A bio-inspired geometric model for sound reconstruction

Ugo Boscain (1, 2, 3) , Dario Prandi (2, 4) , Ludovic Sacchelli (5) , Giuseppina Turco (2, 6)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 CNRS - Centre National de la Recherche Scientifique
3 CaGE - Control And GEometry
4 L2S - Laboratoire des signaux et systèmes
5 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
6 LLF - UMR7110 - Laboratoire de Linguistique Formelle

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

Domaines: Optimisation et contrôle [math.OC]; Linguistique; Equations aux dérivées partielles [math.AP]; Traitement du signal et de l'image [eess.SP]

Ugo Boscain, Dario Prandi, Ludovic Sacchelli, Giuseppina Turco. A bio-inspired geometric model for sound reconstruction. Journal of Mathematical Neuroscience, 2021, 11 (1), pp.2. ⟨10.1186/s13408-020-00099-4⟩. ⟨hal-02531537v2⟩