Non‐Local Image Inpainting Using Low‐Rank Matrix Completion

Li, Wei; Zhao, Lei; Lin, Zhiping; Xu, Dan; Lu, Dongming

doi:10.1111/cgf.12521

Cited by 45 publications

(36 citation statements)

References 41 publications

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“…Taking α j = α k j in (17), f = f k in (18),f =f k in (19), α j = α * j in (20), f = f * in (21),f =f * in (22) and summing, one can get…”

Section: Discussionmentioning

confidence: 99%

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Local block operators and TV regularization based image inpainting

Wan¹,

Huang²,

Li³

2018

Inverse Problems &Amp; Imaging

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In this paper, we propose a novel image blocks based inpainting model using group sparsity and TV regularization. The block matching method is employed to collect similar image blocks which can be formed as sparse image groups. By reducing the redundant information in these groups, we can well restore textures missing in the inpainting areas. We built a variational framework based on a local SVD operator for block matching and group sparsity. In addition, TV regularization is naturally integrated in the model to reduce artificial effects which are caused by image blocks stacking in the block matching method. Besides, enforcing the sparsity of the representation, the SVD operators in our method are iteratively updated and play the role of dictionary learning. Thus it can greatly improve the quality of the restoration. Moreover, we mathematically show the existence of a minimizer for the proposed inpainting model. Convergence results of the proposed algorithm are also given in the paper. Numerical experiments demonstrate that the proposed model outperforms many benchmark methods such as BM3D based image inpainting.

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“…Taking α j = α k j in (17), f = f k in (18),f =f k in (19), α j = α * j in (20), f = f * in (21),f =f * in (22) and summing, one can get…”

Section: Discussionmentioning

confidence: 99%

“…Xu et al [29] proposed two types of patch sparsity of natural image and applied them to the block based inpainting method. The approach in [22] uses low-rank matrix completion for a non-local image inpainting model. In [23], Li et al proposed a universal variational framework for sparsity based image inpainting.…”

mentioning

confidence: 99%

Local block operators and TV regularization based image inpainting

Wan¹,

Huang²,

Li³

2018

Inverse Problems &Amp; Imaging

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show abstract

“…Another category of global methods relies on matrix completion [14,15,16]. However, these techniques are computationally intensive and require a large number of retained pixels (30% or more).…”

Section: Related Workmentioning

confidence: 99%

Extreme image completion

Achanta

Arvanitopoulos

Süsstrunk

2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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It is challenging to complete an image whose 99% pixels are randomly missing. We present a solution to this extreme image completion problem. As opposed to existing techniques, our solution has a computational complexity that is linear in the number of pixels of the full image and is realtime in practice. For comparable quality of reconstruction, our algorithm is thus almost 2 to 5 orders of magnitude faster than existing techniques.

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“…However, such an approach ignores the natural multi-dimensional structure of tensors, and thus neglects some important information. In [30], [37], the authors applied a matrix completion technique to matrices that consist of set of similar patches selected by some patch matching algorithms. However, patch matching is generally time consuming, and it does not work well when there is an extremely high ratio of missing data.…”

Section: Introductionmentioning

confidence: 99%

Smooth PARAFAC Decomposition for Tensor Completion

Yokota

Zhao

Cichocki

2016

IEEE Trans. Signal Process.

242

153

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In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as color and 3D images, where the ratio of missing data is extremely high. In this paper, we consider "smoothness" constraints as well as low-rank approximations, and propose an efficient algorithm for performing tensor completion that is particularly powerful regarding visual data. The proposed method admits significant advantages, owing to the integration of smooth PARAFAC decomposition for incomplete tensors and the efficient selection of models in order to minimize the tensor rank. Thus, our proposed method is termed as "smooth PARAFAC tensor completion (SPC)." In order to impose the smoothness constraints, we employ two strategies, total variation (SPC-TV) and quadratic variation (SPC-QV), and invoke the corresponding algorithms for model learning. Extensive experimental evaluations on both synthetic and real-world visual data illustrate the significant improvements of our method, in terms of both prediction performance and efficiency, compared with many state-of-the-art tensor completion methods.Comment: 13 pages, 9 figure

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Non‐Local Image Inpainting Using Low‐Rank Matrix Completion

Cited by 45 publications

References 41 publications

Local block operators and TV regularization based image inpainting

Local block operators and TV regularization based image inpainting

Extreme image completion

Smooth PARAFAC Decomposition for Tensor Completion

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