Two-Dimentional Spike-Based Fourier Transform

The paper considers the problem of two-dimensional spectral analysis using signals represented by sequences of bipolar pulses (spikes) generated by Integrate-and-Fire (IF) spiking neuron. We adapt the input-output model of the IF neuron and modify the one-dimensional spike-based Fourier transform to work with spatial variables. We propose a two-dimensional spike-based Fourier transform for continuous signals by successively applying the one-dimensional spike-based Fourier transform. We show that when computing two-dimensional spike-based Fourier transform of discrete signals, the effect of discretization must be taken into account. We demonstrate that the proposed two-dimensional spike-based Fourier transform enables the computation of 2D spike spectra of digital images that have a relative mean square error of about 30–50 dB compared to the corresponding DFT spectra. For image reconstruction from their 2D spike spectrum, we also propose an inverse 2D spike-based Fourier transform. Experimental results show that the accuracy of digital image reconstruction corresponds to the accuracy of image reconstruction in lossy systems and can be controlled by the number of spikes per period of spectral harmonics. The main advantage of the proposed 2D spike-based Fourier transform is that its implementation is based on simple summation operations.