PHD Presentation_web

New Approaches Towards a Higher
Resolution Biomedical Imaging
Magnetic Induction Tomography
04/06/2010
Nuno Brás
PhD Thesis Presentation
Universidade Técnica de Lisboa
Instituto Superior Técnico
PhD Dissertation
Doctoral Program In Electrical and Computer
Engineering
António C. Serra and Raúl C. Martins (advisors)

Outline
04/06/2010Nuno B. Brás - PhD Dissertation
!  Motivation
!  The Problem in Hands
!  State of the Art Issues
!  Objectives and Developed Work
!  Experimental Work
!  Forward Problem
!  Inverse Problem
!  Conclusions and Original Contributions
!  Further Work
!  Acknowledgements
2

Outline
04/06/2010Nuno B. Brás - PhD Dissertation 3
!  Motivation
!  Further Work

Motivation
Imaging Systems
In Natural Sciences
Astrophysics; Biophysics; Geophysics, Biology…
In Engineering
biomedical; industrial processes; oil and water
prospecting; search and rescue instrumentation;…

Motivation
Magnetic Induction Tomography
(as a Biomedical Imaging System)
Tomography - recreates maps or images from peripheral
measurements
!  MIT is:
!  Active Tomographic method (instead of Passive);
!  Harmless (instead of Harmful)
!  In-vivo or in-vitro;
!  Functional or Steady Imaging

Motivation
What does MIT try to solve?
Good things about MIT:
!  (very) low price comparing with other tomographic systems
(e.g. MRI machine up to 2.5 million € + installation (25%))
!  biological passivity (low power radiofrequency)
!  excellent penetration abilities in biological phantoms, even in bone-
like tissues (unlike ultrasound tomography )
!  full reconstruction is theoretically achievable

Motivation
Not so good things about MIT:
1.  The underlying image reconstruction problem is a
large, complex and non-linear problem (non-convex)
2.  Its behavior is strongly dependent on the number of
measurements and their intrinsic accuracy
Actual Context
There are no commercial equipments, just prototypes.
First applications are being explored

Outline
!  Motivation
!  State of The Art
!  Further Work
8

What is MIT, conceptually
It is a distributed parameter estimation (DPE) problem
under Electromagnetic Partial Differential equations
(PDE)
The Problem in Hands
9

where is the kernel of the underlying physical process.
Consider an electromagnetic physical process ruled by the following relation:
10
Distributed Parameter Estimation Problems in
electromagnetics

Electric and
magnetic
fields or potentials
(state variables)
Boundary
Conditions
+
Sources
Set Differential
Operators
+
parameters
11
electromagnetics

electromagnetics
12
The inverse problem is the distributed parameter identification problem given by:
The forward problem (well-posed, and typically linear) is the PDE equation

The General Parameter Estimation Model
(Outline of this Thesis)
Experimental Setup (PART 1)
The Forward Problem (PART 2)
The Inverse Problem (PART 3)
Problem in Hands
13

The MIT Setup
Source Currents: Harmonic , tens of
kHz to some MHz;
Current Amplitude: Up to 1 A;
Setup Radius: Typically 15 cm;
Conductivity Values: complex with
absolute value between 0.1 S/m to 2
S/m;
Source and sensing coils size: around
5 cm and 3 cm correspondingly
14

15
The MIT Setup

1
16
The MIT Setup

2
17
The MIT Setup

18
The MIT Setup

19
The MIT Setup
Each d should be as large, independent
and accurate as possible

Outline
!  Motivation
!  Further Work

!  Experimental Issues
!  Typical layout generates ambiguities (gradiometers);
!  Fixed system of acquisition (fixed and low number is allowed)
!  Developed solvers in MIT context are accurate but typically slow;
(it is not possible to use commercial solvers)
!  Non-linear approaches are the best known reconstruction methods.
!  The state of the art method is not efficient when used with a high
number of acquisitions.
State of the Art Issues
21

Outline
!  Motivation
!  Further Work

Objectives - Developed Work
23
General Objective
Implementation of a new Magnetic Induction Tomography prototype
and numerical framework to deal with large number of acquisitions
Developed Work
!  Experimental
!  A new moving prototype was implemented for large number of
acquisitions while attaining the state of the art sensitivity (SCR)
!  A new 3D eddy current PDE solver was developed with a
competitive processing time and low relative error.
!  A new ADMM method was developed and used in 2D and 3D IP.
!  Its feasibility was proved and its advantage was clearly shown for
large datasets scenarios.

