基于POCS的漏积分放电编码带限信号重建
Bandlimited signal reconstruction from leaky integrate-and-fire encoding using POCS
AI总结：
本文针对漏积分放电编码的带限信号重建问题，将LIF编码器建模为广义非均匀采样器，证明POCS方法收敛于加权伪逆，实现完美恢复、最小范数重建及噪声整形，并给出无需奈奎斯特率采样的离散实现。
摘要：
漏积分放电（LIF）编码是生物学中神经元传递函数的一种模型，近年来作为事件驱动采样技术引起了信号处理和神经形态计算社区的关注，用于数据采集。虽然LIF能够同时实现复杂度更低且精度更高的模拟电路信号采样器，但该技术的核心难点在于从LIF编码输出中恢复输入信号。本文在带限输入的背景下研究该问题，将LIF编码器最抽象的特征提取为广义非均匀采样器。在此视角下，LIF输出被视为输入经过已知线性算子的变换。我们证明，投影到凸集（POCS）的信号重建方法收敛于该算子的加权伪逆。这使得在唯一性条件下实现完美恢复，在不完全采样下实现最小范数重建，并实现优于标准伪逆的时间量化噪声整形。在实际方面，POCS方法的单次迭代可用于改进任何其LIF样本与输入不一致的估计，并提出了该迭代的严格离散时间实现，该实现不需要信号的奈奎斯特率表示。
英文摘要：
Leaky integrate-and-fire (LIF) encoding is a model of neuron transfer function in biology that has recently attracted the attention of the signal processing and neuromorphic computing communities as a technique of event-based sampling for data acquisition. While LIF enables the implementation of analog-circuit signal samplers of lower complexity and higher accuracy simultaneously, the core difficulty of this technique is the retrieval of an input from its LIF-encoded output. In this article, we study this problem in the context of bandlimited inputs, by extracting the most abstract features of an LIF encoder as a generalized nonuniform sampler. In this view, the LIF output is seen as the transformation of the input by a known linear operator. We show that the signal reconstruction method of projection onto convex sets (POCS) converges to a weighted pseudo-inverse of this operator. This allows perfect recovery under uniqueness of reconstruction, minimum-norm reconstruction under incomplete sampling, as well as a noise shaping of time quantization that outperforms standard pseudo-inversion. On the practical side, a single iteration of the POCS method can be used to improve any estimate whose LIF samples are not consistent with those of the input, and a rigorous discrete-time implementation of this iteration is proposed that does not require a Nyquist-rate representation of the signals.
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