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A bio-inspired geometric model for sound reconstruction

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 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 dierent role played by time and the dierent 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 in the Heisenberg group and is reconstructed via a Wilson-Cowan diero-integral equation. Preliminary numerical experiments are provided, showing the good reconstruction properties of the algorithm on synthetic sounds concentrated around two frequencies.

  Ugo Boscain AuthorId : 11565180

Author Employer institution : Centre National de la Recherche Scientifique IdHAL : ugo-boscain arXiv : https://arxiv.org/a/Ugo Boscain ORCID : https://orcid.org/0000-0001-5450-275X

  Dario Prandi AuthorId : 874263

Author IdHAL : dario-prandi ORCID : https://orcid.org/0000-0002-8156-5526

  Ludovic Sacchelli AuthorId : 1339429

Author IdHAL : ludovic-sacchelli ORCID : https://orcid.org/0000-0003-3838-9448

  Giuseppina Turco ¹ AuthorId : 12028074

Author