Outline
!  Motivation
!  Further Work
24

Experimental Work
!  Early Experimental Prototypes

Experimental Work
! Twin Coil Setup
Source
Current
Amplifier
Capacitive
Shields
Source
Coil
Motor
systems

Experimental Work
Involved Areas While Designing This Prototype
!  Electromagnetic Compatibility (EMC)
!  Mechanical Setup Design and Characterization
!  Current Source Design
!  Acquisition System
!  Signal Processing

Experimental Work
Involved Areas While Designing This Prototype
!  Electromagnetic Compatibility (EMC)
!  Mechanical Setup Design and Characterization
!  Current Source Design
!  Acquisition System
!  Signal Processing
Measuring System

Symmetry Axis
Without object:
V1-V2 = Residual V ≈ 0, for any angle
With object:
V1-V2 = ∆V
V1
V2
Experimental Work
! Twin Coil Setup
Useful V =∆V– Residual V

!  Shielded Differential coils and cables
!  Gain (low noise) Amplifier =100; with a low-pass filter
!  ADC with 12 bits, up to 60 MSamples/s
!  The Goertzel Transform (second order IIR filter ) to calculate the frequency
bin amplitude and phase (others were tested)
!  Average sliding window applied to avoid 50Hz modulation and reduce noise
!  Principal Component Analysis (PCA) and a reference coil were used to
eliminate long term trends from the source current.
Experimental Work
Acquisition System
Signal Processing System

Experimental Work
!  Results a differential coil pair, during 300 sec time

Experimental Work
!  Results - Stability
Applying an averaging sliding window with 50 values
A minimum measurable SCR of
was obtained which is the stated state of the art value in this case with
a moving system of sensing coils

Outline
!  Motivation
!  Further Work
34

The Forward Solver abilities:
!  Isotropic parameter model
!  Constant
!  Diffusion model approach (no skin currents)
!  Harmonic and stationary equations
!  Multi- level grid allowing mutligrid (MG) techniques and/or
adaptive mesh refinements (AMR) in future iterations
!  Analytical sources, using the Biot-Savart law
The Forward Problem

Normal Component of = 0
The Forward Problem
Formulation:
Imposed directly by (1)
(1)
in
Boundary ConditionsInterface Conditions
where and

The Forward Problem
The Discretization : Finite Integration Technique

The Forward Problem
The proposed FIT formulation:
!  The resultant system is non-singular - the used gauging
ensures a robust regularization of the system;
!  A Laplacian-type instead a curl-curl-type problem, where a
larger set of numerical methods are available;
!  Subgriding implementation;
Moreover…
!  Several Numerical Optimization aspects were implemented;
!  Solved with iterative preconditioned methods (here, iLU
factorization was used);

The Forward Problem
Results – Accuracy

The Forward Problem
Results – Performance

The Forward Problem
Results – Performance and accuracy

The Forward Problem
How this interacts with the inverse problem?

