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Application of Image Restoration Technique in Flow Scalar Imaging
Experiments
Guanghua WangCenter for Aeromechanics Research
Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin
April 28th, 2003
Flow scalar imaging experiments
! Resolution requirements
" λv and λD: smallest local length scales
! Resolution restrictions" CCD camera pixel spacing/size;
" Imaging system blurring effect (especially for FAST optics);
! In this project#Using image restoration technique to
correct imaging system blurring effect;
#Improve resolution and dissipation measurement accuracy;
Introduction
20 40 60 80 100 120
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40
60
80
100
120
20 40 60 80 100 120
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40
60
80
100
120
Scalar Dissipation
Acetone PLIF image
4/321
4/3
Re
Re−−
−
∝
∝
δ
δ
δλδλ
ScD
V
PLIF (Planar Laser Induced Fluorescence) image Red1/2=9600, Sc=1.5, [Tsurikov, 2002]
! Blurring model o(x,y) = i(x,y)**h(x,y) + n(x,y)! True image o(x,y) Flow Scalar field! LSI Filter h(x,y) Point Spread Function (PSF) of imaging system! Noise n(x,y) Additive noise, i.e. CCD camera readout noise
Inverse problem:
Blurring Model
# How to get o(x,y)o(x,y) ?" Known i(x,y) i(x,y) and PSF h(x,y)h(x,y)
" Prior knowledge of o(x,y) o(x,y) and n(x,y)n(x,y)
Prior Knowledge of the PLIF Image
! For acetone PLIF, differential cross section is 10-24 cm2/sr! High signal # Photon counting statistics noise is dominant;! True image o(x,y) # Shot-noise limited;! Poisson noise = Shot-Noise limited
From N2 tanks
Valve
Flow meter
Acetone bubblers
Gas heater
Fog machine Coflow blower
PIV camera
Jet facility
PLIF camera
Laser sheets
Sheet forming optics
PIV laser
PLIF laser
Timing electronics
Image acquisition computers
PLIF (Planar Laser Induced Fluorescence) Experiment Setup [Tsurikov, 2002]
Point Spread Function (PSF) Measurement
! SRFm & SRFcf: Measured & Curve-fitted
Step Response Function! LSF: Line Spread Function
! PSF: Point Spread Function
! MTF: Modulation Transfer Function MTFPSF
LSFSRFSRFtransformFourierIsotropic
dxdcf
fitcurvem
→ →
→ →
Scanning knife edge technique
References:"N.T. Clemens (2002)"W.J. Smith (2000)"T.L. Williams (1999)
Measured SRF, curve-fitted SRFcf and LSFfor a Nikon 105mm f/2.8 [Tsurikov, 2002]
x (mm)
SR
F(x
)
LSF
(x)
0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-8
-7
-6
-5
-4
-3
-2
-1SRF(x) MeasuredSRF(x) Curve fitLSF(x)
R-L-EM Algorithm! Richardson-Lucy Expectation
Maximization (R-L-EM)
! Richardson (1972) and Lucy (1974)
! Well developed in 1990’s for HST
(Hubble Space Telescope) image restoration" It converges to the Maximum Likelihood
(ML) solution for Poisson statistics in the image;
" The restored image is non-negative and flux is conserved at each iteration;
" The restored image is robust against small errors in the PSF;
! Constraints:" Non-negativity;
" Total-Flux conserved;" Finite spatial support;
" Band-limited;
1+= kk
0
),()0(
=k
yxo
∗
∗= ∗+ ),(
),(),(
),(),(),(
)()()1( yxh
yxoyxh
yxiyxoyxo
kkk
),()1( yxo k+
Results – Initial conditions
2.39E-01
7.72E-02
Observed Concentration field
-3-2
-10
12
3
-4
-2
0
2
40
0.05
0.1
0.15
0.2
Measured PSF
RR--LL--EM EM DeconvolutionDeconvolution
Stopping Rules
Noise Handling
O(x,y)O(x,y)
Starck, Pantin and Murtagh (2002)Molina, Nunez, Cortijo and Mateos (2001)Hanisch, White and Gilliland (1997)
Results – Convergence and Conservation
Number of Iterations
Rel
ativ
eE
rror
50 100 150 200 250 300 35010-3
10-2
10-1
100
Number of Iterations
Rat
ioof
To
talF
lux
50 100 150 200 250 300 3500.995
0.996
0.997
0.998
0.999
1
1.001
1.002
1.003
1.004
1.005
∑∑
=
yx
yx
k
yxi
yxo
RatioFluxTotal
,
,
)(
),(
),(
The blurring should not alter the total number of photons detected.
ε≤−+
),(
),(),()(
)()1(
yxo
yxoyxok
kk
Where ε is a small number"V. M. R. Banham and A. K. Katsaggelos (1997)
Results – Dissipation fields
ObservedDissipation
field
RestoredDissipation
field
Pixel
Dis
sip
atio
n
10 20 30 40 50 60 70 80 90 100 110 120
0
0.0001
0.0002
0.0003
0.0004
0.0005 Dissipation - RestoredDissipation - Observed
Pixel
Dis
sip
atio
n
10 20 30 40 50 60 70 80 90 100 110 120
0
0.0001
0.0002
0.0003
0.0004Dissipation - RestoredDissipation - Original
Vertical cut
Horizontal cut
3.51E-04
1.13E-05
3.51E-04
1.13E-05
Results – Dissipation fields
Observed Restored
Pixel
Dis
sip
atio
n
10 20 30 40 50 60 70 80 90 100 110 1200
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006 Dissipation - RestoredDissipation - Original
5.95E-04
1.92E-05
5.95E-04
1.92E-05
1.08E-03
3.49E-05
1.08E-03
3.49E-05
Pixel
Dis
sip
atio
n
10 20 30 40 50 60 70 80 90 100 110 1200
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
Dissipation - RestoredDissipation - Original
Cross-cut profile
What is the impact?
Buch and Dahm (1996), Sc=2075, Re= 2100, Fig.13 and Fig.28(b)
Conclusions and Future Work
! R-L-EM algorithm works well for PLIF image restoration" PLIF image is shot-noise limited (Poisson noise);" Measured PSF by scanning knife edge technique;
! Preliminary PLIF image restoration results show:" Peak dissipation rate is affected most, especially for thin and
clustered dissipation layers;! Image restoration techniques can be used to
" Improve resolution and dissipation measurement accuracy;" Especially for thin and/or clustered dissipation layers;
! Future work" Multi-Channel blind deconvolution # better PSF" Multi-Level deconvolution (i.e. wavelet-Lucy ) # better noise
handling;" Stopping rules # utilizing 2D scalar structure information;
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