Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, P.R. China.
Faculty of Mathematics, Kim Il Sung University, Pyongyang, D.P.R. of Korea.
PLoS One. 2021 Apr 20;16(4):e0250260. doi: 10.1371/journal.pone.0250260. eCollection 2021.
The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We use the framework of the alternating direction method of multipliers to design an efficient minimization algorithm for the proposed model. Since the objective function is the sum of the non-quadratic log-likelihood and nonconvex nondifferentiable regularizer, we propose to solve the intractable subproblems by the majorization-minimization (MM) method and the iteratively reweighted least squares (IRLS) algorithm, respectively. Numerical experiments show the efficiency of the proposed method for Poissonian image restoration including denoising and deblurring.
由于入射到图像传感器上的离散粒子数的不确定性，泊松噪声图像的恢复是许多成像应用中的一项基本任务。在本文中，我们考虑利用混合正则化器进行泊松噪声图像恢复。所提出的正则化器将重叠分组稀疏（OGS）全变差与高阶非凸全变差相结合，可以在保留原始锐利边缘的同时减轻阶梯伪影。我们使用增广乘子法的框架来设计一个用于该模型的有效最小化算法。由于目标函数是二次对数似然和非凸不可微正则项的和，我们分别提出了用大化-最小化（MM）方法和迭代重加权最小二乘法（IRLS）来解决难以处理的子问题。数值实验表明了该方法在泊松图像恢复（包括去噪和去模糊）中的有效性。
