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Annihilating Filter-based Low-Rank Hankel Matrix (ALOHA) for Image Inpainting
Abstract—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. 
Benchmark comparison with state-of-the art inpainting algorithms
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ABOUT US
Our research activities are primarily focused on the signal processing and machine learning for high-resolution high-sensitivity image reconstruction from real world bio-medical imaging systems. Such problems pose interesting challenges that often lead to investigations of fundamental problems in various branches of physics, mathematics, signal processing, biology, and medicine. While most of the biomedical imaging researchers are interested in addressing this problem using off-the-self tools from signal processing, machine learning, statistics, and optimization and combining their domain-specific knowledge, our approaches are unique in the sense that I believe that actual bio-medical imaging applications are a source of endless inspiration for new mathematical theories and we are eager to solve both specific applications and application-inspired fundamental theoretical problems.
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CONTACT US
Bio Imaging. Signal Processing & Learning
Dept. of Bio & Brain Engineering KAIST 291 Daehak-ro, Yuseong-gu Daejeon 305-701, Korea Copyright (c) 2014, BISPL All Rights Reserved. |
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