Estimating the contribution of early and late noise in vision from psychophysical data

In many psychophysical detection and discrimination tasks human performance is thought to be limited by internal or inner noise when neuronal activity is converted into an overt behavioural response. It is unclear, however, to what extent the behaviourally limiting inner noise arises from early noise in the photoreceptors and the retina, or from late noise in cortex at or immediately prior to the decision stage. Presumably, the behaviourally limiting inner noise is a non-trivial combination of both early and late noises. Here we propose a method to quantify the contributions of early and late noise purely from psychophysical data. Our analysis generalizes classical results for linear systems (Burgess and Colborne, 1988) by combining the theory of noise propagation through a nonlinear network (Ahumada, 1987) with the expressions to obtain the perceptual metric along the nonlinear network (Malo and Simoncelli, 2006; Laparra et al., 2010). We show that from threshold-only data the relative contribution of early and late noise can only be determined if the experiments include substantial external noise in some of the stimuli used during experiments. If experimenters collected full psychometric functions, however, then early and late noise sources can be quantified even in the absence of external noise. Our psychophysical estimate of the magnitude of the early noise assuming a standard cascade of linear and nonlinear model stages is substantially lower than the noise in cone photocurrents computed via an accurate model of retinal physiology (Brainard and Wandell, 2020, ISETBIO). This is consistent with the idea that one of the fundamental tasks of early vision is to reduce the comparatively large retinal noise.