Annihilating Filter-Based Low-Rank Hankel Matrix Approach for Image Inpainting

In this paper, we propose a patch-based image inpainting method using a low-rank Hankel structured matrix completion approach. The proposed method exploits the annihilation property between a shift-invariant filter and image data observed in many existing inpainting algorithms. In particular, by exploiting the commutative property of the convolution, the annihilation property results in a low-rank block Hankel structure data matrix, and the image inpainting problem becomes a low-rank structured matrix completion problem. The block Hankel structured matrices are obtained patch-by-patch to adapt to the local changes in the image statistics. To solve the structured low-rank matrix completion problem, we employ an alternating direction method of multipliers with factorization matrix initialization using the low-rank matrix fitting algorithm. As a side product of the matrix factorization, locally adaptive dictionaries can be also easily constructed. Despite the simplicity of the algorithm, the experimental results using irregularly subsampled images as well as various images with globally missing patterns showed that the proposed method outperforms existing state-of-the-art image inpainting methods.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2015-11
Language
ENG
Keywords

RANDOM FIELD MODELS; VARIATIONAL APPROACH; SPARSE REPRESENTATION; SYSTEM-IDENTIFICATION; NONLINEAR DIFFUSION; INVERSE PROBLEMS; EDGE-DETECTION; MISSING DATA; FINITE RATE; DECOMPOSITION

Citation

IEEE TRANSACTIONS ON IMAGE PROCESSING, v.24, no.11, pp.3498 - 3511

ISSN
1057-7149
DOI
10.1109/TIP.2015.2446943
URI
http://hdl.handle.net/10203/200584
Appears in Collection
BiS-Journal Papers(저널논문)
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