Convex Image Denoising via Non-convex Regularization with Parameter Selection
Convex Image Denoising via Non-convex Regularization with Parameter Selection
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DOI：
10.1007/s10851-016-0655-7
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发表时间：
2016-10
影响因子：
2
通讯作者：
A. Lanza;S. Morigi;F. Sgallari
中科院分区：
文献类型：
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作者：
A. Lanza;S. Morigi;F. Sgallari
提出了一种凸非凸（CNC）去噪变分模型，用于恢复加性高斯白噪声损坏的图像。我们提出使用参数化非凸正则化器来有效地诱导解中梯度值的稀疏性，同时保持总代价泛函的严格凸性。评估了一些广泛使用的非凸正则化函数，并分析了一种新的非凸正则化函数，它可以更好地恢复。提出了一种基于交替方向乘法器（ADMM）策略的高效最小化算法，利用差异原理实现图像的同时恢复和正则化参数的自动选择。给出了数控变分模型的理论凸性条件和基于admm的优化子问题的理论凸性条件，保证了算法收敛到唯一的全局最小值。数值算例表明，该方法特别有效，并且非常适合以中等稀疏梯度为特征的图像。
We introduce a convex non-convex (CNC) denoising variational model for restoring images corrupted by additive white Gaussian noise. We propose the use of parameterized non-convex regularizers to effectively induce sparsity of the gradient magnitudes in the solution, while maintaining strict convexity of the total cost functional. Some widely used non-convex regularization functions are evaluated and a new one is analyzed which allows for better restorations. An efficient minimization algorithm based on the alternating direction method of multipliers (ADMM) strategy is proposed for simultaneously restoring the image and automatically selecting the regularization parameter by exploiting the discrepancy principle. Theoretical convexity conditions for both the proposed CNC variational model and the optimization sub-problems arising in the ADMM-based procedure are provided which guarantee convergence to a unique global minimizer. Numerical examples are presented which indicate how the proposed approach is particularly effective and well suited for images characterized by moderately sparse gradients.