For a damaged image, the loss of pixel information can be roughly divided into two categories, random missing and non-random missing. The missing of an entire row or column of the image is a specific structural missing pattern that is extremely difficult to deal with. Although most of the existing methods have partially fixed this information missed problem, the diffusion-based methods tend to produce blur, the exemplar-based methods are prone to error filling, and the neural network-based methods are highly dependent on data, which cannot handle this special structural missing very well. Using the nonlocal self-similarity prior and the low-rank prior, we present multidirectional search and nonlocal low-rank tensor completion (MS-NLLRTC) algorithm based on the tensor ring (TR) decomposition and multidirectional search (MS). The MS method is a newly proposed method that can search similar patches much more diversified. Using MS method, we directly stack the similar patches into a three-dimensional similar tensor instead of pulling them into column vectors, then the similar tensor can be completed by TR decomposition. The optimization results can be obtained by leveraging the alternating direction method under the augmented Lagrangian multiplier framework. Moreover, we add a weighted nuclear norm to the tensor completion model (WNLLRTC), achieving a better inpainting performance. We also combine a noise removal method with WNLLRTC algorithm, which can handle image random missing and image noise removal simultaneously. Experimental results indicate that our proposed algorithms are competitive with some state-of-the-art inpainting algorithms in terms of both numerical evaluation and visual quality.

中文翻译：

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通过低秩张量分解和多向搜索进行图像修复

对于损坏的图像，像素信息的丢失大致可以分为两类，随机丢失和非随机丢失。整行或整列图像的缺失是一种极难处理的特定结构缺失模式。虽然现有的方法大部分已经部分修复了这个信息遗漏的问题，但基于扩散的方法容易产生模糊，基于样本的方法容易出现错误填充，基于神经网络的方法高度依赖数据，不能处理好这种特殊的结构缺失。使用非局部自相似先验和低秩先验，我们提出了基于张量环（TR）分解和多向搜索（MS）的多向搜索和非局部低秩张量补全（MS-NLLRTC）算法。MS方法是一种新提出的方法，可以更加多样化地搜索相似的补丁。使用MS方法，我们直接将相似的patch堆叠成一个三维相似的张量，而不是将它们拉成列向量，然后通过TR分解来完成相似的张量。利用增广拉格朗日乘子框架下的交替方向法可以获得优化结果。此外，我们在张量完成模型（WNLLRTC）中添加了一个加权核范数，实现了更好的修复性能。我们还将噪声去除方法与 WNLLRTC 算法相结合，可以同时处理图像随机丢失和图像噪声去除。