We establish a theoretical connection between wavelet transforms and spiking neural networks through scale-space theory. We rely on the scale-covariant guarantees in the leaky integrate-and-fire neurons to implement discrete mother wavelets that approximate continuous wavelets. A reconstruction experiment demonstrates the feasibility of the approach and warrants further analysis to mitigate current approximation errors. Our work suggests a novel spiking signal representation that could enable more energy-efficient signal processing algorithms.

翻译：我们通过尺度空间理论建立了小波变换与脉冲神经网络之间的理论联系。我们利用泄漏积分-发放神经元的尺度协变性保证，实现了逼近连续小波的离散母小波。重构实验证明了该方法的可行性，并需要通过进一步分析来减轻当前逼近误差。我们的工作提出了一种新型脉冲信号表示方法，有望实现更高能效的信号处理算法。