Primal-dual algorithms for total variation based image restoration under Poisson noise
Primal-dual algorithms for total variation based image restoration under Poisson noise
复制标题
泊松噪声下基于全变分的图像恢复的原对偶算法
DOI：
10.1007/s11425-015-5079-0
复制
发表时间：
2016-01-01
影响因子：
1.4
通讯作者：
Zeng TieYong
中科院分区：
文献类型：
--
作者：
Wen YouWei;Chan Raymond Honfu;Zeng TieYong
研究了被泊松噪声破坏的图像的恢复问题。在极大后测估计的框架下，该问题可转化为目标函数由泊松噪声的Kullback-Leibler （KL）发散项和总变分（TV）正则化项组成的最小化问题。由于kl -散度项的对数函数、TV项的不可微性以及对图像的正性约束，很难设计出稳定高效的算法。近年来，许多研究者提出了乘法器交替方向法（ADMM）来解决这个问题。由于该方法引入了一些辅助变量，并且需要求解一些线性系统，因此迭代过程比较复杂。本文将该问题表述为两个新的约束极大极小问题，并采用Chambolle-Pock一阶原对偶方法求解。他们的理论保证了我们方法的收敛性。与ADMM方法相比，我们的方法需要大约一半的辅助变量，并且不需要矩阵反转。数值结果表明，本文提出的算法是有效的，并且优于ADMM方法。
We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler (KL)-divergence term for the Poisson noise and a total variation (TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers (ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock’s first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.