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ENG-03-0051-0 1Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
UCRL-CONF-226095Signal and Imaging Sciences Workshop, Center for Advanced Signal and Imaging
Sciences, Lawrence Livermore National Laboratory, November 16-17, 2006
Super-Resolution Algorithmsfor Ultrasonic
Nondestructive EvaluationImaging
Grace A. Clark (EE/EETD)
Jessie A. Jackson (EE/DSED)
Steven E. Benson (ME/MMED)
This work was performed under the auspices of the U.S. Department of Energy by the University ofCalifornia, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.
November 16-17, 2006
ENG-03-0051-0 2Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
This document was prepared as an account of work sponsored by an agency of the
United States Government. Neither the United States Government nor the University ofCalifornia nor any of their employees, makes any warranty, express or implied, or
assumes any legal liability or responsibility for the accuracy, completeness, or
usefulness of any information, apparatus, product, or process disclosed, or represents
that its use would not infringe privately owned rights. Reference herein to any specificcommercial product, process, or service by trade name, trademark, manufacturer, or
otherwise, does not necessarily constitute or imply its endorsement, recommendation, or
favoring by the United States Government or the University of California. The views andopinions of authors expressed herein do not necessarily state or reflect those of the
United States Government or the University of California, and shall not be used for
advertising or product endorsement purposes.
Disclaimer and Auspices Statements
This work was performed under the auspices of the U.S. Department of Energy by Universityof California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.
ENG-03-0051-0 3Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Go Boilers!!!
ENG-03-0051-0 4Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Agenda
• Problem Definition:- Ultrasonic NDE measurements- The spatial resolution problem
• Impulse Response Estimation for Enhancing Spatial Resolution- Mitigate “ringing” due to the transducer and
propagation paths
• Bandlimited Spectrum Extrapolation for Super-Resolution
• Examples of Processing Results
ENG-03-0051-0 5Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Ultrasonic Pulse-Echo Signals (A-Scans) Are DistortedBy the Transducer and the Propagation Paths (“Ringing”)
Grace Clark
PulseGenerator Amplifier Lowpass
FilterComputer
Electrical Pulse u(t)
time
xy
z
Transducer
Water Tank
Layered Material Being Insonified
!
"Time Distance
A-Scan x(t)
t , z
The Ideal Reflection
Is An ImpulseSequence
t , z
FrontSurface
InterfaceBack Surface
ENG-03-0051-0 6Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Ultrasonic Pulses Are Bandlimited by the Transducer ==> The Pulses “Ring”, Reducing Spatial Resolution
y(t) = Reflected Pulse
|Y(f)|2 = DFTof the ReflectedPulse
Front Reflection:
Flaw Reflection:
Back Reflection:
ENG-03-0051-0 7Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
We Define Ultrasonic A-, B-, and C-Scans Used inNondestructive Evaluation (NDE) Studies: Grace Clark
t , z
A-Scan x(t)(A Single Waveform)
B-Scan(Family of A-Scans)
C-Scan(Horizontal Slice At Depth z: Use
A Time Gate)
3D Volume(Family of B-Scans)
x
y
x
z
xy
zx
y
zx
y
z
yx
z
!
"Time Distance
ENG-03-0051-0 8Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
The Reference Scatterer is Chosen to Provide theTransducer / Path Response in the Absence of a Flaw
Desired properties of the reference scatterer:• Reflects back most of the energy• Resembles some feature associated with the
flaw environment
ReferenceSignal
x(t) y(t)
Front or BackSurface Reference
Flaw
ReferenceSignal
x(t) y(t)
Corner ReflectorReference
Flaw
ENG-03-0051-0 9Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
System Identification: Estimate the Impulse ResponseGiven: and Estimate:
System+
+System Model
+-
ModelParameterEstimation
Input Signal(Reference) Output Signal
Noise
!
x(t)
!
y(t)
!
u(t)
!
n(t)
!
ˆ u (t)Estimated
Output
Error
!
e t( ) = u t( ) " ˆ u t( )
!
e t( )
!
u(t)
!
h(t)
!
