Population Encoding With Hodgkin-Huxley Neurons.
Population Encoding With Hodgkin-Huxley Neurons.
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DOI：
10.1109/tit.2009.2037040
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发表时间：
2010-02
影响因子：
2.5
通讯作者：
Lazar AA
中科院分区：
文献类型：
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作者：
Lazar AA
研究了用Hodgkin-Huxley神经元群体编码的（弱）刺激的恢复。在没有刺激的情况下，Hodgkin-Huxley神经元被认为是紧张性尖峰。所采用的方法要求1）找到霍奇金-赫胥黎神经元的输入-输出（I/O）等效描述，以及2）为用I/O等效神经元编码的刺激设计恢复算法。具有乘法耦合的Hodgkin-Huxley神经元与具有可变阈值序列的Integrate-and-Fire神经元是I/O等效的。对于带限刺激，只要满足奈奎斯特型速率条件，就可以实现刺激的完全恢复。具有加性耦合和确定性电导的Hodgkin-Huxley神经元与将刺激的投影集成在相位响应曲线上的投影-积分-激发神经元是一阶I/O等效的。在有限长度有界能量信号空间中，将刺激恢复问题转化为样条插值问题。具有加性耦合和随机电导的Hodgkin-Huxley神经元与具有随机阈值的Project-Integrate-and-Fire神经元是一阶I/O等价的。对于建模为Sobolev空间元素的刺激，重建算法最小化正则化的二次最优性准则。最后，所有以前的恢复结果的刺激编码与Hodgkin-Huxley神经元的乘法和加法耦合，和确定性和随机电导扩展到刺激编码的Hodgkin-Huxley神经元的人口。
The recovery of (weak) stimuli encoded with a population of Hodgkin–Huxley neurons is investigated. In the absence of a stimulus, the Hodgkin–Huxley neurons are assumed to be tonically spiking. The methodology employed calls for 1) finding an input–output (I/O) equivalent description of the Hodgkin–Huxley neuron and 2) devising a recovery algorithm for stimuli encoded with the I/O equivalent neuron(s). A Hodgkin–Huxley neuron with multiplicative coupling is I/O equivalent with an Integrate-and-Fire neuron with a variable threshold sequence. For bandlimited stimuli a perfect recovery of the stimulus can be achieved provided that a Nyquist-type rate condition is satisfied. A Hodgkin–Huxley neuron with additive coupling and deterministic conductances is first-order I/O equivalent with a Project-Integrate-and-Fire neuron that integrates a projection of the stimulus on the phase response curve. The stimulus recovery is formulated as a spline interpolation problem in the space of finite length bounded energy signals. A Hodgkin–Huxley neuron with additive coupling and stochastic conductances is shown to be first-order I/O equivalent with a Project-Integrate-and-Fire neuron with random thresholds. For stimuli modeled as elements of Sobolev spaces the reconstruction algorithm minimizes a regularized quadratic optimality criterion. Finally, all previous recovery results of stimuli encoded with Hodgkin–Huxley neurons with multiplicative and additive coupling, and deterministic and stochastic conductances are extended to stimuli encoded with a population of Hodgkin–Huxley neurons.