论文标题
声音重建的生物启发的几何模型
A bio-inspired geometric model for sound reconstruction
论文作者
论文摘要
人类听觉系统在声音重建过程中建立的重建机制仍然是一个辩论问题。这项研究的目的是基于听觉皮层的功能结构（A1）提出声音重建的数学模型。该模型的灵感来自视力的几何建模，后者在过去十年中经历了巨大的发展。但是，由于时间和对称性不同的群体的作用不同，因此存在基本差异。该算法通过短期傅立叶变换在时频域中的“图像”中转换降解的声音。然后在海森伯格组中取消了这样的图像，并通过威尔逊 - 牛奶不同的方程式重建。提供了初步的数值实验，显示了该算法在两个频率附近的合成声音上的良好重建特性。
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.
