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Efficient completion for corrupted low-rank images via alternating direction method

[+] Author Affiliations
Wei Li

Zhejiang University, College of Computer Science and Technology, Hangzhou 310027, China

Lei Zhao

Zhejiang University, College of Computer Science and Technology, Hangzhou 310027, China

Duanqing Xu

Zhejiang University, College of Computer Science and Technology, Hangzhou 310027, China

Dongming Lu

Zhejiang University, College of Computer Science and Technology, Hangzhou 310027, China

J. Electron. Imaging. 23(3), 033018 (Jun 26, 2014). doi:10.1117/1.JEI.23.3.033018
History: Received April 11, 2014; Revised May 19, 2014; Accepted May 29, 2014
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Abstract.  We propose an efficient and easy-to-implement method to settle the inpainting problem for low-rank images following the recent studies about low-rank matrix completion. In general, our method has three steps: first, corresponding to the three channels of RGB color space, an incomplete image is split into three incomplete matrices; second, each matrix is restored by solving a convex problem derived from the nuclear norm relaxation; at last, the three recovered matrices are merged to produce the final output. During the process, in order to efficiently solve the nuclear norm minimization problem, we employ the alternating direction method. Except for the basic image inpainting problem, we also enable our method to handle cases where corrupted images not only have missing values but also have noisy entries. Our experiments show that our method outperforms the existing inpainting techniques both quantitatively and qualitatively. We also demonstrate that our method is capable of processing many other situations, including block-wise low-rank image completion, large-scale image restoration, and object removal.

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Citation

Wei Li ; Lei Zhao ; Duanqing Xu and Dongming Lu
"Efficient completion for corrupted low-rank images via alternating direction method", J. Electron. Imaging. 23(3), 033018 (Jun 26, 2014). ; http://dx.doi.org/10.1117/1.JEI.23.3.033018


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