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:
A Fast and Scalable Polyatomic Frank-Wolfe Algorithm for the LASSO
IEEE Signal Processing Letters. 2022. Vol. 29, p. 637 – 641. DOI : 10.1109/LSP.2022.3149377.Lippmann Photography: A Signal Processing Perspective
Ieee Transactions On Signal Processing. 2022. Vol. 70, p. 3894 – 3905. DOI : 10.1109/TSP.2022.3191473.A Time Encoding Approach to Training Spiking Neural Networks
2022. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022), Singapore, Singapore, May 23-27, 2022. p. 5957 – 5961. DOI : 10.1109/ICASSP43922.2022.9746319.How Asynchronous Events Encode Video
2021. 55th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 31 Oct-3 Nov, 2021. p. 836 – 841. DOI : 10.1109/IEEECONF53345.2021.9723356.CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI
IEEE Transactions on Signal Processing. 2020. Vol. 69, p. 42 – 57. DOI : 10.1109/TSP.2020.3041089.Relax and Recover: Guaranteed Range-Only Continuous Localization
IEEE Robotics and Automation Letters. 2020. Vol. 5, num. 2, p. 2248 – 2255. DOI : 10.1109/LRA.2020.2970952.Sampling and Reconstruction of Bandlimited Signals with Multi-Channel Time Encoding
IEEE Transactions on Signal Processing. 2020. Vol. 68, p. 1105 – 1119. DOI : 10.1109/TSP.2020.2967182.Encoding And Decoding Mixed Bandlimited Signals Using Spiking Integrate-And-Fire Neurons
2020. IEEE International Conference on Acoustics, Speech, and Signal Processing, Barcelona, SPAIN, May 04-08, 2020. p. 9264 – 9268. DOI : 10.1109/ICASSP40776.2020.9053294.Bound and Conquer: Improving Triangulation by Enforcing Consistency
IEEE Transactions on Pattern Analysis and Machine Intelligence. 2019. Vol. 42, num. 9, p. 2321 – 2326. DOI : 10.1109/TPAMI.2019.2939530.Sampling at unknown locations: Uniqueness and reconstruction under constraints
IEEE Transactions on Signal Processing. 2018. Vol. 66, num. 22, p. 5862 – 5874. DOI : 10.1109/TSP.2018.2872019.Super Resolution Phase Retrieval for Sparse Signals
IEEE Transactions On Signal Processing. 2018. Vol. 67, num. 18, p. 4839 – 4854. DOI : 10.1109/TSP.2019.2931169.Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity
IEEE Transactions on Signal Processing. 2018. Vol. 66, num. 17, p. 4642 – 4656. DOI : 10.1109/TSP.2018.2858213.Towards Real-Time High-Resolution Interferometric Imaging with Bluebild
2017.Sampling and Exact Reconstruction of Pulses with Variable Width
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
IEEE Transactions on Signal Processing. 2017. Vol. 65, num. 4, p. 821 – 835. DOI : 10.1109/TSP.2016.2625274.Unlabeled Sensing: Reconstruction Algorithm and Theoretical Guarantees
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 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.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. p. 1596 – 1600. DOI : 10.1109/ICASSP.2016.7471946.Near-Optimal Sensor Placement for Linear Inverse Problems
IEEE Transactions on Signal Processing. 2014. Vol. 62, num. 5, p. 1135 – 1146. DOI : 10.1109/Tsp.2014.2299518.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.Sampling Curves with Finite Rate of Innovation
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
2013. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, 2013. p. 5343 – 5347. DOI : 10.1109/ICASSP.2013.6638683.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. DOI : 10.1109/ICASSP.2011.5947723.Sampling Curves with Finite Rate of Innovation
2011. 9th International Conference on Sampling Theory and Applications, Singapore, May 2-6, 2011.LCAV-MSP