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Constructing Foundations of Super Compressed Sensing and its Applications to Various Tomographic Imaging Modalities

Research Project

Project/Area Number 15K06103
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Measurement engineering
Research InstitutionUniversity of Tsukuba

Principal Investigator

Kudo Hiroyuki  筑波大学, システム情報系, 教授 (60221933)

Co-Investigator(Renkei-kenkyūsha) OKADA Toshiyuki  筑波大学, 医学医療系, 助教 (90733650)
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords圧縮センシング / コンピュータトモグラフィー / CT / 画像再構成 / 画像処理 / 電子線トモグラフィー / 逆問題 / スパースモデリング / 雑音除去 / 深層学習 / インペインティング
Outline of Final Research Achievements

Recently, Compressed Sensing (CS) has been successfully applied to image reconstruction in medical x-ray CT and Transmission Electron Microscopy (TEM). In this research project, we propose a new mathematical framework of CS named as Super Compressed Sensing, which significantly improves the performances of CS with respect to image quality. The key of Super CS is to use the nonlinear filter called Nonlocal Mean Filter to evaluate signal sparsity, which leads to preserving complicated intensity changes in images such as image textures and image gradations. We applied the Super CS to image reconstruction in medical CT and TEM. The results demonstrate that the Super CS significantly outperforms the ordinary CS in terms of image quality.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (54 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (4 results) Journal Article (31 results) (of which Int'l Joint Research: 10 results,  Peer Reviewed: 29 results,  Acknowledgement Compliant: 21 results,  Open Access: 2 results) Presentation (19 results) (of which Int'l Joint Research: 4 results,  Invited: 10 results)

  • [Int'l Joint Research] The British University of Egypt/Suez Canal University(エジプト)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Suez Canal大学(エジプト)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] バージニア工科大学(米国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Suez Canal大学(エジプト)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Millisecond-Order X-ray Phase Tomography by using Compressed Sensing2017

    • Author(s)
      W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo
    • Journal Title

      Jpn. J. Appl. Phys.

      Volume: 56 Issue: 11 Pages: 112503-112503

    • DOI

      10.7567/jjap.56.112503

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simultaneous image reconstruction of attenuation, scatter, and phase using the compressed sensing in sparse-view phase CT2017

    • Author(s)
      Ryosuke Ueda, Hiroyuki Kudo, and Koichi Matsuo
    • Journal Title

      Proceedings of International Conference on X-ray Optics and Application 2017 (XOPT'17)

      Volume: -

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Millisecond hard x-ray phase tomography using gratings2017

    • Author(s)
      Wataru Yashiro, Kentaro Kajiwara, Ryosuke Ueda, and Hiroyuki Kudo
    • Journal Title

      Proceedings International Conference on X-ray Optics and Application 2017 (XOPT'17)

      Volume: -

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Applications of compressed sensing image reconstruction to sparse-view phase tomography2017

    • Author(s)
      Ryosuke Ueda, Hiroyuki Kudo, and Jian Dong
    • Journal Title

      Proceedings of SPIE, Developments in X-Ray Tomography XI

      Volume: 10391 Pages: 16-16

    • DOI

      10.1117/12.2273691

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Grating-based x-ray phase contrast imaging with incomplete data2017

    • Author(s)
      Songzhe Lian and Hiroyuki Kudo
    • Journal Title

      Abstract Book of X-ray and Netron Phase Imaging with Gratings 2017 (XNPIG 2017)

      Volume: -

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Adaptive image denoising approach for low-dose computed tomography2017

    • Author(s)
      Haneen A. Elyamani, Samir A. El-Seoud, Hiroyuki Kudo, and Essam A. Rashed
    • Journal Title

      Proceedings of 12th International Conference on Computer Engineering and Systems (ICCES)

      Volume: - Pages: 66-72

    • DOI

      10.1109/icces.2017.8275279

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Atlas-based image reconstruction for breast CT using non-isocenteric C-arm scanner2017

