Compressed Sensing

In order to reduce the amount of data to be acquired in acoustic imaging scenario, or plainly to reduce the number of sensors, it might be desirable to exploit the sparsity of the waves. This can be done within the recent signal processing paradigm called Compressed Sensing. Applications of Compressed Sensing to acoustics is a major research topic in our signal processing working group, around Laurent Daudet.
The ANR ECHANGE (2009-2012) project, coordinated by INRIA Rennes, and with Institut Langevin, Institut Jean le Rond d’Alembert and Laboratoire Jacques Louis Lions as other partners, aimed at discovering new acoustic sampling paradigms relying on the sparsity of the signals (based on physical principles or a priori knowledge), and this in order to reduce the number of measurements. In the PhD thesis of Gilles Chardon (2009-2012), we have successfully applied this principle to the problem of near-field acoustic holography (NAH) [ACL-Chardon2012], the interpolation of the impulse responses of plates [Chardon2011] and the source localization in reverberant environment [C-ACTI-Chardon2012b]. In the post-doctoral work of Rémi Mignot (2012-2011), we have also applied these techniques to the interpolation of the so-called pleanacoustic function (all Green functions within a given volume) [C-ACTI-Mignot2011a]. Our work on the localization of sources in reverberant environment is currently being improved with the PhD of Thibault Nowakowski (funded by a DGA grant, co-supervision L. Daudet and J. De Rosny), with a novel method taking into account partial information on the room geometry (eg proximity to a wall).
We also apply these techniques in the medical field, with the correction of aberrations due to the skull, during focused ultrasound therapy. This is the subject of PhD student Na Liu (co-supervision L. Daudet, M. Tanter).
Finally, we investigate the use of compressive sampling in optics for imaging through scattering media (Sylvain Gigan team). The post-doctoral researcher Antoine Liutkus explores imaging sparse images through such media, using less sensors than pixels ("super-resolution") - the challenge being in the development of numerical reconstruction techniques robust to errors in the transmission matrix.

[Chardon2012b] Chardon, G., Peillot, A., Ollivier, F., Bertin, N., Gribonval, R., & Daudet, L. (2012). Nearfield Acoustic Holography using sparse regularization and compressive sampling principles. J.Acoust.Soc.Am, a paraitre.

[Chardon2011] Chardon, G., Leblanc, A., & Daudet, L. (2011). Plate impulse response spatial interpolation with sub-Nyquist sampling. J. Sound Vibration, 330(23).

[Chardon2012a] Chardon, G., & Daudet, L. (2012). Narrowband source localization in an unknown reverberant environment using wavefield sparse decomposition. In International Conference on Acoustics, Speech and Signal Processing.

[Mignot2011a] Mignot, R., & Daudet, L. (2011). Compressively sampling the plenacoustic function. In Proceedings of the SPIE XIVth Conference on Wavelet Applications in Signal and Image Processing, San Diego.

[Mignot2011b] Mignot, R., Daudet, L., & Ollivier, F. (2011). Compressed sensing for acoustic response reconstruction: interpolation of the early part. In WASPAA 2011.

[Sturmel2012a] N. Sturmel and L. Daudet, Informed Source Separation using Iterative Reconstruction, IEEE Transactions on Audio, Speech and Language Processing, to appear.

[Sturmel2012b] Sturmel, N., Liutkus, A., Pinel, J., Girin, L., Marchand, S., Richard, G., et al. (2012). Linear mixing models for active listening of music productions in realistic studio conditions. In Proceedings AES 132nd Convention. best peer-reviewed paper award]