Unifying probabilistic and variational estimation
Unifying probabilistic and variational estimation
复制标题
统一概率估计和变分估计
DOI：
10.1109/msp.2002.1028351
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Gozde B. Unal
中科院分区：
文献类型：
--
作者：
A. B. Hamza;H. Krim;Gozde B. Unal
利用马尔可夫或最大熵随机场模型对先验分布进行最大后验（MAP）估计，可以看作是变分问题的极小化，利用鲁棒统计的概念，提出了一种变分滤波器，称为Huber梯度下降流。它是一个结果，优化的胡贝尔功能受到一些噪声约束，并采取混合形式的总变化扩散大梯度幅度和小梯度幅度的线性扩散。使用所获得的洞察力，并作为进一步的扩展，我们提出了一个信息理论的梯度下降流，这是一个结果，最小化的功能，是一个负熵变分积分和总变分之间的混合。说明性的例子表明，在高斯和重尾噪声的存在下，该方法的性能大大改善。在这篇文章中，我们提出了一个变分方法MAP估计与更多的定性和教程的重点。这种方法背后的关键思想是使用几何洞察力来帮助构造正则化泛函，并避免在MAP估计中主观选择先验。使用强大的统计和信息理论的工具，我们表明，我们可以扩展这种策略，并开发两个梯度下降流图像去噪与证明的性能。
A maximum a posteriori (MAP) estimator using a Markov or a maximum entropy random field model for a prior distribution may be viewed as a minimizer of a variational problem.Using notions from robust statistics, a variational filter referred to as a Huber gradient descent flow is proposed. It is a result of optimizing a Huber functional subject to some noise constraints and takes a hybrid form of a total variation diffusion for large gradient magnitudes and of a linear diffusion for small gradient magnitudes. Using the gained insight, and as a further extension, we propose an information-theoretic gradient descent flow which is a result of minimizing a functional that is a hybrid between a negentropy variational integral and a total variation. Illustrating examples demonstrate a much improved performance of the approach in the presence of Gaussian and heavy tailed noise. In this article, we present a variational approach to MAP estimation with a more qualitative and tutorial emphasis. The key idea behind this approach is to use geometric insight in helping construct regularizing functionals and avoiding a subjective choice of a prior in MAP estimation. Using tools from robust statistics and information theory, we show that we can extend this strategy and develop two gradient descent flows for image denoising with a demonstrated performance.
DOI：
10.1109/tpami.1984.4767596
发表时间：
1984-01-01
影响因子：
23.6
作者：
GEMAN, S;GEMAN, D
通讯作者：
GEMAN, D