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Understanding Geometry of Encoder-Decoder CNNs for Inverse Problems

Understanding Geometry of Encoder-Decoder CNNs for Inverse Problems

Plenary Talk, Applied Inverse Problems (AIP) conference, Grenoble, July 11th, 2019

A3d61bc22cd700a92e7d4136a4d29e8f?s=128

Jong Chul Ye

July 11, 2019
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Transcript

  1. Understanding Geometry of Encoder Decoder CNN for Inverse Problems Jong

    Chul Ye, Ph.D Endowed Chair Professor BISPL - BioImaging, Signal Processing, and Learning lab. Dept. Bio & Brain Engineering Dept. Mathematical Sciences KAIST, Korea
  2. Deep Learning Revolution • Deep learning has been successfully used

    for classification, low- level computer vision, etc • Even outperforms human observers Figure modified from Kaiming He’s presentation
  3. Classical Learning vs Deep Learning Diagnosis Classical machine learning Deep

    learning (no feature engineering) Feature Engineering Esteva et al, Nature Medicine, (2019)
  4. Deep Learning Era in Medical Imaging Diabetic eye diagnosis Gulshan,

    V. et al. JAMA (2016) Skin Cancer diagnosis Esteva et al, Nature (2017) OCT diagnosis De Fauw et al, Nature Medicine (2018) Figure courtesy of X. Cao & D. Shen Image registration Image segmentation Ronneberger et al, MICCAI, 2015
  5. Deep Learning for Inverse Problems Diagnosis Diagnosis & analysis Focus

    of this talk: Reconstruction
  6. 6

  7. 7 Wavelet transform level 2 level 1 level 3 level

    4 Wavelet recomposition + Residual learning : Low-resolution image bypass High SNR band CNN (Kang, et al, Medical Physics 44(10))
  8. Full dose Quarter dose

  9. Full dose Ours from Quarter dose

  10. Ours (Kang et al, TMI, 2018)

  11. Ours (Kang et al, TMI, 2018)

  12. MBIR C D Ours MBIR (Kang et al, TMI, 2018)

  13. Figures from internet Extreme Sparse View CT Stationary CT Carry

    on baggage scanner Han et al, arXiv preprint arXiv:1712.10248, (2017); CT Meeting (2017)
  14. Source/detector configuration Han et al, arXiv preprint arXiv:1712.10248, (2017); CT

    Meeting (2017)
  15. 1st view 2nd view 3rd view 4th view 5th view

    6th view 7th view 8th view 9th view
  16. FBP

  17. TV

  18. Deep Learning Han et al, CT meetings, 2018

  19. Deep Learning Pioneers in MR Kwon et al, Medical Physics,

    2017 Hammernik et al, MRM, 2018 Wang et al, ISBI, 2016 Yang et al, NIPS, 2016 Multilayer perceptron Variational network Deep learning prior ADMM-Net
  20. Variational Network (R=4) CG SENSE PI-CS: TGV Learning: VN PI

    PI-CS Learning Hammernik MRM 2018 Courtesy of Florian Knoll
  21. None
  22. Image Domain Learning FBPConvNet Jin et al. TIP 2017

  23. Hybrid Domain Learning Deep Cascade of CNNs for MRI Reconstruction

    Schlemper et al. IEEE TMI 2017 Courtesy of D. Rueckert (a) 11x Undersampled (b) CNN reconstruction (c) Ground Truth
  24. Hybrid Domain Learning Learned Primal and Dual Adler et al,

    IEEE TMI 2018
  25. Domain-transform Learning AUTOMAP Zhu et al, Nature, 2018

  26. Sensor-domain Learning CNN k-space deep learning Han et al, IEEE

    TMI; Lee et al, MRM (in press, 2019)
  27. Why so popular this time ? q Accuracy: high quality

    recon > CS q Fast reconstruction time q Business model: vendor-driven training q Interpretable models q Flexibility: more than recon Imaging time Reconstruction time Conventional Compressed Sensing Machine Learning
  28. INTERPRETATION OF DEEP LEARNING FOR RECON

  29. Too Simple to Analyze..? Convolution & pooling à stone age

    tools of signal processing What do they do ?
  30. Dark Age of Applied Mathematics ?

