  Fairness in image restoration tasks is the desire to treat different
sub-groups of images equally well. Existing definitions of fairness in image
restoration are highly restrictive. They consider a reconstruction to be a
correct outcome for a group (e.g., women) only if it falls within the group's
set of ground truth images (e.g., natural images of women); otherwise, it is
considered entirely incorrect. Consequently, such definitions are prone to
controversy, as errors in image restoration can manifest in various ways. In
this work we offer an alternative approach towards fairness in image
restoration, by considering the Group Perceptual Index (GPI), which we define
as the statistical distance between the distribution of the group's ground
truth images and the distribution of their reconstructions. We assess the
fairness of an algorithm by comparing the GPI of different groups, and say that
it achieves perfect Perceptual Fairness (PF) if the GPIs of all groups are
identical. We motivate and theoretically study our new notion of fairness, draw
its connection to previous ones, and demonstrate its utility on
state-of-the-art face image super-resolution algorithms.