ˆ h (t)
!
x(t)
!
u(t)
!
ˆ h (t)
!
ˆ h (t)
ENG-03-0051-0 10Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
The Inverse Problem Is Very Difficult We Must Regularize the Problem
• Ill-Posed (Infinite Number of possible solutions)
• Bandlimited Transducer Spectral Response
• Ill-Conditioned - Numerical Errors Due to Spectral Zeros
ENG-03-0051-0 11Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
The System Model and Processing AlgorithmsAre Summarized in Block Diagrams
Pre-Process-
ing
System Identification
(Wiener)
Band-LimitedSpectrum
Extrapolation!
x0t( )
!
u0t( )
!
x t( )
!
u t( )
!
ˆ h t( )
!
ˆ h e
t( )
h(t)System +
!
0
!
h(t)
!
tFront BackFlaw
!
x t( )
!
u t( )
!
n t( )
!
y t( )
System Model
Processing Algorithms
The Ideal Impulse Responseis a Series of Delta Functions
EstimatedImpulse Response
Spectrum ExtrapolatedEst. of Impulse Response
Grace Clark
ENG-03-0051-0 12Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
We Use Bandlimited Spectrum ExtrapolationTo Improve Spatial Resolution
!
h(t)
!
H( f )
!
f
Ideal Measured or Estimated
!
h(t)
!
t
Ideal Impulse Response
Ideal Spectrum
!
ˆ H ( f )
!
f
!
f1
!
f2
RegionWe
Trust
Measured orEstimated Spectrum
!
ˆ h (t)
!
t
Measured orEstimated Impulse
Response
ENG-03-0051-0 13Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Complex Variable Theory Gives Us a Solid Theoretical Basis for Spectrum Extrapolation
• Our temporal signals have bounded support:- They are transient (finite length) signals in the time domain
• The Fourier Transform of a signal with bounded supportis ANALYTIC (continuous, all derivatives exist).
• If any analytic function in the complex plane is known exactly in an arbitrarily small (but finite) region of thatplane, then the entire function can be found (uniquely)by ANALYTIC CONTINUATION.
!
ˆ H ( f )
!
f
!
f1
!
f2
RegionWe
Trust
ENG-03-0051-0 14Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Analytic Continuation Algorithms are Hypersensitive to Noise - Must Regularize
• Prior knowledge can be used as constraints to regularizethe problem
• Iterative algorithms (method of successive approximations)are slow, not unique, but can incorporate constraints.
• Non-iterative algorithms are faster, but can’t usuallyincorporate constraints.
• Often, it is not necessary to determine the inverse of the distortion operator- Good for nonlinear or time-varying operators
ENG-03-0051-0 15Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
We Use an Iterative Algorithm for Regularized Analytic Continuation• Estimate the impulse response at the next iteration as a
function F of the impulse response at the last iteration:
• Iterate between the time and frequency domains(Method of Alternating Orthogonal Projections)
• Convergence is proved using contraction mapping theoremsfrom functional analysis
• Use an “adaptive algorithm” that assumes the impulse responseto be a sequence of impulses - constrain the time domainsignal to be an impulse train:
!
hk+1(t) = Fh
k(t), for k = 0,1, 2,L
!
h(t) = ci
i
" # t $ ti( )
!
u(t) = ci
i
" x t # ti( ) + n(t)!
h(t)
!
t
Ideal Impulse Response
ENG-03-0051-0 16Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
We Constrain the Temporal and Spectral SupportUsing Projection Operators
TemporalProjectionOperators
!
