Full identification of a linear-nonlinear system via cross-correlation analysis

A statistical model used extensively in vision research consists of a cascade of a linear operator followed by a static (memoryless) nonlinearity. Common applications include the measurement of simple-cell receptive fields in primary visual cortex and the modeling of human performance in various psychophysical tasks. It is well known that the front-end linear filter of the model can readily be recovered, up to a multiplicative constant, using reverse-correlation techniques. However, a full identification of the model also requires an estimation of the output nonlinearity. Here, we show that for a large class of static nonlinearities, one can obtain analytical expressions for the estimates. The technique works with both Gaussian and binary noise stimuli. The applicability of the method in physiology and psychophysics is demonstrated. Finally, the proposed technique is shown to converge much faster than the currently used linear-reconstruction method.