation2011. 9th International Conference on Sampling Theory and Applications, Singapore, May 2-6, 2011.
Sparse spectral factorization: Unicity and Reconstruction Algorithms2011. International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 22-27, 2011. p. 5976-5979.