Image inpainting using sparse multiscale representations: Image recovery performance guarantees
Image inpainting using sparse multiscale representations: Image recovery performance guarantees
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DOI：
10.1016/j.acha.2020.05.001
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发表时间：
2020-09
影响因子：
2.5
通讯作者：
K. Guo;D. Labate;J. P. R. Ayllon
中科院分区：
文献类型：
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作者：
K. Guo;D. Labate;J. P. R. Ayllon
对于图像中缺失部分的恢复，已经应用了几种策略，恢复性能在很大程度上取决于图像类型和缺失数据的几何形状。为了更深入地理解这类图像恢复问题，King等人最近引入了一个严格的多尺度分析框架，并证明了当缺失数据为线奇点时，基于shearlet的补图方法优于基于更传统的多尺度表示的方法。在本文中，我们扩展并改进了对包含曲线奇异点的图像的更现实和更具有挑战性的图像绘制问题的分析。我们推导了绘制性能保证，表明如果丢失的奇点的大小小于图像的适当功能表示的结构元素的大小，则可以实现精确的图像恢复。我们的证明主要依赖于shearlet表示的微局部和稀疏性。
Several strategies have been applied for the recovery of the missing parts in an image, with recovery performance depending significantly on the image type and the geometry of missing data. To provide a deeper understanding of such image restoration problem, King et al. recently introduced a rigorous multiscale analysis framework and proved that a shearlet based inpainting approach outperforms methods based on more conventional multiscale representations when missing data are line singularities. In this paper, we extend and improve the analysis of the inpainting problem to the more realistic and more challenging setting of images containing curvilinear singularities. We derive inpainting performance guarantees showing that exact image recovery is achieved if the size of the missing singularity is smaller than the size of the structure elements of appropriate functional representations of the image. Our proof relies critically on the microlocal and sparsity properties of the shearlet representation.