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