  31. WHY DEEP LEARNING WORKS FOR RECON ? DOES IT CREATE

    ANY ARTIFICIAL FEATURES ?
  32. Ye et al, SIAM J. Imaging Sciences, 2018; Ye et

    al, ICML, 2019 Understanding Geometry of CNN
  33. CNN Encoder-Decoder CNN for Inverse Problems

  34. CNN Encoder-Decoder CNN for Inverse Problems

  35. CNN Successful applications to various inverse problems Encoder-Decoder CNN for

    Inverse Problems
  36. Why Same Architecture Works for Different Inverse Problems ?

  37. Classical Methods for Inverse Problems Synthesis frame Analysis frame coefficients

    Step 1: Signal Representation x = X i hbi, xi˜ bi <latexit sha1_base64="1xOFabKTay95z7c6ZUXCSJWXZAE=">AAACE3icbVDLSsNAFJ3UV62vqEs3g0UQkZKooBuh4MZlC/YBTQiTyaQdOpmEmYm0hIKf4MZfceNCEbdu3Pk3TpMutPXAhTPn3Mvce/yEUaks69soLS2vrK6V1ysbm1vbO+buXlvGqcCkhWMWi66PJGGUk5aiipFuIgiKfEY6/vBm6nfuiZA05ndqnBA3Qn1OQ4qR0pJnnoyuHZlGHoXQYYj3GYG+R0/hyBHFy1GUBbnomVWrZuWAi8SekSqYoeGZX04Q4zQiXGGGpOzZVqLcDAlFMSOTipNKkiA8RH3S05SjiEg3y2+awCOtBDCMhS6uYK7+nshQJOU48nVnhNRAzntT8T+vl6rwys0oT1JFOC4+ClMGVQynAcGACoIVG2uCsKB6V4gHSCCsdIwVHYI9f/IiaZ/V7POa1byo1psPRRxlcAAOwTGwwSWog1vQAC2AwSN4Bq/gzXgyXox346NoLRmzCPfBHxifP6mnndg=</latexit>
  38. Eg. Compressed Sensing Classical Methods for Inverse Problems Step 2:

    Basis Search by Optimization x = X i ˜ bi hbi, xi <latexit sha1_base64="dRyoeK2luEuIb3X8ywuvlvflFPU=">AAACEnicbZBNS8MwGMdTX+d8q3r0EhyCgoxWBb0IQy8eJ7gXWEtJ03QLS9OSpLJR9hm8+FW8eFDEqydvfhvTrgfd/EPgl//zPCTP308Ylcqyvo2FxaXlldXKWnV9Y3Nr29zZbcs4FZi0cMxi0fWRJIxy0lJUMdJNBEGRz0jHH97k9c4DEZLG/F6NE+JGqM9pSDFS2vLM49GVI9PIo9BRlAUE+jkyxPus4BM4ckRx88yaVbcKwXmwS6iBUk3P/HKCGKcR4QozJGXPthLlZkgoihmZVJ1UkgThIeqTnkaOIiLdrFhpAg+1E8AwFvpwBQv390SGIinHka87I6QGcraWm//VeqkKL92M8iRVhOPpQ2HKoIphng8MqCBYsbEGhAXVf4V4gATCSqdY1SHYsyvPQ/u0bp/VrbvzWuO6jKMC9sEBOAI2uAANcAuaoAUweATP4BW8GU/Gi/FufExbF4xyZg/8kfH5AyCNnR8=</latexit>
  39. Why do They Look so Different ? Any Link between

    Them ?
  40. Our Theoretical Findings y = X i hbi(x), xi˜ bi(x)

