脉冲噪声下图像去模糊非光滑非凸最小化问题的近端线性化最小化算法

去除脉冲噪声是图像复原中的重要任务之一.我们提出一类非光滑非凸模型来恢复模糊和脉冲噪声污染的图像,该模型具有灵活的先验信息引入机制,如盒子约束或低秩等.为了求解所提非凸问题,我们采用近端线性化最小化算法.对于算法中的子问题,我们运用交替方向乘子法.在目标函数满足Kurdyka-Lojasiewicz性质的假设下,我们证明所提算法的全局收敛性.数值实验表明,在主观和客观质量评价方面,我们的方法优于$\ell_{1}$TV和非凸TV模型.

Proximal Linearized Minimization Algorithm for Nonsmooth Nonconvex Minimization Problems in Image Deblurring with Impulse Noise

Impulse noise removal is an important task in image restoration. In this paper, we introduce a general nonsmooth nonconvex model for recovering images degraded by blur and impulsive noise, which can easily include some prior information, such as box constraint or low rank, etc. To deal with the nonconvex problem, we employ the proximal linearized minimization algorithm. For the subproblem, we use the alternating direction method of multipliers to solve it. Furthermore, based on the assumption that the objective function satisfies the Kurdyka-Lojasiewicz property, we prove the global convergence of the proposed algorithm. Numerical experiments demonstrate that our method outperforms both the $\ell_{1}$TV and Nonconvex TV models in terms of subjective and objective quality measurements.