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C. W. Tyler, L. L. Kontsevich; The bizarre effects of multiplicative noise. Journal of Vision 2001;1(3):440. https://doi.org/10.1167/1.3.440.
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© ARVO (1962-2015); The Authors (2016-present)
Most signal detection analyses assume additive noise (with an attentional component introduced in the form of Uncertainty Theory). Mammalian neurophysiological data, on the other hand, (beginning with Tolhurst et al. 1983, Exp. Brain Res.) suggests that cortical noise is multiplicative, increasing with some power exponent of response strength of 0.5–0.75. The effect of such multiplicative noise on detection thresholds is little short of bizarre. If the noise exponent is 0.5, psychophysical sensitivity should increase with number of detection events at a (slightly) supralinear rate on the basis of attentional (or ‘probability’) summation alone, resembling linear spatial or temporal summation. The implication would be that summation experiments of receptive or perceptive field size would not measure neural summation properties, only output nonlinearities. Noise generated by eye movements should have a multiplicative exponent of 1.0, implying that detection and discrimination thresholds are unmeasurable since the signal/noise ratio does not depend on stimulus contrast. This theoretical result implies that eye movement noise is negligible in all viable psychophysical paradigms (and may explain the inability of some observers to perform psychophysics). A new analysis that allows separate estimates of the signal and noise exponents in the contrast discrimination task reveals that, in humans, the internal noise exponent is about 0.8 and the signal exponent a little above 2.0 at all contrasts (effectively the quadratic nonlinearity required for computing contrast energy). These results confirm the applicability of multiplicative noise in the human perception of contrast, but show that its effects are ameliorated by an accelerating signal transducer throughout the contrast range.
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