    <latexit sha1_base64="DaaFmbtzayW3V2tBvW3rbADydJY=">AAACGXicbZDLSsNAFIYnXmu9RV26GSxCBSmJCroRim5cVrAXaEKYTCbt0MkkzEykIfQ13Pgqblwo4lJXvo3TNoK2/jDw851zOHN+P2FUKsv6MhYWl5ZXVktr5fWNza1tc2e3JeNUYNLEMYtFx0eSMMpJU1HFSCcRBEU+I21/cD2ut++JkDTmdypLiBuhHqchxUhp5JlWdunINPIohA5DvMcI9D1aHR4dw6EjpsBRlAU/3DMrVs2aCM4buzAVUKjhmR9OEOM0IlxhhqTs2lai3BwJRTEjo7KTSpIgPEA90tWWo4hIN59cNoKHmgQwjIV+XMEJ/T2Ro0jKLPJ1Z4RUX87WxvC/WjdV4YWbU56kinA8XRSmDKoYjmOCARUEK5Zpg7Cg+q8Q95FAWOkwyzoEe/bkedM6qdmnNev2rFK/KuIogX1wAKrABuegDm5AAzQBBg/gCbyAV+PReDbejPdp64JRzOyBPzI+vwEaXJ8Y</latexit> Ye et al, SIIMS, 2018; Ye et al, ICML, 2019
  41. y = X i hbi(x), xi˜ bi(x) <latexit sha1_base64="DaaFmbtzayW3V2tBvW3rbADydJY=">AAACGXicbZDLSsNAFIYnXmu9RV26GSxCBSmJCroRim5cVrAXaEKYTCbt0MkkzEykIfQ13Pgqblwo4lJXvo3TNoK2/jDw851zOHN+P2FUKsv6MhYWl5ZXVktr5fWNza1tc2e3JeNUYNLEMYtFx0eSMMpJU1HFSCcRBEU+I21/cD2ut++JkDTmdypLiBuhHqchxUhp5JlWdunINPIohA5DvMcI9D1aHR4dw6EjpsBRlAU/3DMrVs2aCM4buzAVUKjhmR9OEOM0IlxhhqTs2lai3BwJRTEjo7KTSpIgPEA90tWWo4hIN59cNoKHmgQwjIV+XMEJ/T2Ro0jKLPJ1Z4RUX87WxvC/WjdV4YWbU56kinA8XRSmDKoYjmOCARUEK5Zpg7Cg+q8Q95FAWOkwyzoEe/bkedM6qdmnNev2rFK/KuIogX1wAKrABuegDm5AAzQBBg/gCbyAV+PReDbejPdp64JRzOyBPzI+vwEaXJ8Y</latexit> Our

    Theoretical Findings Ye et al, SIIMS, 2018; Ye et al, ICML, 2019
  42. y = X i hbi(x), xi˜ bi(x) <latexit sha1_base64="DaaFmbtzayW3V2tBvW3rbADydJY=">AAACGXicbZDLSsNAFIYnXmu9RV26GSxCBSmJCroRim5cVrAXaEKYTCbt0MkkzEykIfQ13Pgqblwo4lJXvo3TNoK2/jDw851zOHN+P2FUKsv6MhYWl5ZXVktr5fWNza1tc2e3JeNUYNLEMYtFx0eSMMpJU1HFSCcRBEU+I21/cD2ut++JkDTmdypLiBuhHqchxUhp5JlWdunINPIohA5DvMcI9D1aHR4dw6EjpsBRlAU/3DMrVs2aCM4buzAVUKjhmR9OEOM0IlxhhqTs2lai3BwJRTEjo7KTSpIgPEA90tWWo4hIN59cNoKHmgQwjIV+XMEJ/T2Ro0jKLPJ1Z4RUX87WxvC/WjdV4YWbU56kinA8XRSmDKoYjmOCARUEK5Zpg7Cg+q8Q95FAWOkwyzoEe/bkedM6qdmnNev2rFK/KuIogX1wAKrABuegDm5AAzQBBg/gCbyAV+PReDbejPdp64JRzOyBPzI+vwEaXJ8Y</latexit> Our

    Theoretical Findings Ye et al, SIIMS, 2018; Ye et al, ICML, 2019
  43. analysis basis y = X i hbi(x), xi˜ bi(x) <latexit

    sha1_base64="DaaFmbtzayW3V2tBvW3rbADydJY=">AAACGXicbZDLSsNAFIYnXmu9RV26GSxCBSmJCroRim5cVrAXaEKYTCbt0MkkzEykIfQ13Pgqblwo4lJXvo3TNoK2/jDw851zOHN+P2FUKsv6MhYWl5ZXVktr5fWNza1tc2e3JeNUYNLEMYtFx0eSMMpJU1HFSCcRBEU+I21/cD2ut++JkDTmdypLiBuhHqchxUhp5JlWdunINPIohA5DvMcI9D1aHR4dw6EjpsBRlAU/3DMrVs2aCM4buzAVUKjhmR9OEOM0IlxhhqTs2lai3BwJRTEjo7KTSpIgPEA90tWWo4hIN59cNoKHmgQwjIV+XMEJ/T2Ro0jKLPJ1Z4RUX87WxvC/WjdV4YWbU56kinA8XRSmDKoYjmOCARUEK5Zpg7Cg+q8Q95FAWOkwyzoEe/bkedM6qdmnNev2rFK/KuIogX1wAKrABuegDm5AAzQBBg/gCbyAV+PReDbejPdp64JRzOyBPzI+vwEaXJ8Y</latexit> Encoder Our Theoretical Findings Ye et al, SIIMS, 2018; Ye et al, ICML, 2019
  44. analysis basis synthesis basis y = X i hbi(x), xi˜

