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Missing Cone Artifact Removal in ODT Using
Unsupervised Deep Learning in the Projection
Domain
BISPL - BioImaging, Signal Processing,
and Learning lab.
KAIST, Korea
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Optical Diffraction Tomography
 Measures 3D refractive index with optical illumination
 Reconstruction through field-retrieval (Fourier diffraction theorem)
 GP used to enhance resolution
2
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Missing cone prblem
3
… …
𝑘𝑚, 𝑘𝑛
𝑘𝑝
Measurement
(hologram)
 Problem arising in diffraction tomography
• Low axial resolution, elongation in the optical axes
Fourier
Diffraction
theorem
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Missing cone prblem
4
… …
𝑘𝑚, 𝑘𝑛
𝑘𝑝
Measurement
(hologram)
 Problem arising in diffraction tomography
• Low axial resolution, elongation in the optical axes
Fourier
Diffraction
theorem
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Missing cone prblem
5
… …
𝑘𝑚, 𝑘𝑛
𝑘𝑝
Measurement
(hologram)
 Problem arising in diffraction tomography
• Low axial resolution, elongation in the optical axes
Fourier
Diffraction
theorem
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Missing cone prblem
6
… …
𝑘𝑚, 𝑘𝑛
𝑘𝑝
Measurement
(hologram)
Missing cone
Missing cone problem in 3D
 Problem arising in diffraction tomography
• Low axial resolution, elongation in the optical axes
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Missing cone prblem
7
Low resolution
 Problem arising in diffraction tomography
• Low axial resolution, elongation in the optical axes
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Research Motivation
8
Parallel-ray
projections
gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography
Approximation possible!
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Research Motivation
9
Parallel-ray
projections
gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography
• Projections aligned w. measurement angle: high resolution
• Projections un-aligned w. measurement angle: low resolution
𝒴Ω
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Research Motivation
10
Parallel-ray
projections
gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography
• Projections aligned w. measurement angle: high resolution
• Projections un-aligned w. measurement angle: low resolution
𝒴Ω 𝒴Ωc
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Research Motivation
11
Parallel-ray
projections
gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography
• Projections aligned w. measurement angle: high resolution
• Projections un-aligned w. measurement angle: low resolution
𝒴Ω 𝒴Ωc
projectionGAN
0° 20° 40° 80° 100°
60°
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
projectionGAN
Field-retrieval
GP-reconstruction
… …
1st 23th 49th
Cell
Source
Incident Wave
Diffracted
Wave
Measured
Hologram
1. Reconstruction
12
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
projectionGAN
Field-retrieval
GP-reconstruction
… …
1st 23th 49th
Cell
Source
Incident Wave
Diffracted
Wave
TomoGAN
Final reconstruction
X-ray transform
𝜔1 𝜔2 𝜔3 𝜔4 𝜔5
𝜔1 𝜔2 𝜔3 𝜔4 𝜔5
FBP
Measured
Hologram
13
2. projectionGAN
1. Reconstruction
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Results: numerical simulation
14
Elongation
False signal
projectionGAN
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Results: microbead
15
Missing cone
Inhomogeneous
shape
RI (True: 1.46)
projectionGAN
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Results: biological cells
16
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Results: biological cells
17
Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain
Results: biological cells
18

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Missing cone artifact removal in odt using unsupervised deep learning in the projection domain

  • 1. Missing Cone Artifact Removal in ODT Using Unsupervised Deep Learning in the Projection Domain BISPL - BioImaging, Signal Processing, and Learning lab. KAIST, Korea
  • 2. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Optical Diffraction Tomography  Measures 3D refractive index with optical illumination  Reconstruction through field-retrieval (Fourier diffraction theorem)  GP used to enhance resolution 2
  • 3. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Missing cone prblem 3 … … 𝑘𝑚, 𝑘𝑛 𝑘𝑝 Measurement (hologram)  Problem arising in diffraction tomography • Low axial resolution, elongation in the optical axes Fourier Diffraction theorem
  • 4. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Missing cone prblem 4 … … 𝑘𝑚, 𝑘𝑛 𝑘𝑝 Measurement (hologram)  Problem arising in diffraction tomography • Low axial resolution, elongation in the optical axes Fourier Diffraction theorem
  • 5. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Missing cone prblem 5 … … 𝑘𝑚, 𝑘𝑛 𝑘𝑝 Measurement (hologram)  Problem arising in diffraction tomography • Low axial resolution, elongation in the optical axes Fourier Diffraction theorem
  • 6. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Missing cone prblem 6 … … 𝑘𝑚, 𝑘𝑛 𝑘𝑝 Measurement (hologram) Missing cone Missing cone problem in 3D  Problem arising in diffraction tomography • Low axial resolution, elongation in the optical axes
  • 7. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Missing cone prblem 7 Low resolution  Problem arising in diffraction tomography • Low axial resolution, elongation in the optical axes
  • 8. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Research Motivation 8 Parallel-ray projections gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography Approximation possible!
  • 9. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Research Motivation 9 Parallel-ray projections gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography • Projections aligned w. measurement angle: high resolution • Projections un-aligned w. measurement angle: low resolution 𝒴Ω
  • 10. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Research Motivation 10 Parallel-ray projections gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography • Projections aligned w. measurement angle: high resolution • Projections un-aligned w. measurement angle: low resolution 𝒴Ω 𝒴Ωc
  • 11. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Research Motivation 11 Parallel-ray projections gp-reconstruction  Close relationship btw. non-diffraction / diffraction tomography • Projections aligned w. measurement angle: high resolution • Projections un-aligned w. measurement angle: low resolution 𝒴Ω 𝒴Ωc projectionGAN 0° 20° 40° 80° 100° 60°
  • 12. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain projectionGAN Field-retrieval GP-reconstruction … … 1st 23th 49th Cell Source Incident Wave Diffracted Wave Measured Hologram 1. Reconstruction 12
  • 13. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain projectionGAN Field-retrieval GP-reconstruction … … 1st 23th 49th Cell Source Incident Wave Diffracted Wave TomoGAN Final reconstruction X-ray transform 𝜔1 𝜔2 𝜔3 𝜔4 𝜔5 𝜔1 𝜔2 𝜔3 𝜔4 𝜔5 FBP Measured Hologram 13 2. projectionGAN 1. Reconstruction
  • 14. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Results: numerical simulation 14 Elongation False signal projectionGAN
  • 15. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Results: microbead 15 Missing cone Inhomogeneous shape RI (True: 1.46) projectionGAN
  • 16. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Results: biological cells 16
  • 17. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Results: biological cells 17
  • 18. Part I: Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain Results: biological cells 18