em 3d reconstruction
TRANSCRIPT
Cryo-EM 3D reconstruction
Fan Zhitao
NUS Graduate School
February 20, 2014
Images are everywhere
In our life
In research
Z.T. Fan — Cryo-EM 3D reconstruction 2/11
EM imaging process
Z.T. Fan — Cryo-EM 3D reconstruction 3/11
The EM images
Z.T. Fan — Cryo-EM 3D reconstruction 4/11
Mathematical modeling
The mathematical model is
Af = g
Z.T. Fan — Cryo-EM 3D reconstruction 5/11
Challenges
Challenges:
I large noise
I large data: 100, 000 projections with size 512
I A is hard to write out
Contribution
I Proposed a memory-saving tight wavelet frame basedalgorithm
I Done the convergence analysis of this algorithm
Z.T. Fan — Cryo-EM 3D reconstruction 6/11
Sparse representation
I The image has a sparse representation under wavelet system.
I If we have a sparse representation, we may formulate amathematical model:
minf‖g − Af ‖2 + λ‖Wf ‖1
I W is the discrete wavelet transform. Dong and Shen 2005,Ron and Shen 1995
Z.T. Fan — Cryo-EM 3D reconstruction 7/11
The algorithm
fk+1 = (I − µA>A)W>TλWfk + µA>g
Algorithm 1
The advantageI Simple: one soft-thresholding and one gradient descent
I Small memory footprint: one wavelet transform
Z.T. Fan — Cryo-EM 3D reconstruction 8/11
Simulated data: E. coli ribosome
Simulated 2D noisy projections
3D reconstruction
Ground truth BP Proposed algorithm
Z.T. Fan — Cryo-EM 3D reconstruction Experiment results 9/11
Real data: Adenovirus
2D noisy projections
3D reconstruction
BP Proposed algorithm
Z.T. Fan — Cryo-EM 3D reconstruction Experiment results 10/11
Thank you!
Special thanks toI DR Li Ming, Chinese Academy of Science
I Prof Ji Hui, NUS mathematics
I Prof Shen Zuowei, NUS mathematics
Z.T. Fan — Cryo-EM 3D reconstruction Acknowledgement 11/11