Jong just sent me the following:
Hi Igor,Thanks Jong ! Here is the paper:
I would like to bring your attention to our latest paper which will appear in IEEE Trans. on Image Processing.
Kyong Hwan Jin and Jong Chul Ye "Annihilating Filter based Low Rank Hankel Matrix Approach for Image Inpainting", IEEE Trans. Image Processing (in press), 2015
In this paper, we demonstrated that an image in-painting problem can be solved by exploiting the sparsity in the reciprocal domain. An actual implementation algorithm can be easily implemented using annihilating filter based low rank matrix (ALOHA) completion. You can download the paper from the following link:
Annihilating Filter based Low Rank Hankel Matrix Approach for Image Inpainting by Kyong Hwan Jin and Jong Chul Ye
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. Specifically, 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 multiplier (ADMM) method with factorization matrix initialization using the low rank matrix fitting (LMaFit) algorithm. As a side product of the matrix factorization, locally adaptive dictionaries can be also easily constructed. Despite the simplicity of the algorithm, 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.
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