Outline
!  Motivation
!  Inverse Problems
!  Further Work
43

Inverse Problems
!  Implemented Methods :
!  Two versions of the Alternating Direction Method of
Multipliers (Augmented Lagrangian Method) in an
elliptic 2D inverse problem with total variation
regularization and Wavelets regularization
!  Gauss Newton in ellipitc 2D Inverse Problem
!  ADMM version adapted to solve the MIT 3D

Inverse Problems
The ADMM – a sequence of simple problems
Closed form

Inverse Problems
The ADMM – a sequence of simple problems
Closed form
Either implementing a fixed point iteration for a
continuous approximation of
(ADMM with fixed point iteration)
or
Using a second Alternate Direction split
Closed Solution (DIPESAL Method)

Inverse Problems
2D Elliptical IP - The same model, a simpler problem

Inverse Problems
Gauss Newton using an
unconstrained version of
the problem
ADMM with a fixed
point iteration and
TV Regularization
ADMM with a fixed point
iteration and Wavelet
Regularization

Inverse Problems
GN ADMM

Inverse Problems
GN
ADMM

Inverse Problems
DIPESAL
ADMM with fixed point iteration
2.2% better reconstruction and 7% faster,
with better image reconstruction quality
5% noise and LARGER problem

Inverse Problems
!  Some remarks for 3D MIT inverse problem
!  Two things changes for MIT problem:
!  Size: Each Iterations of the ADMM problem have to be
solved iteratively: The Second Order Stationary method was
applied.
!  Different discretization and equations: The new equations
were referred before;

Inverse Problems
!  3D MIT inverse problem
Inversion scenarios

Inverse Problems

Inverse Problems
!  Relative Error Evolution and Constrain Imposition

Inverse Problems
!  Performance Assessment

Outline
!  Motivation
!  Further Work
60

Conclusions and Original Contributions
!  A new prototype was implemented for moving sensing and source
coils, allowing acquire large sets of accurate data
!  System sensitivity, a state of the art value, is stable during a large
amount of time (>300 sec), allowing to implement a moving setup
with high sensitivity.
This work resulted in 7 congress papers during the PhD period

!  A new hybrid formulation of Finite Integration Technique
!  The processing time was optimized to be included in an
inverse problem attaining a low relative error
!  Total relative error ~ 1.5 %
!  Processing time ~19 sec. per eddy current problem
This work was published on IEEE Transactions on Magnetics
(May 2010)

!  2D Elliptic Inverse Problem
!  A new method ADMM algorithm (DIPESAL) was implemented
with closed solution for Total Variation regularization
!  Lower relative error (2,2%);
!  7% faster.
!  Better qualitative images in general
This work was submitted to IEEE Transactions on Image Processing
(May 2010)

!  3D MIT Inverse Problem Solution
!  The ADMM algorithm feasibility in 3D MIT
problems was achieved
!  A complete new approach with clear advantages in large
number of measurements conditions.
!  Its application to the MIT originates state of the art
simulated reconstructed maps.
This work was submitted to IEEE Transactions on Medical Imaging
(May 2010)

Outline
!  Motivation
!  Further Work
65

Further Work
!  Experimental
!  Use large arrays of Giant Magnetic Resistors as sensors – This can
dramatically change MIT since it can increase dramatically the number
of acquisitions and their accuracy.
!  Use strong permeability material cores to increase magnetic field.
!  Use of transient signals to increase SNR
!  Numerical
!  Multigrid scheme for preconditioning and code parallelization to
accelerate even more the forward and inverse problem.
!  Field Regularization – there is very experiments clearly shows
advantages in using this
!  Improve ADMM to MIT – There is space to improve, namely in the
regularization process

Outline
!  Motivation
!  Further Work
67

Acknowledgements
!  Supervisors: A. C. Serra And Raúl C. Martins
!  Other professor and researchers
!  Professor José Bioucas Dias (Elect. and Comp. Dep.)
!  Professor Artur Lopes Ribeiro (Elect. and Comp. Dep.)
!  Professor Paulo Martins (Mechanical Dep.)
!  Professor Helena Ramos (Elect. and Comp. Dep.)
!  Dr. Tomas Radil (Elect. and Comp. Dep.)
!  Professor Pedro Santos (Mathematics Dep.)
!  Professor Carlos Alves (Mathematics Dep.)
!  Eng. Luis Soares
!  Eng. Alexandre Pestana
!  Eng. José Gouveia

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