Parallel CGLS technique for solving
large scale EIT inverse problem
Presenter: Chuan Li YangDept of Electronic and Electrical
Engineering
Introduction
Hardware Mathematical model
Method for solving large scale EIT
Conclusion and Future improvement
Contents
What is EIT (electrical impedance tomography )?
An imaging technique in which an image of the conductivity or permittivity of part of the body is inferred from surface electrical measurements.
Introduction
Includes: Control computer, DAQ unit, multiplexers and phantom.
How does it work?
Control
Computer
National
Instrument
Data
Acquisition
Card
Multiplexer switching pattern
Multiplexer
1
Multiplexer
2
EIT
Phantom
Excitation
Sink
Measurement 2
Measurement 1
EIT hardware ( sensors)
Phantom design
2D 32 electrodes phantom
3D 4x4 plane array sensor
3D 32 electrodes phantom (2x 16) 32 channel square fabric sensor
How does it work? Measurement Patterns
Mathematical modelForward problem
Inverse problem
One of the most typical regularization schemes is Tikhonov regularization.
What is large scale mean?
More than 128 electrodes.
Require large space to store the Jacobian matrix.
When EIT problem becomes large scale
Sparse matrix with parallel CGLS reconstruction
Sparse Jacobian thresholding ( Memory and time save)
Block-wise parallel CGLS (Multiple CPUs)( Further time save)
Method introduced
The matrix J can be divided in to blocks
Block-wise matrix
• can be expressed as the sum of all blocks,
1
1
lT T
k kk
J r J r
Results on speed
128 electrodes 3D EIT system FEM mesh
True image (A sphere with radius of 2.5 cm)
Original reconstruction(400 iterations) LOS=100% Time=1527.90 s
Threshold= 0.001* max(100)J LOS= 45.87% Time= 1307.22s
Threshold= 0.002* max(100)J LOS= 36.36% Time= 1224.12s
Simulation for 128 electrodes
Phantom pictures Original reconstruction(300 iterations) LOS=100% Time=42.18 s
Threshold= 0.001* max(100)J LOS= 88.40% Time= 42.03s
Threshold= 0.002* max(100)J
LOS= 79.81% Time= 41.76s
Threshold= 0.004* max(100)J
LOS=72.47%
Time= 40.41s
Threshold= 0.006* max(100)J
LOS= 63.22% Time= 31.10s
Experimental images(32 electrodes)
We have introduced the basics of electrical impedance tomography.
A PC is now efficient enough to produce satisfying results for large scale EIT system while using the developed software.
This program will be utilized by HPC in the future.
Conclusion and future improvement
Thanks to my supervisor Dr. M Soleimani for his guidance and consistently support of my project.
Acknowledgement
Thank you!Questions?