This document discusses a method called projectionGAN for removing missing cone artifacts from optical diffraction tomography (ODT) reconstructions using unsupervised deep learning. ODT suffers from low axial resolution and elongation artifacts due to the missing cone problem. ProjectionGAN trains a GAN to generate missing angular projections, which are then used in reconstruction to improve resolution and remove artifacts. Results on numerical phantoms, microbeads, and cells demonstrate projectionGAN effectively reduces elongation and produces sharper, more homogeneous reconstructions compared to conventional ODT.

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