In this study we tested predictions of two important theories of visual coding, contrast energy and sparse coding theory, on the dependence of population activity level and metabolic demands on spatial structure of the visual input. With carefully calibrated displays we find that in humans neither the V1 blood oxygenation level dependent (BOLD) response nor the initial visually evoked fields in magnetoencephalography (MEG) are sensitive to phase perturbations in photographs of natural scenes. As a control, we quantitatively show that the applied phase perturbations decrease sparseness (kurtosis) of our stimuli but preserve their root mean square (RMS) contrast. Importantly, we show that the lack of sensitivity of the V1 population response level to phase perturbations is not due to a lack of sensitivity of our methods because V1 responses were highly sensitive to variations of image RMS contrast. Our results suggest that the transition from a sparse to a distributed neural code in the early visual system induced by reducing image sparseness has negligible consequences for population metabolic cost. This result imposes a novel and important empirical constraint on quantitative models of sparse coding: Population metabolic rate and population activation level is sensitive to second order statistics (RMS contrast) of the input but not to its spatial phase and fourth order statistics (kurtosis).