    bi(x) <latexit sha1_base64="DaaFmbtzayW3V2tBvW3rbADydJY=">AAACGXicbZDLSsNAFIYnXmu9RV26GSxCBSmJCroRim5cVrAXaEKYTCbt0MkkzEykIfQ13Pgqblwo4lJXvo3TNoK2/jDw851zOHN+P2FUKsv6MhYWl5ZXVktr5fWNza1tc2e3JeNUYNLEMYtFx0eSMMpJU1HFSCcRBEU+I21/cD2ut++JkDTmdypLiBuhHqchxUhp5JlWdunINPIohA5DvMcI9D1aHR4dw6EjpsBRlAU/3DMrVs2aCM4buzAVUKjhmR9OEOM0IlxhhqTs2lai3BwJRTEjo7KTSpIgPEA90tWWo4hIN59cNoKHmgQwjIV+XMEJ/T2Ro0jKLPJ1Z4RUX87WxvC/WjdV4YWbU56kinA8XRSmDKoYjmOCARUEK5Zpg7Cg+q8Q95FAWOkwyzoEe/bkedM6qdmnNev2rFK/KuIogX1wAKrABuegDm5AAzQBBg/gCbyAV+PReDbejPdp64JRzOyBPzI+vwEaXJ8Y</latexit> Encoder Decoder Our Theoretical Findings Ye et al, SIIMS, 2018; Ye et al, ICML, 2019
  45. Linear Encoder-Decoder (ED) CNN Learned filters y = ˜ BB>x

    = X i hx, bi i˜ bi <latexit sha1_base64="bo3reUJLRRRgiLys4OrWvNpVArY=">AAACJ3icbVBNSwMxEM36bf2qevQSLIIHKbsq6KUievGoaK3QrSWbzrah2eySzIpl8d948a94EVREj/4T03YP2joQePPePCbzgkQKg6775UxMTk3PzM7NFxYWl5ZXiqtr1yZONYcqj2WsbwJmQAoFVRQo4SbRwKJAQi3onvb12h1oI2J1hb0EGhFrKxEKztBSzeJRr+KjkC2gJ/Tk1sc4ofe0Qn2TRk1BfclUWwK936FBv9XDNndYqlksuWV3UHQceDkokbzOm8VXvxXzNAKFXDJj6p6bYCNjGgWX8FDwUwMJ413WhrqFikVgGtngzge6ZZkWDWNtn0I6YH87MhYZ04sCOxkx7JhRrU/+p9VTDA8bmVBJiqD4cFGYSoox7YdGW0IDR9mzgHEt7F8p7zDNONpoCzYEb/TkcXC9W/b2yu7Ffun4Mo9jjmyQTbJNPHJAjskZOSdVwskjeSZv5N15cl6cD+dzODrh5J518qec7x9ZY6R3</latexit> pooling un-pooling
  46. Linear E-D CNN w/ Skipped Connection more redundant expression Learned

    filters y = ˜ BB>x = X i hx, bi i˜ bi <latexit sha1_base64="bo3reUJLRRRgiLys4OrWvNpVArY=">AAACJ3icbVBNSwMxEM36bf2qevQSLIIHKbsq6KUievGoaK3QrSWbzrah2eySzIpl8d948a94EVREj/4T03YP2joQePPePCbzgkQKg6775UxMTk3PzM7NFxYWl5ZXiqtr1yZONYcqj2WsbwJmQAoFVRQo4SbRwKJAQi3onvb12h1oI2J1hb0EGhFrKxEKztBSzeJRr+KjkC2gJ/Tk1sc4ofe0Qn2TRk1BfclUWwK936FBv9XDNndYqlksuWV3UHQceDkokbzOm8VXvxXzNAKFXDJj6p6bYCNjGgWX8FDwUwMJ413WhrqFikVgGtngzge6ZZkWDWNtn0I6YH87MhYZ04sCOxkx7JhRrU/+p9VTDA8bmVBJiqD4cFGYSoox7YdGW0IDR9mzgHEt7F8p7zDNONpoCzYEb/TkcXC9W/b2yu7Ffun4Mo9jjmyQTbJNPHJAjskZOSdVwskjeSZv5N15cl6cD+dzODrh5J518qec7x9ZY6R3</latexit>
  47. Deep Convolutional Framelets x = ˜ BB>x = X i

