融合改进的张量相关全变分的鲁棒张量修补用于图像修复
Robust Tensor Completion Fusing Improved Tensor Correlated Total Variation for Image Restoration
DOI: 10.12677/airr.2024.132027, PDF,   
作者: 黄 凯：西南大学数学与统计学院，重庆；李忠宁：银川能源学院基础部，宁夏 银川
关键词: 鲁棒补全；改进的张量相关全变分；先验信息；图像修复；Robust Completion； Improved Tensor Correlated Total Variation； Prior Information； Image Restoration
摘要: 图像在采集和捕捉过程中，往往存在噪声污染和缺失等退化情况，而鲁棒补全对此发挥着重要作用。目前这些方法大多利用图像的全局低秩和局部平滑先验来对其进行建模，包括独立编码方法和融合编码方法。然而，这些方法要么需要对两个以上参数进行繁琐的调整，要么平等地对待梯度矩阵/张量的每个奇异值，从而限制了处理实际问题的灵活性。在本文中，我们提出了改进的张量相关全变分(ITCTV)范数，以充分利用梯度张量的内在结构特性。所提出的ITCTV正则化器不需要权衡参数来平衡两个先验，并且进一步有效地利用了梯度张量奇异值的先验分布信息。我们将提出的方法应用在多种类型的视觉张量数据上，实验结果证明了所提出方法在图像修复上的有效性。
Abstract: In the process of image acquisition and capture, there is often degradation such as noise pollution and missing, and robust completion plays an important role in this. Most current methods for image restoration exploit global low-rankness and local smoothness priors to model them, including independent coding methods and fusion coding methods. However, these methods either require tedious tuning of more than two parameters or treat each singular value of the gradient matrices/tensors equally, thus limiting the flexibility to deal with practical problems. In this paper, we propose an improved tensor correlated total variation (ITCTV) norm to take full advantage of the intrinsic structural properties of the gradient tensors. The proposed ITCTV regularizer does not need to trade-off parameters to balance the two priors, and further effectively utilizes the prior distribution information of the singular values of the gradient tensors. We apply the proposed method to various types of visual tensor data, and the experimental results prove the effectiveness of the proposed method in image restoration.
文章引用：黄凯, 李忠宁. 融合改进的张量相关全变分的鲁棒张量修补用于图像修复[J]. 人工智能与机器人研究, 2024, 13(2): 255-264. https://doi.org/10.12677/airr.2024.132027

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