Estimating nonlinear receptive fields from natural images

The response of visual cells is a nonlinear function of their stimuli. In addition, an increasing amount of evidence shows that visual cells are optimized to process natural images. Hence, finding good nonlinear models to characterize visual cells using natural stimuli is important. The Volterra model is an appealing nonlinear model for visual cells. However, their large number of parameters and the limited size of physiological recordings have hindered its application. Recently, a substantiated hypothesis stating that the responses of each visual cell could depend on an especially low-dimensional subspace of the image space has been proposed. We use this low-dimensional subspace in the Volterra relevant-space technique to allow the estimation of high-order Volterra models. Most laboratories characterize the response of visual cells as a nonlinear function on the low-dimensional subspace. They estimate this nonlinear function using histograms and by fitting parametric functions to them. Here, we compare the Volterra model with these histogram-based techniques. We use simulated data from cortical simple cells as well as simulated and physiological data from cortical complex cells. Volterra models yield equal or superior predictive power in all conditions studied. Several methods have been proposed to estimate the low-dimensional subspace. In this article, we test projection pursuit regression (PPR), a nonlinear regression algorithm. We compare PPR with two popular models used in vision: spike-triggered average (STA) and spike-triggered covariance (STC). We observe that PPR has advantages over these alternative algorithms. Hence, we conclude that PPR is a viable algorithm to recover the relevant subspace from natural images and that the Volterra model, estimated through the Volterra relevant-space technique, is a compelling alternative to histogram-based techniques.