Methods for first-order kernel estimation: simple-cell receptive fields from responses to natural scenes

Recent studies have recovered receptive-field maps of simple cells in visual cortex from their responses to natural scene stimuli. Natural scenes have many theoretical and practical advantages over traditional, artificial stimuli; however, the receptive-field estimation methods are more complex than for white-noise stimuli. Here, we describe and justify several of these methods—spectral correction of the reverse correlation estimate, direct least-squares solution, iterative least-squares algorithms and regularized least-squares solutions. We investigate the pros and cons of the different methods, and evaluate them in a head-to-head comparison for simulated simple-cell data. This shows that, at least for quasilinear simulated simple cells, a regularized solution (‘reginv’) is most efficient, requiring fewer stimulus presentations for high-resolution reconstruction of the first-order kernel. We also investigate several practical issues that determine the success of this kind of experiment—the effects of neuronal nonlinearities, response variability and the choice of stimulus regime.