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Compressive Sensing in Acoustic Imaging

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Compressed Sensing and its Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Acoustic sensing is at the heart of many applications, ranging from underwater sonar and nondestructive testing to the analysis of noise and their sources, medical imaging, and musical recording. This chapter discusses a palette of acoustic imaging scenarios where sparse regularization can be leveraged to design compressive acoustic imaging techniques. Nearfield acoustic holography (NAH) serves as a guideline to describe the general approach. By coupling the physics of vibrations and that of wave propagation in the air, NAH can be expressed as an inverse problem with a sparsity prior and addressed through sparse regularization. In turn, this can be coupled with ideas from compressive sensing to design semi-random microphone antennas, leading to improved hardware simplicity, but also to new challenges in terms of sensitivity to a precise calibration of the hardware and software scalability. Beyond NAH, this chapter shows how compressive sensing is being applied to other acoustic scenarios such as active sonar, sampling of the plenacoustic function, medical ultrasound imaging, localization of directive sources, and interpolation of plate vibration response.

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Notes

  1. 1.

    Experiments performed by Franois Ollivier and Antoine Peillot at Institut Jean Le Rond d’Alembert, UPMC Univ. Paris 6

  2. 2.

    This is no longer true as soon as \(\Psi\) and Ω are not square and invertible matrices [14].

References

  1. Ajdler, T., Vetterli, M.: Acoustic based rendering by interpolation of the plenacoustic function. In: SPIE/IS &T Visual Communications and Image Processing Conference, pp. 1337–1346. EPFL (2003)

    Google Scholar 

  2. Benichoux, A., Vincent, E., Gribonval, R.: A compressed sensing approach to the simultaneous recording of multiple room impulse responses. In: IEEE Workshop on Applications of Signal Processing to Audio and Acoustics 2011, p. 1, New Paltz, NY, USA (2011)

    Google Scholar 

  3. Bilen, C., Puy, G., Gribonval, R., Daudet, L.: Blind Phase Calibration in Sparse Recovery. In:EUSIPCO - 21st European Signal Processing Conference-2013, IEEE, Marrakech, Maroc (2013)

    Google Scholar 

  4. Bilen, C., Puy G., Gribonval, R., Daudet, L.: Blind Sensor Calibration in Sparse Recovery Using Convex Optimization. In: SAMPTA - 10th International Conference on Sampling Theory and Applications - 2013, Bremen, Germany (2013)

    Google Scholar 

  5. Bilen, C., Puy, G., Gribonval, R., Daudet, L.: Convex optimization approaches for blind sensor calibration using sparsity. IEEE Trans. Signal Process. 99(1), (2014)

    Google Scholar 

  6. Boufounos, P.: Compressive sensing for over-the-air ultrasound. In: Proceedings of ICASSP, pp. 5972–5975, Prague, Czech Republic, (2011)

    Google Scholar 

  7.  Chardon, G,  Leblanc, A,  Daudet L.: Plate impulse response spatial interpolation with sub-nyquist sampling. J. Sound Vib. 330(23), 5678–5689 (2011)

    Article  Google Scholar 

  8. Chardon, G., Bertin, N., Daudet, L.: Multiplexage spatial aléatoire pour l’échantillonnage compressif - application à l’holographie acoustique. In: XXIIIe Colloque GRETSI, Bordeaux, France (2011)

    Google Scholar 

  9. Chardon, G., Daudet, L., Peillot, A., Ollivier, F., Bertin, N., Gribonval, R.: Nearfield acoustic holography using sparsity and compressive sampling principles. J. Acoust. Soc. Am. 132(3), 1521–1534 (2012) Code & data for reproducing the main figures of this paper are available at http://echange.inria.fr/nah.

