Robust online reconstruction of continuous-time signals from a lean spike train ensemble code
This work addresses the challenge of efficient signal processing for sensory encoding in biological systems, offering a robust method with potential applications in neuromorphic engineering, though it is incremental in advancing existing spike-based coding frameworks.
The paper tackled the problem of reconstructing continuous-time signals from sparse spike trains, deriving a closed-form solution and an efficient iterative method that achieves excellent reconstruction accuracy at spike rates as low as one-fifth of the Nyquist rate, outperforming state-of-the-art sparse coding techniques.
Sensory stimuli in animals are encoded into spike trains by neurons, offering advantages such as sparsity, energy efficiency, and high temporal resolution. This paper presents a signal processing framework that deterministically encodes continuous-time signals into biologically feasible spike trains, and addresses the questions about representable signal classes and reconstruction bounds. The framework considers encoding of a signal through spike trains generated by an ensemble of neurons using a convolve-then-threshold mechanism with various convolution kernels. A closed-form solution to the inverse problem, from spike trains to signal reconstruction, is derived in the Hilbert space of shifted kernel functions, ensuring sparse representation of a generalized Finite Rate of Innovation (FRI) class of signals. Additionally, inspired by real-time processing in biological systems, an efficient iterative version of the optimal reconstruction is formulated that considers only a finite window of past spikes, ensuring robustness of the technique to ill-conditioned encoding; convergence guarantees of the windowed reconstruction to the optimal solution are then provided. Experiments on a large audio dataset demonstrate excellent reconstruction accuracy at spike rates as low as one-fifth of the Nyquist rate, while showing clear competitive advantage in comparison to state-of-the-art sparse coding techniques in the low spike rate regime.