Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications
Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications
复制标题
DOI：
10.1109/tip.2011.2168232
复制
发表时间：
2012-03-01
影响因子：
10.6
通讯作者：
Unser, Michael
中科院分区：
文献类型：
--
作者：
Lefkimmiatis, Stamatios;Bourquard, Aurelien;Unser, Michael
我们提出了非二次海森的正则化方法，可以有效地用于图像恢复问题的变分框架。的巨大成功的全变差（TV）功能的动机，我们将其扩展到也包括二阶微分算子。具体而言，我们推导出二阶正则化，涉及矩阵规范的海森算子。这些功能的定义是基于电视的另一种解释，依赖于方向衍生物的混合规范。我们表明，由此产生的正则化保留了一些最有利的性质的电视，即，凸性、均匀性、旋转和平移不变性，同时有效地处理阶梯效应。我们进一步开发了一个有效的最小化方案，相应的目标函数。所提出的算法是迭代重加权最小二乘类型和结果从优化最小化方法。它依赖于特定问题的预处理共轭梯度法，这使得整体最小化方案非常有吸引力，因为它可以有效地应用于大图像在一个合理的计算时间。我们通过在标准和生物医学图像上的加性高斯噪声下的去模糊实验来验证整体提出的正则化框架。
We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.