    hx, bi i˜ bi <latexit sha1_base64="9EuOyjKGC2x9hAgBpajvIdywLlA=">AAACJ3icbVBNSwMxEM36bf2qevQSLIIHKbsq6EWRevGoaK3QXZdsOq2h2eySzEpL6b/x4l/xIqiIHv0npu0etDoQePPePCbzolQKg6776UxMTk3PzM7NFxYWl5ZXiqtr1ybJNIcqT2SibyJmQAoFVRQo4SbVwOJIQi1qnw702j1oIxJ1hd0Ugpi1lGgKztBSYfG4c+SjkA2gFVq59TFJaYceUd9kcSioL5lqSaCdHRoNWj1qc4elwmLJLbvDon+Bl4MSyes8LL74jYRnMSjkkhlT99wUgx7TKLiEfsHPDKSMt1kL6hYqFoMJesM7+3TLMg3aTLR9CumQ/enosdiYbhzZyZjhnRnXBuR/Wj3D5mHQEyrNEBQfLWpmkmJCB6HRhtDAUXYtYFwL+1fK75hmHG20BRuCN37yX3C9W/b2yu7FfunkMo9jjmyQTbJNPHJATsgZOSdVwskDeSKv5M15dJ6dd+djNDrh5J518qucr29XoqR2</latexit> Perfect reconstruction Ye et al, SIIMS 2018; Ye et al, ICML 2019 Frame conditions w skipped connection w/o skipped connection
  48. Deep Convolutional Framelets x = ˜ BB>x = X i

    hx, bi i˜ bi <latexit sha1_base64="9EuOyjKGC2x9hAgBpajvIdywLlA=">AAACJ3icbVBNSwMxEM36bf2qevQSLIIHKbsq6EWRevGoaK3QXZdsOq2h2eySzEpL6b/x4l/xIqiIHv0npu0etDoQePPePCbzolQKg6776UxMTk3PzM7NFxYWl5ZXiqtr1ybJNIcqT2SibyJmQAoFVRQo4SbVwOJIQi1qnw702j1oIxJ1hd0Ugpi1lGgKztBSYfG4c+SjkA2gFVq59TFJaYceUd9kcSioL5lqSaCdHRoNWj1qc4elwmLJLbvDon+Bl4MSyes8LL74jYRnMSjkkhlT99wUgx7TKLiEfsHPDKSMt1kL6hYqFoMJesM7+3TLMg3aTLR9CumQ/enosdiYbhzZyZjhnRnXBuR/Wj3D5mHQEyrNEBQfLWpmkmJCB6HRhtDAUXYtYFwL+1fK75hmHG20BRuCN37yX3C9W/b2yu7FfunkMo9jjmyQTbJNPHJATsgZOSdVwskDeSKv5M15dJ6dd+djNDrh5J518qucr29XoqR2</latexit> Perfect reconstruction Ye et al, SIAM J. Imaging Science, 2018 Frame conditions w skipped connection w/o skipped connection
  49. Role of ReLUs? Generator for Multiple Expressions y = ˜

    B(x)B(x)>x = X i hx, bi(x)i˜ bi(x) <latexit sha1_base64="T/1m1u26m8O8vLHErH3u6EKQhAM=">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</latexit> ⌃l(x) = 2 6 6 6 4 1 0 · · · 0 0 2 · · · 0 . . . . . . ... . . . 0 0 · · · ml 3 7 7 7 5 <latexit sha1_base64="1HHS4n8UkvGQcnzeL2YdPrnnXeg=">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</latexit> Input dependent {0,1} matrix --> Input adaptivity
  50. Input Space Partitioning for Multiple Expressions

  51. Input Space Partitioning for Multiple Expressions A CNN performs automatic

    assignment of distinct linear representation depending on input
  52. Expressivity of E-D CNN # of representation # of network

    elements
  53. Expressivity of E-D CNN # of representation # of network

    elements # of channel
  54. Expressivity of E-D CNN # of representation # of network

    elements # of channel Network depth
  55. Expressivity of E-D CNN # of representation # of network

    elements # of channel Network depth Skipped connection
  56. Lipschitz Continuity K = max p Kp, Kp = k