    • Author(s)
      Essam A. Rashed and Hiroyuki Kudo
    • Journal Title

      Conference Record of 2016 IEEE Nuclear Science Symposium and Medical Imaging Conference

      Volume: なし

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Needle detection in interventional pain management with 3D image reconstruction2017

    • Author(s)
      Essam A. Rashed, Mohammad al-Shatouri, Mona Selim, and Hiroyuki Kudo
    • Journal Title

      Conference Record of 2016 IEEE Nuclear Science Symposium and Medical Imaging Conference

      Volume: なし

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Atlas-based interior tomography2017

    • Author(s)
      Mona Selim, Essam A. Rashed, and Hiroyuki Kudo
    • Journal Title

      Conference Record of 2016 IEEE Nuclear Science Symposium and Medical Imaging Conference

      Volume: なし

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Accelerated Algorithm for Compressed Sensing Using Nonlinear Sparsifying Transform in CT Image Reconstruction2017

    • Author(s)
      Jian Dong and Hiroyuki Kudo
    • Journal Title

      Medical Imaging Technology

      Volume: 35 Issue: 1 Pages: 63-73

    • DOI

      10.11409/mit.35.63

    • NAID

      130005308501

    • ISSN
      0288-450X, 2185-3193
    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Practical interior tomography2017

    • Author(s)
      Hiroyuki Kudo and Takuya Nemoto
    • Journal Title

      Proceedings of Intenational Forum on Medical Imaging in Asia 2017

      Volume: なし

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Practical interior tomography with small region piecewise model prior2017

    • Author(s)
      Ryosuke Ueda, Takuya Nemoto, and Hiroyuki Kudo
    • Journal Title

      Proceedings of SPIE, Medical Imaging 2017: Physics of Medical Imaging

      Volume: 10132 Pages: 101320P-101320P

    • DOI

      10.1117/12.2255706

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Investigation into image quality difference between total variation and nonlinear sparsifying transform based compressed sensing2017

    • Author(s)
      Jian Dong and Hiroyuki Kudo
    • Journal Title

      Proceedings of SPIE, Medical Imaging 2017: Physics of Medical Imaging

      Volume: 10132 Pages: 1013231-1013231

    • DOI

      10.1117/12.2255081

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Compressed sensing of sparsity-constrained total variation minimization for CT image reconstruction2017

    • Author(s)
      Jian Dong, Hiroyuki Kudo, and Essam A. Rashed
    • Journal Title

      Proceedings of SPIE, Medical Imaging 2017: Physics of Medical Imaging

      Volume: 10132 Pages: 1013233-1013233

    • DOI

      10.1117/12.2255084

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] FBP embedded iterative method to efficiently solve the low-dose CT2017

    • Author(s)
      Ryosuke Ueda, Fukashi Yamazaki, and Hiroyuki Kudo
    • Journal Title

      Proceedings of SPIE, Medical Imaging 2017: Physics of Medical Imaging

      Volume: 10132 Pages: 1013234-1013234

    • DOI

      10.1117/12.2255729

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A very fast iterative algorithm for TV-regularized image reconstruction with applications to low-dose and few-view CT2016

    • Author(s)
      Hiroyuki Kudo, Fukashi Yamazaki, Keita Takaki, and Takuya Nemoto
    • Journal Title

      Proceedings of SPIE, Developments in X-Ray Tomography X

      Volume: 9967 Pages: 996711-996711

    • DOI

      10.1117/12.2236788

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Proposal of fault-tolerant tomographic image reconstruction2016

    • Author(s)
      Hiroyuki Kudo, Keita Takaki, Fukashi Yamazaki, and Takuya Nemoto
    • Journal Title

      Proceedings of SPIE, Developments in X-Ray Tomography

      Volume: 9967 Pages: 99671K-99671K

    • DOI

      10.1117/12.2237107

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Low-dose multiphase abdominal CT reconstruction with phase-induced swap prior2016

