Retinal Contrast Adaptation as Kalman Filtering

Abstract

Abstract: : Purpose: A recent theoretical work postulated that the goal of sensory adaptation is to minimize errors in the performance of particular tasks (Grzywacz & Balboa, Neural Comp., 2002, 14:543). Here, we extend that theory to estimate optimally the changing state of the environment from the temporal stream of responses. We then apply the resulting theory to retinal contrast adaptation. Methods: The extension of the theory used a Bayesian formulation. It required prior knowledge of the statistics of the natural environment and of its temporal changes, and prior knowledge of the limitations of the neural mechanisms processing the information. The application to contrast adaptation assumed that its goal was to maximize retinal contrast information. Results: We show that if sensory adaptation followed this extension of the theory, then adaptation would be a generalized form of Kalman filtering. This is a technique used by engineers to track changing variables optimally amidst noisy backgrounds (e.g., tracking a satellite with atmospheric turbulence). Hence, if a system adapted as in Kalman filtering, then this system would adjust with optimal temporal protocols. The retina may use such optimization as demonstrated by the application of the theory to contrast adaptation. Computer simulations show that this application accounts for surprising features of the experimental data. For example, it accounts for the differences in ganglion-cell responses to increase and decrease of mean contrasts in the environment. In addition, it accounts for the two-phase decay of contrast gain when the mean contrast in the environment rises suddenly. Conclusions: The success of this and related theories suggests that retinal adaptation is a form of constrained biological optimization. This optimization would be in the performance of particular tasks (e.g., maximization of contrast information). In turn, the constraints would come from the limitations of the biological hardware (e.g., photoreceptor noise).

Keywords: ganglion cells • contrast sensitivity • computational modeling