Multiple Subspace Model and Image-Inpainting Algorithm Based on Multiple Matrix Rank Minimization
Multiple Subspace Model and Image-Inpainting Algorithm Based on Multiple Matrix Rank Minimization
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DOI：
10.1587/transinf.2020edp7086
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Tomohiro Takahashi;K. Konishi;Kazunori Uruma;T. Furukawa
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文献类型：
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作者：
Tomohiro Takahashi;K. Konishi;Kazunori Uruma;T. Furukawa
提出了一种基于多线性模型和矩阵秩最小化的图像修复算法。先前已经基于图像可以使用自回归（AR）模型建模的假设提出了几种修复算法。然而，这些算法在应用于自然照片时表现不佳，因为它们假设图像由具有固定模型阶数的位置不变线性模型建模。为了提高图像修复的质量，本文引入了多重AR模型，提出了一种基于多重矩阵秩最小化和稀疏正则化的图像修复算法。在此基础上，给出了一种基于迭代部分矩阵收缩算法的实用算法，数值算例表明了该算法的有效性。
SUMMARY This paper proposes an image inpainting algorithm based on multiple linear models and matrix rank minimization. Several inpainting algorithms have been previously proposed based on the assumption that an image can be modeled using autoregressive (AR) models. However, these algorithms perform poorly when applied to natural photographs because they assume that an image is modeled by a position-invariant linear model with a fixed model order. In order to improve inpainting quality, this work introduces a multiple AR model and proposes an image inpainting algo-rithm based on multiple matrix rank minimization with sparse regularization. In doing so, a practical algorithm is provided based on the iterative partial matrix shrinkage algorithm, with numerical examples showing the e ff ectiveness of the proposed algorithm.