    • Author(s)
      Essam A. Rashed, Mona Selim, and Hiroyuki Kudo
    • Journal Title

      Proceedings of SPIE, Developments in X-Ray Tomography

      Volume: 9967 Pages: 99671P-99671P

    • DOI

      10.1117/12.2237110

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] 圧縮センシングを用いたトモグラフィー画像再構成2016

    • Author(s)
      工藤博幸,董建,加茂勝己,堀井則孝,古河弘光,波多聰,村山光宏,佐藤和久,宮崎伸介
    • Journal Title

      日本顕微鏡学会誌『顕微鏡』

      Volume: 51 Pages: 48-53

    • NAID

      130007695942

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] New Designs of CT Scanners and Compressed Sensing2016

    • Author(s)
      工藤博幸
    • Journal Title

      Journal of the Japan Society for Precision Engineering

      Volume: 82 Issue: 6 Pages: 506-512

    • DOI

      10.2493/jjspe.82.506

    • NAID

      130005154099

    • ISSN
      0912-0289, 1882-675X
    • Related Report
      2016 Research-status Report 2015 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Image Reconstruction in Interior CT: Exact Solution Methods without Compressed Sensing and with Compressed Sensing2016

    • Author(s)
      工藤博幸
    • Journal Title

      Medical Imaging Technology

      Volume: 34 Issue: 4 Pages: 186-197

    • DOI

      10.11409/mit.34.186

    • NAID

      130005265964

    • ISSN
      0288-450X, 2185-3193
    • Related Report
      2016 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Proposal of Compressed Sensing Using Nonlinear Sparsifying Transform for CT Image Reconstruction2016

    • Author(s)
      Jian Dong and Hiroyuki Kudo
    • Journal Title

      Medical Imaging Technology

      Volume: 34 Issue: 5 Pages: 235-244

    • DOI

      10.11409/mit.34.235

    • NAID

      130005171453

    • ISSN
      0288-450X, 2185-3193
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] In-situ straining and time-resolved electron tomography data acquisition in a transmission electron microscope2016

    • Author(s)
      Satoshi Hata, Shinsuke Miyazaki, Takashi Gondo, Katsumi Kawamoto, Noritaka Horii, Kazuhisa Sato, Hiromitsu Furukawa, Hiroyuki Kudo, Hiroya Miyazaki, and Mitsu Murayama
    • Journal Title

      Microscopy

      Volume: 66 Pages: 143-153

    • DOI

      10.1093/jmicro/dfw109

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Probabilistic atlas prior for CT image reconstruction2016

    • Author(s)
      Essam A. Rashed and Hiroyuki Kudo
    • Journal Title

      Computer Methods and Programs in Biomedicine

      Volume: 128 Pages: 119-136

    • DOI

      10.1016/j.cmpb.2016.02.017

    • NAID

      120007135500

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 圧縮センシングを用いたトモグラフィー画像再構成2016

    • Author(s)
      工藤博幸,董建,加茂勝己,堀井則孝,古河弘光,波多聰,村山光宏,佐藤和久,宮崎伸介
    • Journal Title

      日本顕微鏡学会誌顕微鏡

      Volume: 51

    • NAID

      130007695942

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A very fast iterative algorithm for TV-regularized image reconstruction with applications to low-dose and few-view CT2016

    • Author(s)
      Hiroyuki Kudo, Fukashi Yamazaki, Takuya Nemoto, and Keita Takaki
    • Journal Title

      Proceedings of SPIE Optical Engineeing + Applications (Developments in X-ray Tomography)

      Volume: 印刷中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Proposal of fault-tolerant tomographic image reconstruction2016

    • Author(s)
      Hiroyuki Kudo, Keita Takaki, Fukashi Yamazaki, and Takuya Nemoto
    • Journal Title