  10. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic Decomposition by Basis Pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1999)

    Article  MathSciNet  Google Scholar 

  11. Daudet, L.: Sparse and structured decompositions of signals with the molecular matching pursuit. IEEE Trans Audio Speech Lang. Process. 14(5), 1808–1816 (2006)

    Article  Google Scholar 

  12. Duarte, M.F.,  Sarvotham, S.,  Baron, D., Wakin, M.B., Baraniuk, R.G.: Distributed compressed sensing of jointly sparse signals. In: Proceedings of Asilomar Conference Signals, Systems and Computers, pp. 1537–1541 (2005)

    Google Scholar 

  13. Ekanadham, C., Tranchina, D., Simoncelli, E.P.: Recovery of sparse translation-invariant signals with continuous basis pursuit. IEEE Trans. Signal Process. 59(10), 4735–4744 (2011)

    Article  MathSciNet  Google Scholar 

  14. Elad, M., Milanfar, P., Rubinstein, R.: Analysis versus synthesis in signal priors. Inverse Prob. 23, 947–968 (2007)

    Article  MathSciNet  Google Scholar 

  15. Giryes, R.,  Nam, S., Elad, M.,  Gribonval, R., Davies, M.E.: Greedy-Like algorithms for the cosparse analysis model. arXiv preprint arXiv:1207.2456 (2013)

    Google Scholar 

  16. Gribonval, R., Bacry, E.: Harmonic decomposition of audio signals with matching pursuit. IEEE Trans. Signal Process. 51(1), 101–111 (2003)

    Article  MathSciNet  Google Scholar 

  17. Gribonval, R., Chardon, G., Daudet, L.: Blind Calibration For Compressed Sensing By Convex Optimization. In:IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, Kyoto, Japan (2012)

    Google Scholar 

  18. Kitić, S., Bertin, N.,  Gribonval, R.: A review of cosparse signal recovery methods applied to sound source localization. In:Le XXIVe colloque Gretsi, Brest, France (2013)

    Google Scholar 

  19. Kitic, S., Bertin, N.,  Gribonval, R.: Hearing behind walls: localizing sources in the room next door with cosparsity. In: 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, Italy (2014)

    Google Scholar 

  20. Liebgott, H., Basarab, A., Kouamé, D.,  Bernard, O., Friboulet, D.: Compressive Sensing in Medical Ultrasound. pp. 1–6. IEEE, Dresden (Germany)(2012)

    Google Scholar 

  21. Liebgott, H., Prost R.,  Friboulet, D.: Pre-beamformed RF signal reconstruction in medical ultrasound using compressive sensing. Ultrasonics 53(2), 525–533 (2013)

    Article  Google Scholar 

  22. Maynard, J.D., Williams, E.G., Lee, Y.: Nearfield acoustic holography: I, theory of generalized holography and the development of NAH. J. Acoust. Soc. Am. 78(4), 1395–1413 (1985)

    Article  Google Scholar 

  23. Mignot, R.,  Chardon, G.,  Daudet, L.: Low frequency interpolation of room impulse responses using compressed sensing. IEEE/ACM Trans. Audio Speech Lang. Process. 22(1), 205–216 (2014)

    Article  Google Scholar 

  24. Mignot, R.. Daudet, L., F. Ollivier. Room reverberation reconstruction: Interpolation of the early part using compressed sensing. IEEE Trans. Audio, Speech, Lang. Process. 21(11), 2301–2312 (2013)

    Google Scholar 

  25. Moiola, A., Hiptmair, R., Perugia, I.: Plane wave approximation of homogeneous helmholtz solutions. Z. Angew. Math. Phys. (ZAMP) 62, 809–837 (2011). 10.1007/s00033-011-0147-y

    Google Scholar 

  26. Nam, S., Davies, M.E., Elad, M., Gribonval, R.: The cosparse analysis model and algorithms. Appl. Comput. Harmon. Anal. 34(1), 30–56 (2013)

    Article  MathSciNet  Google Scholar 

  27. Nam, S., Davies, M.E.,  Elad, M.,  Gribonval, R.: Recovery of cosparse signals with greedy analysis pursuit in the presence of noise. In: 2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 361–364. IEEE, New York (2011)