    ˜ B(zp)B(zp)>k2 <latexit sha1_base64="zV0QFc8bcwR20HLOVcDQeQMOtmY=">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</latexit> z1 <latexit sha1_base64="Ob3+IEXFhF5uWyRIGKNYQ89lNRY=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8eK9gPaUDbbTbt0swm7E6GG/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmFldW19o7hZ2tre2d0r7x80TZxqxhsslrFuB9RwKRRvoEDJ24nmNAokbwWjm6nfeuTaiFg94DjhfkQHSoSCUbTS/VPP65UrbtWdgSwTLycVyFHvlb+6/ZilEVfIJDWm47kJ+hnVKJjkk1I3NTyhbEQHvGOpohE3fjY7dUJOrNInYaxtKSQz9fdERiNjxlFgOyOKQ7PoTcX/vE6K4ZWfCZWkyBWbLwpTSTAm079JX2jOUI4toUwLeythQ6opQ5tOyYbgLb68TJpnVe+86t5dVGrXeRxFOIJjOAUPLqEGt1CHBjAYwDO8wpsjnRfn3fmYtxacfOYQ/sD5/AEPZo2k</latexit> zp <latexit sha1_base64="Q3WIlMLDjf+qfP58xUVUuKL5KD4=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8eK9gPaUDbbSbt0swm7G6GG/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVDBssFrFqB1Sj4BIbhhuB7UQhjQKBrWB0M/Vbj6g0j+WDGSfoR3QgecgZNVa6f+olvXLFrbozkGXi5aQCOeq98le3H7M0QmmYoFp3PDcxfkaV4UzgpNRNNSaUjegAO5ZKGqH2s9mpE3JilT4JY2VLGjJTf09kNNJ6HAW2M6JmqBe9qfif10lNeOVnXCapQcnmi8JUEBOT6d+kzxUyI8aWUKa4vZWwIVWUGZtOyYbgLb68TJpnVe+86t5dVGrXeRxFOIJjOAUPLqEGt1CHBjAYwDO8wpsjnBfn3fmYtxacfOYQ/sD5/AFu4o3j</latexit> Related to the generalizability Dependent on the Local Lipschitz
  57. Optimization Issue • Optimization Landscape • All local minimizers are

    global minimizers • Ex) overparameterized network • Implicit bias • Specific global minimizers are determine d by the optimization algorithms Q) Nonconvex optimization problem à Can we prove convergence ? o <latexit sha1_base64="4DjPcWEGh5PQIKL0eIUnsOTwihE=">AAAB8XicbVDLSgMxFL1TX7W+qi7dBIvgqsyooCspuHFZwdZiO5RMmmlD8xiSjFCG/oUbF4q49W/c+Tdm2llo64HA4Zx7ybknSjgz1ve/vdLK6tr6RnmzsrW9s7tX3T9oG5VqQltEcaU7ETaUM0lblllOO4mmWEScPkTjm9x/eKLaMCXv7SShocBDyWJGsHXSY09gO4riTE371Zpf92dAyyQoSA0KNPvVr95AkVRQaQnHxnQDP7FhhrVlhNNppZcammAyxkPadVRiQU2YzRJP0YlTBihW2j1p0Uz9vZFhYcxERG4yT2gWvVz8z+umNr4KMyaT1FJJ5h/FKUdWofx8NGCaEssnjmCimcuKyAhrTKwrqeJKCBZPXibts3pwXvfvLmqN66KOMhzBMZxCAJfQgFtoQgsISHiGV3jzjPfivXsf89GSV+wcwh94nz/vApER</latexit> x <latexit 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  58. Benign Optimization Landscape full-rank condition Independent features Nguyen, et al,

    ICML, 2018
  59. Benign Optimization Landscape full-rank condition Independent features Independent features full-rank

    condition Nguyen, et al, ICML, 2018 Ye et al, ICML, 2019
  60. Regularized Recon vs. Deep Recon Diagnosis Classical Regularized Recon (basis

    engineering) Deep Recon (no basis engineering) Basis Engineering
  61. THEORY-DRIVEN CNN DESIGN :some snapshots

  62. Deep Beamformer Khan et al, MICCAI, 2019

  63. Focused / Plane Wave Ultrasound Imaging Focused Imaging Plane Wave

    Imaging Couade M, JVDI, 2015 Yoon et al, TMI, 2018
  64. Adaptive Beamformer Conventional Beamforming Pipeline  I Q = 

    zl[n] H(zl)[n] <latexit sha1_base64="Mv7jnJQUjhxiLpE3LDXNSJ47/J8=">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</latexit> Data specific weights
  65. Deep Beamformer Khan et al, MICCAI (accepted), 2019 Adaptive and