      Proceedings of SPIE Optical Engineeing + Applications (Developments in X-ray Tomography)

      Volume: 印刷中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Low-dose multiphase abdominal CT reconstruction with phase-induced swap prior2016

    • Author(s)
      Essam A. Rashed and Hiroyuki Kudo
    • Journal Title

      Proceedings of SPIE Optical Engineeing + Applications (Developments in X-ray Tomography)

      Volume: 印刷中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Sparsity-constrained three-dimensional image reconstruction for C-arm angiography2015

    • Author(s)
      Essam A. Rashed, Mohammad al-Shatoury, and Hiroyuki Kudo
    • Journal Title

      Computers in Biology and Medicine

      Volume: 62 Pages: 141-163

    • DOI

      10.1016/j.compbiomed.2015.04.014

    • NAID

      120007135498

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Three-Dimensional Observation of Lattice Defects Using Electron Tomography2015

    • Author(s)
      波多聰,光原昌寿, 中島英治,池田賢一,佐藤和久,村山光宏,工藤博幸,古河弘光,宮崎伸介
    • Journal Title

      Nihon Kessho Gakkaishi

      Volume: 57 Issue: 5 Pages: 276-284

    • DOI

      10.5940/jcrsj.57.276

    • NAID

      130005105682

    • ISSN
      0369-4585, 1884-5576
    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Low-dose CT image reconstruction method with probabilistic atlas prior2015

    • Author(s)
      Mona Selim, Hiroyuki Kudo, and Essam A. Rashed
    • Journal Title

      Conference Record of 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference

      Volume: なし

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] 最先端トモグラフィー画像再構成ーX線CTから拡散光トモグラフィーへの展開ー2018

    • Author(s)
      工藤博幸
    • Organizer
      筑波大学計算科学研究センター計算メディカルサイエンスキックオフシンポジウム
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 最先端CT画像再構成の研究動向ースパースビューCT・インテリアCT・低線量CTへの応用-2018

    • Author(s)
      工藤博幸
    • Organizer
      応用物理学会放射線分科会医療放射線技術研究会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 深層学習による放射型CTの画像補正2018

    • Author(s)
      鈴木朋浩, 工藤博幸
    • Organizer
      第37回日本医用画像工学会大会(JAMIT2018)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 非局所トータルバリエーションを用いたスパースビューCT画像再構成の画質改善2018

    • Author(s)
      金鎔采, 工藤博幸
    • Organizer
      第37回日本医用画像工学会大会(JAMIT2018)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Applications of compressed sensing to CT image reconstruction2018

    • Author(s)
      Hiroyuki Kudo
    • Organizer
      Complex Medical Engineering 2018 (CME 2018)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Development of an in-situ straining and time-resolved electron tomography data acquisition system2018

    • Author(s)
      Satoshi Hata, Shinsuke Miyazaki, Takashi Gondo, Katsumi Kawamoto, Noritaka Horii, Kazuhisa Sato, Hiromitsu Furukawa, Hiroyuki Kudo, Hiroya Miyazaki, and Mitsu Murayama
    • Organizer
      4-th International Congress on 3D Materials Science 2018 (3DMS 2018)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 圧縮センシングとトモグラフィーへの応用2017

    • Author(s)
      工藤博幸
    • Organizer
      日本顕微鏡学会2016年度超高分解能顕微鏡法分科会研究会
    • Place of Presentation
      まほろばマインズ三浦海岸(神奈川県三浦市)
    • Year and Date
      2017-02-18
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Fundamentals of statistical image reconstruction for medical x-ray CT, SPECT, and PET2017

    • Author(s)
      Hiroyuki Kudo
    • Organizer
      Conference on Inverse Problems and Medical Imaging
    • Place of Presentation
      東京大学(東京都目黒区駒場)
    • Year and Date
      2017-02-13
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 圧縮センシングと新方式コンピュータトモグラフィーへの応用2017

