1. Image Alignment / Reconstruction
Evelyn Cueva, Matthias Ehrhardt, Paul Quinn,
Shaerdan Shataer, Jordan TayloR

2. The Problem
Object

3. The Problem
Object
Ideal Sinogram

4. The Problem
Object
Reality

5. The Problem
Reconstruction
Reality

6. Options
De-jitter the sinogram before image reconstruction (Variational Method; Machine Learning)
Joint de-jitter and image reconstruction from sinogram data

7. De-noising using Auto-Encoders

8. What are Auto-Encoders?X

9. What are Auto-Encoders?X
Encoder 𝑓

10. What are Auto-Encoders?X
X′ =𝑓(𝑔 X )
Decoder 𝑔

11. What are Auto-Encoders?X
X′ =𝑓(𝑔 X )
min θ X−X′

12. De-jitter Auto-EncodersX
X′ =𝑓(𝑔 X )
min θ X −X′

13. Direct Reconstruction
𝜃 𝑖 𝑢

14. Direct Reconstruction
𝜃 𝑖 𝑢
𝑠 𝑖

15. Direct Reconstruction
𝜃 𝑖 𝑢
𝑅( 𝑇 𝑠 𝑖 , 𝜃 𝑖 ⊥ (𝑢)) = 𝑥 𝑖 + 𝜀
𝑠 𝑖

16. Direct Reconstruction
𝜃 𝑖 𝑢
𝑅 𝜃 𝑖 ( 𝑇 𝑠 𝑖 , 𝜃 𝑖 ⊥ (𝑢)) = 𝑥 𝑖 + 𝜀
min 𝑢, 𝑠 𝑖 𝑖 𝑅 𝜃 𝑖 ( 𝑇 𝑠 𝑖 , 𝜃 𝑖 ⊥ (𝑢)) − 𝑥 𝑖 2
𝑠 𝑖

17. Going Forward
• Sinogram reconstruction (Variational Method; Machine Learning)
• Direct image reconstruction