    Compressive Deep Beamformer Conventional Beamforming Pipeline Input partitioning à Data specific representation
  66. B-mode Focused Mode Deep Beamformer Khan et al, MICCAI (accepted),

    2019
  67. Plane Wave Deep Beamformer Khan et al, MICCAI (accepted), 2019

  68. k-Space Deep Learning Han et al, IEEE Trans. Medical Imaging

    (in press), 2019 Lee et al, MRM (in press), 2019
  69. Duality between Sparsity and Low-Rankness Ye et al, IEEE Trans.

    Information Theory, 2017;Jin et al, IEEE TCI, 2017; Lee et al, MRM, 2017
  70. Annihilating Filter-based Low-rank Hankel Matrix Approach (ALOHA) Jin KH et

    al IEEE TCI, 2016, Lee et al, MRM, 2015; Ye et al, IEEE TIT, 2016
  71. Single coil MRI Jin KH et al IEEE TCI, 2016

    Lee et al, MRM, 2015
  72. Parallel MRI Jin KH et al IEEE TCI, 2016 Lee

    et al, MRM, 2015
  73. Optimization Problem Equivalent to search for frame basis to make

    the nonzero-coefficents sparse
  74. : Non-local basis : Local basis Convolution Framelets (Yin et

    al, SIIMS, 2017) > = I > = I
  75. : Non-local basis : Local basis Convolution Framelets (Yin et

    al, SIIMS, 2017) > = I > = I
  76. : Non-local basis : Local basis Convolution Framelets (Yin et

    al, SIIMS, 2017) > = I > = I
  77. ˜ T = I : Non-local basis : Local basis

    :Nonlocal basis : Local basis Deep Convolutional Framelets (Y, Han, Cha, SIIMS, 2018) ˜ T = I <latexit sha1_base64="nsw6gd0e+4ZO1ci14Ht6KPpot+8=">AAAB/XicbZDLSsNAFIZPvNZ6i5edm8EiuCqJCroRim50V6E3aGKZTCbt0MmFmYlQQ/FV3LhQxK3v4c63cdJmoa0/DHz85xzOmd9LOJPKsr6NhcWl5ZXV0lp5fWNza9vc2W3JOBWENknMY9HxsKScRbSpmOK0kwiKQ4/Ttje8zuvtByoki6OGGiXUDXE/YgEjWGmrZ+47dckcxbhPc7pvoEt02zMrVtWaCM2DXUAFCtV75pfjxyQNaaQIx1J2bStRboaFYoTTcdlJJU0wGeI+7WqMcEilm02uH6Mj7fgoiIV+kUIT9/dEhkMpR6GnO0OsBnK2lpv/1bqpCi7cjEVJqmhEpouClCMVozwK5DNBieIjDZgIpm9FZIAFJkoHVtYh2LNfnofWSdU+rVp3Z5XaVRFHCQ7gEI7BhnOowQ3UoQkEHuEZXuHNeDJejHfjY9q6YBQze/BHxucPPbyUaw==</latexit>
  78. ˜ T = I : Non-local basis : Local basis

    : Pooling : Convolution filters Deep Convolutional Framelets (Y, Han, Cha, SIIMS, 2018) ˜ T = I <latexit sha1_base64="nsw6gd0e+4ZO1ci14Ht6KPpot+8=">AAAB/XicbZDLSsNAFIZPvNZ6i5edm8EiuCqJCroRim50V6E3aGKZTCbt0MmFmYlQQ/FV3LhQxK3v4c63cdJmoa0/DHz85xzOmd9LOJPKsr6NhcWl5ZXV0lp5fWNza9vc2W3JOBWENknMY9HxsKScRbSpmOK0kwiKQ4/Ttje8zuvtByoki6OGGiXUDXE/YgEjWGmrZ+47dckcxbhPc7pvoEt02zMrVtWaCM2DXUAFCtV75pfjxyQNaaQIx1J2bStRboaFYoTTcdlJJU0wGeI+7WqMcEilm02uH6Mj7fgoiIV+kUIT9/dEhkMpR6GnO0OsBnK2lpv/1bqpCi7cjEVJqmhEpouClCMVozwK5DNBieIjDZgIpm9FZIAFJkoHVtYh2LNfnofWSdU+rVp3Z5XaVRFHCQ7gEI7BhnOowQ3UoQkEHuEZXuHNeDJejHfjY9q6YBQze/BHxucPPbyUaw==</latexit> Hd(f) Hd(f) = ˜ T ˜ T C C = T Hd(f) C = T (f ~ ) Encoder: Unlifting: f = (˜C) ~ ⌧(˜ ) convolution pooling un-pooling convolution Decoder:
  79. Single Resolution Network Architecture