    • Author(s)
      工藤博幸
    • Organizer
      日本磁気学会第212回研究会
    • Place of Presentation
      中央大学駿河台記念館(東京都千代田区神田)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 電子線トモグラフィーによる金属の塑性変形の三次元観察2016

    • Author(s)
      波多聰,佐藤和久,工藤博幸,川本克巳,堀井則孝,加茂勝己,古河弘光,權堂貴志,宮崎裕也,宮崎伸介,村山光宏
    • Organizer
      2016日本金属学会秋期講演大会
    • Place of Presentation
      大阪大学(大阪府豊中市)
    • Year and Date
      2016-09-21
    • Related Report
      2016 Research-status Report
  • [Presentation] 改良型トータルバリエーション正則化を用いたデノイジングおよび画像再構成2016

    • Author(s)
      楊海圏,楊美花,工藤博幸
    • Organizer
      第35回日本医用画像工学会大会
    • Place of Presentation
      千葉大学(千葉県千葉市)
    • Year and Date
      2016-07-21
    • Related Report
      2016 Research-status Report
  • [Presentation] Proposal of compressed sensing using nonlinear sparsify transform for CT image reconstruction2016

    • Author(s)
      Jian Dong and Hiroyuki Kudo
    • Organizer
      第35回日本医用画像工学会大会
    • Place of Presentation
      千葉大学(千葉県千葉市)
    • Year and Date
      2016-07-21
    • Related Report
      2016 Research-status Report
  • [Presentation] 新方式コンピュータトモグラフィーと圧縮センシング2016

    • Author(s)
      工藤博幸
    • Organizer
      第35回日本医用画像工学会大会
    • Place of Presentation
      千葉大学(千葉県千葉市)
    • Year and Date
      2016-07-21
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] New designs of CT scanners and associated image reconstruction methods2016

    • Author(s)
      Hiroyuki Kudo
    • Organizer
      Workshop on Recent Advances in Medical Imaging: Applications in Low-Dose CT
    • Place of Presentation
      イスマイリア, エジプト
    • Year and Date
      2016-03-28
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 最先端CT画像再構成の研究動向-インテリアCT,圧縮センシング,統計的再構成-2015

    • Author(s)
      工藤博幸
    • Organizer
      日本放射光学会X線ナノ集光技術研究会
    • Place of Presentation
      東京大学(東京都文京区)
    • Year and Date
      2015-10-31
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] フィルタ補正型前処理を用いた高速な統計的CT画像再構成法2015

    • Author(s)
      山嵜深,根本拓也,高木景太,工藤博幸
    • Organizer
      電子情報通信学会医用画像研究会
    • Place of Presentation
      電気通信大学(東京都調布市)
    • Year and Date
      2015-09-08
    • Related Report
      2015 Research-status Report
  • [Presentation] フォルトトレラントCT画像再構成法の提案2015

    • Author(s)
      高木景太,山嵜深,根本拓也,工藤博幸
    • Organizer
      電子情報通信学会医用画像研究会
    • Place of Presentation
      電気通信大学(東京都調布市)
    • Year and Date
      2015-09-08
    • Related Report
      2015 Research-status Report
  • [Presentation] 新方式コンピュータトモグラフィーと位相イメージング画像処理への挑戦2015

    • Author(s)
      工藤博幸
    • Organizer
      JST-ERATO百生量子ビーム位相イメージングプロジェクトキックオフシンポジウム
    • Place of Presentation
      東北大学(宮城県仙台市)
    • Year and Date
      2015-07-14
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 圧縮センシング技術を応用したトモグラフィー再構成手法・ISERの開発と応用2015

    • Author(s)
      加茂勝己,堀井則孝,工藤博幸,古河弘光
    • Organizer
      日本顕微鏡学会第71回学術講演会
    • Place of Presentation
      国立京都国際会館(京都府京都市)
    • Year and Date
      2015-05-15
    • Related Report
      2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2022-02-16  

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