Fast Kalman filtering on quasilinear dendritic trees

Optimal filtering of noisy voltage signals on dendritic trees is a key problem in computational cellular neuroscience. However, the state variable in this problem -- the vector of voltages at every compartment -- is very high-dimensional: realistic multicompartmental models often have on the order of N = 104 compartments. Standard implementations of the Kalman filter require O(N3 ) time and O(N2 ) space, and are therefore impractical. Here we take advantage of three special features of the dendritic filtering problem to construct an efficient filter: (1) dendritic dynamics are governed by a cable equation on a tree, which may be solved using sparse matrix methods in O(N) time; and current methods for observing dendritic voltage (2) provide low SNR observations and (3) only image a relatively small number of compartments at a time. The idea is to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which may be obtained in O(N) t...

• Type: Journal
• Year: 2010
• Where: JCNS
• Authors: Liam Paninski
• Keywords: Dendritic, Dendritic Dynamics, Dendritic Filtering Problem, JCNS 2010