Sergej Voronenko, BCCN Berlin / GRK 1589 / HU Berlin

Nonlinear signal processing by noisy spiking neurons

In general, Neurons process incoming signals in a nonlinear fashion, the exact mathematical description of which is still an open problem in neuroscience. In this thesis, the broad topic of nonlinear signal processing is approached from two directions. The first part of the thesis is devoted to the question how input signals modulate the neural response. The second part of the thesis is concerned with the nonlinear reconstruction of input signals from the neural output and with the estimation of the amount of the transmitted information.
The nonlinear modulation of the neural response is studied by extending the linear response theory for the time-dependent firing rate. For the analytically tractable leaky integrate-and-fire model, we derive a weakly nonlinear theory that reveals several interesting features of nonlinear signal processing, as for example the excitation of higher harmonics, or a strong nonlinear interaction of multiple input signals.

The nonlinear reconstruction of input signals and the nonlinear estimation of the information content of the neural spike count is studied by extending the well-known linear signal reconstruction. For the special case of a static input signal, we then derive a nonlinear lower bound which can be used as a simple estimate of the amount of information which the neural output transmits about the input signal. For two different neuron models we demonstrate that a nonlinear reconstruction of the input signal strongly outperforms the linear reconstruction and that the nonlinear lower bound significantly improves the estimation of the true mutual information as compared to the linear lower bound.The results of this thesis demonstrate how existing linear theories can be extended to capture nonlinear contributions of the signal to the neural response or to incorporate nonlinear correlations into the estimation of the transmitted information. More importantly, however, our analysis demonstrates that these extensions do not merely provide small corrections to the existing linear theories but can account for qualitatively novel effects which are completely missed by the linear theories.

Additional Information

PhD defence within the GRK 1589 "Sensory Computation in Neural Systems"

Organized by

Benjamin Lindner / Robert Martin