    Google Scholar 

  28.  Nam, S.,  Gribonval, R.: Physics-driven structured cosparse modeling for source localization. In:2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5397–5400. IEEE, New York (2012)

    Google Scholar 

  29. Quinsac, C., Basarab, A.,  Kouam, D.: Frequency domain compressive sampling for ultrasound imaging. Adv. Acoust. Vib. Adv. Acoust. Sens. Imag. Signal Process. 12 1–16 (2012)

    Google Scholar 

  30. Rauhut, H.: Random sampling of sparse trigonometric polynomials. Appl. Comput. Harmon. Anal. 22(1), 16–42 (2007)

    Article  MathSciNet  Google Scholar 

  31.  Richy, J.,  Liebgott, H.,  Prost, R.,  Friboulet, D.: Blood velocity estimation using compressed sensing. In:IEEE International Ultrasonics Symposium, pp. 1427–1430. Orlando (2011)

    Google Scholar 

  32. Schiffner, M.F., Schmitz, G.: Fast pulse-echo ultrasound imaging employing compressive sensing. In:Ultrasonics Symposium (IUS), 2011 IEEE International, pp 688–691. IEEE, New York (2011)

    Google Scholar 

  33. Stefanakis, N., Marchal, J.,  Emiya, V.,  Bertin, N.,  Gribonval, R.,  Cervenka, P.: Sparse underwater acoustic imaging: a case study. In: Proceeding of International Conference Acoustics, Speech, and Signal Processing. Kyoto, Japan (2012)

    Google Scholar 

  34. Wabnitz, A., Epain, N., van Schaik, A., Jin, C.: Time domain reconstruction of spatial sound fields using compressed sensing. In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 465–468. IEEE, New York (2011)

    Google Scholar 

  35. Wagner, N., Eldar, Y.C., Feuer, A., Danin, G., Friedman, Z.: Xampling in ultrasound imaging. SPIE Medical Imaging Conference, 7968 (2011)

    Google Scholar 

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Acknowledgements

The authors wish to warmly thank François Ollivier, Jacques Marchal, and Srdjan Kitic for the figures, as well as Gilles Chardon, Rmi Mignot, Antoine Peillot, and the colleagues from the ECHANGE and PLEASE project whose contributions have been essential in the work described in this chapter. This work was supported in part by French National Research, ECHANGE project (ANR-08-EMER-006 ECHANGE) and by the European Research Council, PLEASE project (ERC-StG-2011-277906).

Author information

Authors and Affiliations

  1. IRISA - CNRS UMR 6074, PANAMA team (Inria & CNRS), Campus de Beaulieu, F-35042, Rennes Cedex, France

    Nancy Bertin

  2. Paris Diderot University, Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, F-75005, Paris, France

    Laurent Daudet

  3. Aix-Marseille Université, CNRS, LIF UMR 7279, F-13288, Marseille Cedex 9, France

    Valentin Emiya

  4. Inria, PANAMA team (Inria & CNRS), Campus de Beaulieu, F-35042, Rennes Cedex, France

    Rémi Gribonval

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  1. Nancy Bertin
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  2. Laurent Daudet
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  4. Rémi Gribonval
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Correspondence to Nancy Bertin .

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Editors and Affiliations

  1. Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, München, Bayern, Germany

    Holger Boche

  2. Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina, USA

    Robert Calderbank

  3. Institut für Mathematik, Technische Universität Berlin, Berlin, Berlin, Germany

    Gitta Kutyniok

  4. Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Jan Vybíral

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Bertin, N., Daudet, L., Emiya, V., Gribonval, R. (2015). Compressive Sensing in Acoustic Imaging. In: Boche, H., Calderbank, R., Kutyniok, G., Vybíral, J. (eds) Compressed Sensing and its Applications. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16042-9_6

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