Abstract
The reconstruction mechanisms built by the human auditory system during sound reconstruction are still a matter of debate. The purpose of this study is to refine the auditory cortex model introduced in [9], and inspired by the geometrical modelling of vision. The algorithm lifts the time-frequency representation of the degraded sound to the Heisenberg group, where it is reconstructed via a Wilson-Cowan integro-differential equation. Numerical experiments on a library of speech recordings are provided, showing the good reconstruction properties of the algorithm.
This study was supported by the IdEx Université de Paris, “ANR-18-IDEX-0001” and by the ANR RUBIN-VASE project, grant ANR-20-CE48-0003 of the French Agence Nationale de la Recherche.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The speech material used in the current study is part of an ongoing psycholinguistic project on spoken word recognition. Speech material comprises 49 Italian words and 118 French words. The two sets of words were produced by two (40-year-old) female speakers (a French monolingual speaker and an Italian monolingual speaker) and recorded using a headset microphone AKG C 410 and a Roland Quad Capture audio interface. Recordings took place in the soundproof cabin of the Laboratoire de Phonétique et Phonologie (LPP) of Université de Paris Sorbonne-Nouvelle. Both informants were told to read the set of words as fluently and naturally as possible.
References
Agrachev, A., Barilari, D., Boscain, U.: A comprehensive introduction to Sub-Riemannian geometry. In: Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (2019)
Assmann, P., Summerfield, Q.: The perception of speech under adverse conditions. In: Assmann, P. (ed.) Speech Processing in the Auditory System. SHAR, vol. 18, pp. 231–308. Springer, New York (2004). https://doi.org/10.1007/0-387-21575-1_5
Barilari, D., Boarotto, F.: Kolmogorov-fokker-planck operators in dimension two: heat kernel and curvature (2017)
Bertalmío, M., Calatroni, L., Franceschi, V., Franceschiello, B., Gomez Villa, A., Prandi, D.: Visual illusions via neural dynamics: Wilson-cowan-type models and the efficient representation principle. J. Neurophysiol. 123, 1606 (2020)
Bertalmío, M., Calatroni, L., Franceschi, V., Franceschiello, B., Prandi, D.: A cortical-inspired model for orientation-dependent contrast perception: a link with Wilson-Cowan equations. In: Lellmann, J., Burger, M., Modersitzki, J. (eds.) SSVM 2019. LNCS, vol. 11603, pp. 472–484. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-22368-7_37
Bertalmío, M., Calatroni, L., Franceschi, V., Franceschiello, B., Prand i, D.: Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling. J. Math. Imaging Vis. 63, 263 (2020)
Boscain, U., Chertovskih, R., Gauthier, J.P., Remizov, A.: Hypoelliptic diffusion and human vision: a semi-discrete new twist on the petitot theory. SIAM J. Imaging Sci. 7(2), 669–695 (2014)
Boscain, U., Duplaix, J., Gauthier, J.P., Rossi, F.: Anthropomorphic image reconstruction via hypoelliptic diffusion (2010)
Boscain, U., Prandi, D., Sacchelli, L., Turco, G.: A bio-inspired geometric model for sound reconstruction. J. Math. Neurosci. 11(1), 1–18 (2020). https://doi.org/10.1186/s13408-020-00099-4
Boscain, U.V., Chertovskih, R., Gauthier, J.P., Prandi, D., Remizov, A.: Highly corrupted image inpainting through hypoelliptic diffusion. J. Math. Imaging Vis. 60(8), 1231–1245 (2018)
Bressloff, P.C., Cowan, J.D., Golubitsky, M., Thomas, P.J., Wiener, M.C.: Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. Philos. Trans. R. Soc. Lond. B Biol. Sci. 356(1407), 299–330 (2001)
Citti, G., Sarti, A.: A cortical based model of perceptual completion in the Roto-Translation space. J. Math. Imaging Vis. 24(3), 307–326 (2006)
Ermentrout, G.B., Cowan, J.D.: A mathematical theory of visual hallucination patterns. Biol. Cybern. 34, 137–150 (1979)
Franken, E., Duits, R.: Crossing-preserving coherence-enhancing diffusion on invertible orientation scores. Int. J. Comput. Vis. 85(3), 253–278 (2009)
Hubel, D.H., Wiesel, T.N.: Receptive fields of single neurons in the cat’s striate cortex. J. Physiol. 148(3), 574–591 (1959)
Loebel, A., Nelken, I., Tsodyks, M.: Processing of sounds by population spikes in a model of primary auditory cortex. Front. Neurosci. 1(1), 197–209 (2007)
Mattys, S., Davis, M., Bradlow, A., Scott, S.: Speech recognition in adverse conditions: a review. Lang. Cogn. Neurosci. 27(7–8), 953–978 (2012)
Nelken, I., Calford, M.B.: Processing strategies in auditory cortex: comparison with other sensory modalities. In: Winer, J., Schreiner, C. (eds.) The Auditory Cortex, pp. 643–656. Springer, Boston (2011). https://doi.org/10.1007/978-1-4419-0074-6_30
Papoulis, A.: Probability, Random Variables and Stochastic Processes, 3rd edn., p. 138. McGraw-Hill Companies, New York (1991)
Petitot, J., Tondut, Y.: Vers une neurogéométrie. fibrations corticales, structures de contact et contours subjectifs modaux. Mathématiques et Sci. humaines 145, 5–101 (1999)
Prandi, D., Gauthier, J.P.: A Semidiscrete Version of the Citti-petitot-sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition. BRIEFSMATH, Springer, Cham (2017). https://doi.org/10.1007/978-3-319-78482-3
Rankin, J., Sussman, E., Rinzel, J.: Neuromechanistic model of auditory bistability. PLoS Comput. Biol. 11(11), e1004555 (2015)
Rauschecker, J.P.: Auditory and visual cortex of primates: a comparison of two sensory systems. Eur. J. Neurosci. 41(5), 579–585 (2015)
Reimann, H.M.: Signal processing in the cochlea: the structure equations. J. Math. Neurosci. 1(1), 43 (2011)
Tian, B., Kuśmierek, P., Rauschecker, J.P.: Analogues of simple and complex cells in rhesus monkey auditory cortex. Proc. Nat. Acad. Sci. 110(19), 7892–7897 (2013)
Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12(1), 1–24 (1972)
Yang, X., Wang, K., Shamma, S.: Auditory representations of acoustic signals. IEEE Trans. Inf. Theory 38, 68 (1992)
Zulfiqar, I., Moerel, M., Formisano, E.: Spectro-temporal processing in a two-stream computational model of auditory cortex. Front. Comput. Neurosci. 13, 95 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Asswad, R., Boscain, U., Turco, G., Prandi, D., Sacchelli, L. (2021). An Auditory Cortex Model for Sound Processing. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-80209-7_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-80208-0
Online ISBN: 978-3-030-80209-7
eBook Packages: Computer ScienceComputer Science (R0)