Obtaining natural and realistic restorations from the noisy images contaminated by multiplicative noise is a challenging task in image processing. To get over this conundrum, by introducing the non-convex potential functions into the total variation and high-order total variation regularizers, we investigate a novel hybrid non-convex optimization model for image restoration. Numerically, to optimize the resulting high-order PDE system, a proximal linearized alternating minimization method, based on the classical iteratively reweighted ${\ell }_1$ algorithm and variable splitting technique, is designed in detail. Meanwhile, the convergence of the constructed algorithm is also established on the basis of convex analysis. The provided numerical experiments point out that our new scheme shows superiorities in both visual effects and quantitative comparison, especially in terms of the staircase aspects suppression and edge details preservation, compared with some popular denoising methods.

从被乘性噪声污染的噪声图像中获得自然和逼真的恢复是图像处理中的一项具有挑战性的任务。为了克服这个难题，通过将非凸势函数引入总变差和高阶总变差正则化器，我们研究了一种用于图像恢复的新型混合非凸优化模型。在数值上，为了优化得到的高阶 PDE 系统，一种基于经典迭代重加权的近端线性化交替最小化方法${\ell }_1$算法和变量分裂技术，进行了详细设计。同时，所构建算法的收敛性也是建立在凸分析的基础上的。提供的数值实验表明，与一些流行的去噪方法相比，我们的新方案在视觉效果和定量比较方面都显示出优势，特别是在楼梯方面的抑制和边缘细节保留方面。