Single Image Super Resolution by <I>l</I><SUB>2</SUB> Approximation with Random Sampled Dictionary

Takanori FUJISAWA; Taichi YOSHIDA; Kazu MISHIBA; Masaaki IKEHARA

doi:10.1587/transfun.E99.A.612

Single Image Super Resolution by l₂ Approximation with Random Sampled Dictionary

Takanori FUJISAWA, Taichi YOSHIDA, Kazu MISHIBA, Masaaki IKEHARA

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In this paper, we propose an example-based single image super resolution (SR) method by l₂ approximation with self-sampled image patches. Example-based super resolution methods can reconstruct high resolution image patches by a linear combination of atoms in an overcomplete dictionary. This reconstruction requires a pair of two dictionaries created by tremendous low and high resolution image pairs from the prepared image databases. In our method, we introduce the dictionary by random sampling patches from just an input image and eliminate its training process. This dictionary exploits the self-similarity of images and it will no more depend on external image sets, which consern the storage space or the accuracy of referred image sets. In addition, we modified the approximation of input image to an l₂-norm minimization problem, instead of commonly used sparse approximation such as l₁-norm regularization. The l₂ approximation has an advantage of computational cost by only solving an inverse problem. Through some experiments, the proposed method drastically reduces the computational time for the SR, and it provides a comparable performance to the conventional example-based SR methods with an l₁ approximation and dictionary training.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.2 pp.612-620

Publication Date: 2016/02/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E99.A.612

Type of Manuscript: PAPER

Category: Image

Authors

Takanori FUJISAWA
  Keio University
Taichi YOSHIDA
  Nagaoka University of Technology
Kazu MISHIBA
  Tottori University
Masaaki IKEHARA
  Keio University

Keyword

single image super resolution, l₂-norm minimization, example-based

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Takanori FUJISAWA, Taichi YOSHIDA, Kazu MISHIBA, Masaaki IKEHARA, "Single Image Super Resolution by l2 Approximation with Random Sampled Dictionary" in IEICE TRANSACTIONS on Fundamentals, vol. E99-A, no. 2, pp. 612-620, February 2016, doi: 10.1587/transfun.E99.A.612.
Abstract: In this paper, we propose an example-based single image super resolution (SR) method by l₂ approximation with self-sampled image patches. Example-based super resolution methods can reconstruct high resolution image patches by a linear combination of atoms in an overcomplete dictionary. This reconstruction requires a pair of two dictionaries created by tremendous low and high resolution image pairs from the prepared image databases. In our method, we introduce the dictionary by random sampling patches from just an input image and eliminate its training process. This dictionary exploits the self-similarity of images and it will no more depend on external image sets, which consern the storage space or the accuracy of referred image sets. In addition, we modified the approximation of input image to an l₂-norm minimization problem, instead of commonly used sparse approximation such as l₁-norm regularization. The l₂ approximation has an advantage of computational cost by only solving an inverse problem. Through some experiments, the proposed method drastically reduces the computational time for the SR, and it provides a comparable performance to the conventional example-based SR methods with an l₁ approximation and dictionary training.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.612/_p

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@ARTICLE{e99-a_2_612,
author={Takanori FUJISAWA, Taichi YOSHIDA, Kazu MISHIBA, Masaaki IKEHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Single Image Super Resolution by l2 Approximation with Random Sampled Dictionary},
year={2016},
volume={E99-A},
number={2},
pages={612-620},
abstract={In this paper, we propose an example-based single image super resolution (SR) method by l₂ approximation with self-sampled image patches. Example-based super resolution methods can reconstruct high resolution image patches by a linear combination of atoms in an overcomplete dictionary. This reconstruction requires a pair of two dictionaries created by tremendous low and high resolution image pairs from the prepared image databases. In our method, we introduce the dictionary by random sampling patches from just an input image and eliminate its training process. This dictionary exploits the self-similarity of images and it will no more depend on external image sets, which consern the storage space or the accuracy of referred image sets. In addition, we modified the approximation of input image to an l₂-norm minimization problem, instead of commonly used sparse approximation such as l₁-norm regularization. The l₂ approximation has an advantage of computational cost by only solving an inverse problem. Through some experiments, the proposed method drastically reduces the computational time for the SR, and it provides a comparable performance to the conventional example-based SR methods with an l₁ approximation and dictionary training.},
keywords={},
doi={10.1587/transfun.E99.A.612},
ISSN={1745-1337},
month={February},}

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TY - JOUR
TI - Single Image Super Resolution by l2 Approximation with Random Sampled Dictionary
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 612
EP - 620
AU - Takanori FUJISAWA
AU - Taichi YOSHIDA
AU - Kazu MISHIBA
AU - Masaaki IKEHARA
PY - 2016
DO - 10.1587/transfun.E99.A.612
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2016
AB - In this paper, we propose an example-based single image super resolution (SR) method by l₂ approximation with self-sampled image patches. Example-based super resolution methods can reconstruct high resolution image patches by a linear combination of atoms in an overcomplete dictionary. This reconstruction requires a pair of two dictionaries created by tremendous low and high resolution image pairs from the prepared image databases. In our method, we introduce the dictionary by random sampling patches from just an input image and eliminate its training process. This dictionary exploits the self-similarity of images and it will no more depend on external image sets, which consern the storage space or the accuracy of referred image sets. In addition, we modified the approximation of input image to an l₂-norm minimization problem, instead of commonly used sparse approximation such as l₁-norm regularization. The l₂ approximation has an advantage of computational cost by only solving an inverse problem. Through some experiments, the proposed method drastically reduces the computational time for the SR, and it provides a comparable performance to the conventional example-based SR methods with an l₁ approximation and dictionary training.
ER -