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?