Subspace reverse-correlation estimation of receptive fields during free viewing.

Accurately mapping receptive fields under naturalistic viewing requires correcting for distortions introduced by eye movements. Current approaches often rely on parameterized "shifter networks" optimized with Poisson generalized linear models, but these methods are computationally intensive and limited to small regions of interest. We present a new framework that exploits the translation properties of Hartley basis functions to model eye position effects directly as phase shifts, eliminating the need for explicit retinal image reconstruction. This formulation admits closed-form gradients, enabling efficient parameter optimization and rapid convergence. Validation on simulated data shows that the method accurately recovers both ground-truth receptive fields and the underlying image transformation. Applied to high-density mouse V1 recordings, the approach substantially improves receptive field sharpness compared to naive estimates. While the method is specific to Hartley basis stimuli, once calibrated, it provides a reusable mapping between eye position and retinal translation. This efficiency and scalability make the technique a practical tool for receptive field mapping in free-viewing experiments and for integration with optical imaging and large-scale electrophysiology. We discuss the relative advantages, limitations, and applicability of the method in comparison with existing convolutional neural network/shifter-network approaches.