EFFICIENT MCMC-BASED IMAGE DEBLURRING WITH NEUMANN BOUNDARY CONDITIONS
EFFICIENT MCMC-BASED IMAGE DEBLURRING WITH NEUMANN BOUNDARY CONDITIONS
复制标题
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
J. M. B. Marylesa;J. G. Nagy;J. M. Bardsley;And M. HOWARD;J. G. Nagy
中科院分区：
文献类型：
--
作者：
J. M. B. Marylesa;J. G. Nagy;J. M. Bardsley;And M. HOWARD;J. G. Nagy
.反问题的不确定性量化问题是近年来研究的一个重要课题。然而，UQ需要更多的比经典的方法计算反问题的解决方案。在本文中，我们采取了贝叶斯方法解决不适定的反卷积问题的对称卷积核和Neumann边界条件。先验被建模为高斯马尔可夫随机（cid：2）场（GMRF）具有相同的边界条件和对称性假设。这些假设在某些情况下产生更好的结果，并且还允许使用离散余弦变换进行快速计算。此外，我们对噪声精度（逆方差）和先验精度参数使用分层模型。这会产生一个后验密度函数，我们可以使用基本的马尔可夫链蒙特卡罗（MCMC）方法根据该函数计算样本。所得到的样本然后可以用于估计（使用，例如，样品平均值）和不确定性定量（CID：2）（使用，例如，直方图、样本方差或从图像样本创建的电影）。我们提供了一个数值实验表明，该方法是有效的，计算效率（cid：2）cient，并为某些问题，边界条件可以产生显着（cid：2）cantly更好的结果比，如果一个周期性的边界假设。在工作中的新奇在于MCMC方法，诺依曼边界条件，GMRF先验的组合，并在使用的电影可视化的不确定性在未知的图像。
. The problem of uncertainty quanti(cid:2)cation (UQ) for inverse problems has become of signi(cid:2)cant recent interest. However, UQ requires more than the classical methods for computing solutions of inverse problems. In this paper, we take a Bayesian approach for the solution of ill-posed deconvolution problems with a symmetric convolution kernel and Neumann boundary conditions. The prior is modeled as a Gaussian Markov random (cid:2)eld (GMRF) with the same boundary conditions and symmetry assumptions. These assumptions yield better results in certain instances and also allow for the use of the discrete cosine transform for fast computations. Moreover, we use a hierarchical model for the noise precision (inverse-variance) and prior precision parameters. This leads to a posterior density function from which we can compute samples using a basic Markov Chain Monte Carlo (MCMC) method. The resulting samples can then be used for both estimation (using, e.g., the sample mean) and uncertainty quanti(cid:2)cation (using, e.g., histograms, the sample variance, or a movie created from the image samples). We provide a numerical experiment showing that the method is effective, computationally ef(cid:2)cient, and that for certain problems, the boundary conditions can yield signi(cid:2)cantly better results than if a periodic boundary is assumed. The novelty in the work lies in the combination of the MCMC method, Neumann boundary conditions, GMRF priors, and in the use of a movie to visualize uncertainty in the unknown image.