Presentation for NGS Symposium 2014

1. Cryo-EM 3D reconstruction
Fan Zhitao
NUS Graduate School
February 20, 2014

2. Images are everywhere
In our life
In research
Z.T. Fan — Cryo-EM 3D reconstruction
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3. EM imaging process
Z.T. Fan — Cryo-EM 3D reconstruction
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4. The EM images
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5. Mathematical modeling
The mathematical model is
Af = g
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6. Challenges
Challenges:
large noise
large data: 100, 000 projections with size 512
A is hard to write out
Contribution
Proposed a memory-saving tight wavelet frame based
algorithm
Done the convergence analysis of this algorithm
Z.T. Fan — Cryo-EM 3D reconstruction
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7. Sparse representation
The image has a sparse representation under wavelet system.
If we have a sparse representation, we may formulate a
mathematical model:
min g − Af
f
2
+ λ Wf
1
W is the discrete wavelet transform. Dong and Shen 2005,
Ron and Shen 1995
Z.T. Fan — Cryo-EM 3D reconstruction
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8. The algorithm
Algorithm 1
fk+1 = (I − µA A)W Tλ Wfk + µA g
The advantage
Simple: one soft-thresholding and one gradient descent
Small memory footprint: one wavelet transform
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9. Simulated data: E. coli ribosome
Simulated 2D noisy projections
3D reconstruction
Ground truth
Z.T. Fan — Cryo-EM 3D reconstruction
BP
Proposed algorithm
Experiment results
9/11

10. Real data: Adenovirus
2D noisy projections
3D reconstruction
BP
Z.T. Fan — Cryo-EM 3D reconstruction
Proposed algorithm
Experiment results
10/11

11. Thank you!
Special thanks to
DR Li Ming, Chinese Academy of Science
Prof Ji Hui, NUS mathematics
Prof Shen Zuowei, NUS mathematics
Z.T. Fan — Cryo-EM 3D reconstruction
Acknowledgement
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