Blind Deconvolution of Hodgkin-Huxley neuronal model
Neuron transforms information via a complex interaction between its previous states, its intrinsic properties, and the synaptic input it receives from other neurons. Inferring synaptic input of a neuron only from its membrane potential (output) that contains both sub-threshold and action potentials can effectively elucidate the information processing mechanism of a neuron. The term coined blind deconvolution of Hodgkin-Huxley (HH) neuronal model is defined, for the first time in this paper, to address the problem of reconstructing the hidden dynamics and synaptic input of a single neuron modeled by the HH model as well as estimating its intrinsic parameters only from single trace of noisy membrane potential. The blind deconvolution is accomplished via a recursive algorithm whose iterations contain running an extended Kalman filtering followed by the expectation maximization (EM) algorithm. The accuracy and robustness of the proposed algorithm have been demonstrated by our simulations. The capability of the proposed algorithm makes it particularly useful to understand the neural coding mechanism of a neuron.