Nonlocal foveated principal components

Patch foveation corresponds to a spatially variant representation where the center of the patch is sharp while the periphery is blurred. This mimics the non-uniformity of the human visual system, whose acuity is maximal at the fixation point (imaged by the fovea, i.e. the central part of the retina) and low at the periphery of the visual field. We introduce patch foveation for patch clustering in dictionary learning. In particular, we consider principal components learned from clusters of foveated patches extracted from natural images corrupted by additive noise. Experiments demonstrate that the first few foveated principal components provide a better representation of the actual (non-foveated) image than the usual principal components learned from clusters of patches or windowed patches. These new results confirm the effectiveness of patch foveation as regularization and preconditioning prior when processing natural images.