Laboratoire des Signaux et Systèmes (CNRS-SUPELECUPS), 91192 Gif-sur-Yvette Cedex, France.
IEEE Trans Image Process. 2001;10(7):1001-9. doi: 10.1109/83.931094.
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, the Geman and Yang's and Geman and Reynolds's constructions are revisited, with a view to establishing the 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 the Geman and Reynolds's construction.
本文针对图像恢复问题，研究了凸半二次准则及其相关的最小化算法。本文在凸对偶的基础上，提出了一些统一的数学表述，引入了一些原创性的元素。首先，我们重新审视了 Geman 和 Yang 以及 Geman 和 Reynolds 的构造，以确定当原始非二次准则已经凸时，所得半二次增广准则的凸性。其次，我们揭示了一类包含交互辅助变量的凸 Gibbs 能量，作为 Geman 和 Reynolds 构造的潜在有益扩展。
