Convex half-quadratic criteria and interacting auxiliary variables for image restoration

This paper deals with convex half-quadratic criteria and associated minimization algorithms for the purpose of image restoration. It brings a number of original elements within a unified mathematical presentation based on convex duality. Firstly, Geman and Yang’s [1] and Geman and Reynolds’s [2] constructions are revisited, with a view to establish convexity properties of the resulting half-quadratic augmented criteria, when the original nonquadratic criterion is already convex. Secondly, a family of convex Gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of Geman and Reynolds’s construction.