What causes non-monotonic tuning of fMRI response to noisy images?

Although images are defined both by the amplitude and phase of their Fourier components, it is phase structure that is the major determinant of their appearance [1–3]. Rainer et al. [4] recently examined how phase structure impacts on cortical activity by measuring the BOLD fMRI signal in anaesthetized monkeys that were shown stimuli containing a blend of phases from images and noise. They showed that cells in V1 respond most strongly to natural images, most weakly to 50:50 image–noise blends, and then recovered for pure noise images. Given the strict monotonic dependence of psychophysical detectability on signal-to-noise ratio, this non-monotonicity was surprising and generated some excitement [5]. The authors' interpretation centres around the notion that sparseness is a desirable property of a cortical visual code [6–8]. They reasoned that the non-monotonicity is a trade-off between a few V1 cells responding vigorously to natural images versus many V1 cells responding weakly to noise images. Here, we offer another explanation: Rainer et al.'s phase blending fails to consider the directional nature of phase which leads to an over-representation of near-0° phase-components in their stimuli. This has the side-effect of altering the second-order (contrast) and fourth-order (kurtosis/sparse-ness) statistics of stimuli in a manner broadly consistent with observed changes in the BOLD signal. These changes do not inevitably arise from phase blending: using the weighted mean phase (WMP) produces monotonic changes in all of these statistics. We conclude that one cannot rule out an explanation of BOLD non-monotonicity based on simple image statistics rather than a cortical trade-off. We used a subset of eight of the images used in the original study; all had identical amplitude spectra, and were zero-mean in the range (-127,127). We estimated image phase (ϕ image) and the phase of uniform random noise images (ϕ noise) using the Fast Fourier transform. Two ways of combining (ϕ image) and (ϕ noise) were compared (see text box below). For both techniques w = 1 indicates full signal and w = 0 indicates full noise. The difference between the techniques lies in what phase distributions result at intermediate values of w. Equation (1) fails to take into account the directional nature of phase, and using it to combine large numbers of phases will systematically over-represent angles close to 0° simply because there are many more ways for two arithmetically weighted directions to sum to 0° than to any other direction. Figure 1B shows …