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