  80. Multi-Resolution Network Architecture

  81. ALOHA CNN k-Space Deep Learning Han et al, IEEE TMI,2019

  82. K-space Deep Learning (Radial R=6) Ground-truth Acceleration Image learning CS

    K-space learning Han et al, IEEE TMI (in press)
  83. K-space Deep Learning (Radial R=6) Ground-truth Acceleration Image learning CS

    K-space learning Han et al, IEEE TMI (in press)
  84. EPI Ghost Artifact Correction Gx RO G y PE G

    z SS R F Ghost artifact image In EPI, Gradient is distorted by eddy currents and this causes phase shift Distorted gradient FT Even and odd echo mismatch causes ghost artifact! Phase shift
  85. k-space Deep Learning for EPI Ghost Correction Image domain loss

    L2 loss is calculated on the image domain k-space (with Ghost) e eo o … e e o o … ALOHA IFT e e o o … Coil 1 … coil P Coil 1 … coil P Coil 1 … coil P Neural network k-space (with Ghost) e e o o … e e o o … IFT e e o o … Coil 1 … coil P Coil 1 … coil P Coil 1 … coil P k-space learning Network Input Network Label 34 Lee et al, MRM (in press), 2019
  86. 7T EPI result (R=2) ALOHA Ghost image Half ROI learning

    With Reference PEC-SENSE Proposed (Full ROI) GSR : 10.48% GSR : 9.71% GSR : 15.04% GSR : 8.80% GSR : 4.92% 49 Lee et al, MRM (in press), 2019
  87. Improving U-Net Ye et al, SIAM J. Imaging Science, 2018

    Han et al, IEEE Trans. Medical Imaging, 2018 Yoo et al, SIAM J. Applied Math, 2019
  88. Problem of U-net Pooling does NOT satisfy the frame condition

    JC Ye et al, SIAM Journal Imaging Sciences, 2018 Y. Han et al, TMI, 2018. ext > ext = I + > 6= I
  89. Improving U-net using Deep Conv Framelets • Dual Frame U-net

    • Tight Frame U-net JC Ye et al, SIAM Journal Imaging Sciences, 2018 Y. Han and J. C. Ye, TMI, 2018
  90. U-Net versus Dual Frame U-Net Y. Han and J. C.

    Ye, TMI, 2018; Yoo et al, SIJAM, 2018
  91. Tight-Frame U-Net JC Ye et al, SIAM Journal Imaging Sciences,

    2018
  92. Denoising: U-Net vs. Tight-Frame U-Net

  93. Inpainting: U-Net vs. Tight-Frame U-Net

  94. Style Transfer : Power of Tight Frame U-net

  95. None
  96. None
  97. None
  98. None
  99. Summary • Deep learning is a novel signal representation using

    combinatorial framelets • ReLUs generate multiple linear representation by partitioning the input space • Local Lipschitz controls the global Liptschiz continuity • Skipped connection improves the optimization landscape • Black-box nature of neural networks have been being unveiled.
  100. Outlooks q End-to-End AI for radiological imaging Ø From AI-powered

    image acquisition to diagnosis for clear and rapid radiological imaging Existing AI Solutions: Diagnosis Our future: from acquisition to diagnosis
  101. Acknowledgement • Daniel Rueckert (Imperial College) • Florian Knoll (NYU)

    • Fang Liu (Univ. of Wisconsin) • Mehmet Akcakaya (Univ. of Minnesota) • Dong Liang (SIAT, China) • Dinggang Shen (UNC) • Peder Larson (UCSF) • Grant – NRF of Korea – Ministry of Trade Industry and Energy • Hyunwook Park (KAIST) • Sung-hong Park (KAIST) • Jongho Lee (SNU) • Doshik Hwang (Yonsei Univ) • Won-Jin Moon (KonkukUniv Medical Center) • Eungyeop Kim (Gachon Univ. Medical Center) • Leonard Sunwoo (SNUBH) • Kyuhwan Jung (Vuno)
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