Temporal modulation of luminance adapts time constant of fly movement detectors
Biological Cybernetics
An introduction to signal detection and estimation (2nd ed.)
An introduction to signal detection and estimation (2nd ed.)
Two-dimensional motion perception in flies
Neural Computation
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
A simple model of long-term spike train regularization
Neural Computation
Reconstruction of sensory stimuli encoded with integrate-and-fire neurons with random thresholds
EURASIP Journal on Advances in Signal Processing - Special issue on statistical signal processing in neuroscience
Phase locking below rate threshold in noisy model neurons
Neural Computation
Information filtering by synchronous spikes in a neural population
Journal of Computational Neuroscience
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Recently, methods of statistical estimation theory have been applied by Bialek and collaborators (1991) to reconstruct time-varying velocity signals and to investigate the processing of visual information by a directionally selective motion detector in the fly's visual system, the H1 cell. We summarize here our theoretical results obtained by studying these reconstructions starting from a simple model of H1 based on experimental data. Under additional technical assumptions, we derive a closed expression for the Fourier transform of the optimal reconstruction filter in terms of the statistics of the stimulus and the characteristics of the model neuron, such as its firing rate. It is shown that linear reconstruction filters will change in a nontrivial way if the statistics of the signal or the mean firing rate of the cell changes. Analytical expressions are then derived for the mean square error in the reconstructions and the lower bound on the rate of information transmission that was estimated experimentally by Bialek et al. (1991). For plausible values of the parameters, the model is in qualitative agreement with experimental data. We show that the rate of information transmission and mean square error represent different measures of the reconstructions: in particular, satisfactory reconstructions in terms of the mean square error can be achieved only using stimuli that are matched to the properties of the recorded cell. Finally, it is shown that at least for the class of models presented here, reconstruction methods can be understood as a generalization of the more familiar reverse-correlation technique.