PT(k) = Envelope
X(k)
max X(k)
" # $
% & '
Spectral ProjectionOperators
Tapered
Rectangular
Rectangular
Adaptive
ENG-03-0051-0 17Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
ith Iteration of the Spectrum Extrapolation Algorithm:Alternating Orthogonal Projections, w/Adaptive Algorithm
ENG-03-0051-0 18Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
We Constructed a “Phantom” Part - Aluminum BlockContaining Flat-Bottom Holes
ENG-03-0051-0 19Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
We Can Combine CAD Models With 3-D DataWe Can Combine CAD Models With 3-D DataTo Clarify Ultrasonic Evaluation ResultsTo Clarify Ultrasonic Evaluation Results
3-D data and CAD Model-Solid
3-D data and CAD Model-Lines
3-D Ultrasonic Data Set
ENG-03-0051-0 20Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
A-scan and B-scan Data Show that Material Interface Reflections Are Blurred Because of Transducer Ringing
ENG-03-0051-0 21Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
System Identification and Spectrum Extrapolation ResultsAre Summarized for the Flat-Bottom Hole Phantom Signals
ENG-03-0051-0 22Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Graphite Fiber Composite Material: ThicknessMeasurements from Superimposed Layer Reflections
The layer thicknesses are muchsmaller than the transducer
ring-down time
ENG-03-0051-0 23Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Ultrasonic Pulse-Echo Signals Are Distorted by theTransducer and the Propagation Paths
Grace Clark
Welds AreScanned forPenetrationThickness
Blank
FrontTransducer
Back
Time (Proportional to Distance)
Raw SignalFront
EstimatedImpulse
Response
Bandwidth-Extrapolated
ImpulseResponse
Back
Front
FrontBack
Back
ENG-03-0051-0 24Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Adhesive Thickness MeasurementsRequire Resolved Layer Reflections
ENG-03-0051-0 25Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Adhesive Thickness Measurements fromSuperimposed Layer Reflections
!
x(t)
!
ˆ h (t)
!
u(t)
!
ˆ h e(t)
The layer thickness << Transducer ring-down time
TransducerRing-Down
ENG-03-0051-0 26Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Conclusions
• We have MATLAB software for these algorithms- From a recent Engineering Techbase project
• Future work: New programmatic applications- Contact the author
This work was performed under the auspices of the U.S. Department of Energy bythe University of California, Lawrence Livermore National Laboratory under ContractNo. W-7405-ENG-48.
Contingency VG’s
Grace A. Clark
ENG-03-0051-0 28Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
Our Objective is to Improve Temporal Resolutionby Extrapolating Spectra• The transducer bandlimits our signals
- System identification solutions are not unique- System identification solutions are valid only in a
finite frequency interval [f1, f2]. They give us the optimal least squares solution, given the bandwidth of the transducer.
- We can never obtain narrow impulses in the time domain
• We wish to extrapolate spectra beyond [f1, f2]. - This can allow us to obtain better approximations to
impulses in the time domain.
• We propose to extrapolate the spectra of:
!
ˆ h t( )
!
u t( ) The measured pulse-echo signalThe estimated impulse response
ENG-03-0051-0 29Clark-11/14/06, UCRL-CONF-217116 Grace A. Clark, Ph.D.
We Use a Reference Scatterer to Help Remove Distortion:Conceptually, This is a “System Identification” Problem
!
G( f )SendingTrans-ducer
!
TF ( f )
ForwardPropagationPath (BeamSpreading)
!
PF ( f )
ScatteringFrom Flaw
!
H( f )
ReturnPropagation
Path(SphericalSpreading)
!
PR ( f )
ReceivingTrans-ducer
!
TR ( f )
!
Y ( f )
Experiment to Measure the Scattered Signal
!
Y ( f )
Experiment to Measure the Reference Signal
!
X( f )
!
G( f )SendingTrans-ducer
!
TF ( f )
ForwardPropagationPath (BeamSpreading)
!
PF ( f )
ReferenceScatterer
!
HR ( f ) "1
ReturnPropagation
Path(SphericalSpreading)
!
PR ( f )
ReceivingTrans-ducer
!
TR ( f )
!
X( f )
Conceptually:
!
Y ( f )
X( f )=TF ( f )PF ( f )H( f )PR ( f )TR ( f )
TF ( f )PF ( f ) (1) PR ( f )TR ( f )" H( f )
F#1
$ % & & h(t)