Non-Local Robust Quaternion Matrix Completion for Large-Scale Color Image and Video Inpainting

The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on i...

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Bibliographic Details
Published in:IEEE transactions on image processing 2022-01, Vol.31, p.3868-3883
Main Authors: Jia, Zhigang, Jin, Qiyu, Ng, Michael K., Zhao, Xi-Le
Format: Article
Language:English
Subjects:
Algorithms
Color
color image inpainting
Color imagery
color video
Electronic mail
Image color analysis
Image processing
Image reconstruction
Low-rank approximation
Machine learning
Machining
Mathematical analysis
nonlocal self-similarity
quaternion singular value decomposition
Quaternions
Robustness (mathematics)
Self-similarity
Sparse matrices
Tensors
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Summary:The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on its working principle in the literature. In this paper, we discover a potential causality between NSS and low-rank property of color images, which is also available to grey images. A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images. The numerical low-rank property of patched matrices is also rigorously proved. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new tensor NSS-based QMC method is also presented to solve the color video inpainting problem based on quaternion tensor representation. The numerical experiments on color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2022.3176133