  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.
