Inpainting and Zooming Using Sparse Representations
Inpainting and Zooming Using Sparse Representations
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DOI：
10.1093/comjnl/bxm055
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发表时间：
2009-01-01
期刊：
影响因子：
1.4
通讯作者：
Murtagh, F.
中科院分区：
文献类型：
--
作者：
Fadili, M. J.;Starck, J. -L.;Murtagh, F.
将待绘制的图像表示在适当的稀疏表示字典中，并结合贝叶斯统计和现代调和分析的元素，提出了一种用于图像修复和内插的期望最大化(EM)算法。从统计学的角度来看，修复/内插可以看作是一个缺失数据的估计问题。为此，我们提出了在贝叶斯框架中使用EM机制的想法，在该框架中，对重构的系数施加稀疏性促进先验惩罚。EM框架给出了一种原则性的方法来正式建立基于稀疏表示的丢失样本可以恢复/内插的想法。首先介绍了一种简单高效的基于稀疏表示的图像修复迭代算法。此外，我们还推导了它的理论收敛性质。与其竞争对手相比，该算法允许高度的灵活性来恢复图像中不同的结构成分(分段平滑、曲线、纹理等)。我们还提出了一些准则来自动调整正则化参数。
Representing the image to be inpainted in an appropriate sparse representation dictionary, and combining elements from Bayesian statistics and modern harmonic analysis, we introduce an expectation maximization (EM) algorithm for image inpainting and interpolation. From a statistical point of view, the inpainting/interpolation can be viewed as an estimation problem with missing data. Toward this goal, we propose the idea of using the EM mechanism in a Bayesian framework, where a sparsity promoting prior penalty is imposed on the reconstructed coefficients. The EM framework gives a principled way to establish formally the idea that missing samples can be recovered/interpolated based on sparse representations. We first introduce an easy and efficient sparse-representation-based iterative algorithm for image inpainting. Additionally, we derive its theoretical convergence properties. Compared to its competitors, this algorithm allows a high degree of flexibility to recover different structural components in the image (piecewise smooth, curvilinear, texture, etc.). We also suggest some guidelines to automatically tune the regularization parameter.