On the foundations of vision modeling: I. Weber’s law and Weberized TV restoration

Most conventional image processors consider little the influence of human vision psychology. Weber’s law in psychology and psychophysics claims that humans’ perception and response to the intensity fluctuation δu of visual signals are weighted by the background stimulus u, instead of being plainly uniform. This paper attempts to integrate this well known perceptual law into the classical total variation (TV) image restoration model of Rudin et al. [Physica D 60 (1992) 259]. We study the issues of existence and uniqueness for the proposed Weberized nonlinear TV restoration model, making use of the direct method in the space of functions with bounded variations. We also propose an iterative algorithm based on the linearization technique for the associated nonlinear Euler–Lagrange equation.