Abstract
AbstractThe reconstruction mechanisms built by the human auditory system during sound reconstruction are still a matter of debate. The purpose of this study is to propose a mathematical model of sound reconstruction based on the functional architecture of the auditory cortex (A1). The model is inspired by the geometrical modelling of vision, which has undergone a great development in the last ten years. There are, however, fundamental dissimilarities, due to the different role played by time and the different group of symmetries. The algorithm transforms the degraded sound in an ‘image’ in the time–frequency domain via a short-time Fourier transform. Such an image is then lifted to the Heisenberg group and is reconstructed via a Wilson–Cowan integro-differential equation. Preliminary numerical experiments are provided, showing the good reconstruction properties of the algorithm on synthetic sounds concentrated around two frequencies.
Funder
Agence national de la recherche
Idex Université de Paris
Publisher
Springer Science and Business Media LLC
Subject
Neuroscience (miscellaneous)
Reference46 articles.
1. Cambridge Studies in Advanced Mathematics;A Agrachev,2020
2. Assmann P, Summerfield Q. The Perception of Speech Under Adverse Conditions. New York: Springer; 2004. p. 231–308.
3. Barilari D, Boarotto F. Kolmogorov–Fokker–Planck operators in dimension two: heat kernel and curvature. SIAM J Control Optim. 2018.
4. 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. 2020;PMID:32159409.
5. 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: Scale Space and Variational Methods in Computer Vision. Cham: Springer; 2019.
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