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Application of Image Restoration Technique in Flow Scalar Imaging ExperimentsGuanghua WangCenter for Aeromechanics Research Department of Aerospace Engineering and Engineering Mechanics The University of Texas at AustinApril 28th, 2003Flow scalar imaging experiments! Resolution requirements" λvand 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;Introduction20 40 60 80 100 1202040608010012020 40 60 80 100 12020406080100120Scalar DissipationAcetone PLIF image4/3214/3ReRe−−−∝∝δδδλδλScDVPLIF (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 noiseInverse problem:Blurring Model# How to get o(x,y)o(x,y)?" Known i(x,y) i(x,y) and PSFh(x,y)h(x,y)" Prior knowledge of o(x,y) o(x,y) andn(x,y)n(x,y)Prior Knowledge of the PLIF Image! For acetone PLIF, differential cross section is 10-24cm2/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 FunctionMTFPSFLSFSRFSRFtransformFourierIsotropicdxdcffitcurvem→→→→Scanning knife edge techniqueReferences:"N.T. Clemens (2002)"W.J. Smith (2000)"T.L. Williams (1999)Measured SRF, curve-fitted SRFcfand LSFfor a Nikon 105mm f/2.8 [Tsurikov, 2002]x(mm)SRF (x)LSF(x)0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.200.10.20.30.40.50.60.70.80.91-8-7-6-5-4-3-2-1SRF(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+= kk0),()0(=kyxo∗∗=∗+),(),(),(),(),(),()()()1(yxhyxoyxhyxiyxoyxokkk),()1(yxok+Results – Initial conditions2.39E-017.72E-02Observed Concentration field-3-2-10123-4-202400.050.10.150.2Measured PSFRR--LL--EM EM DeconvolutionDeconvolutionStopping RulesNoise HandlingO(x,y)O(x,y)Starck, Pantin and Murtagh (2002)Molina, Nunez, Cortijo and Mateos (2001)Hanisch, White and Gilliland (1997)Results – Convergence and ConservationNumber of IterationsRelative Error50 100 150 200 250 300 35010-310-210-1100Number of IterationsRatio of Total Flux50 100 150 200 250 300 3500.9950.9960.9970.9980.99911.0011.0021.0031.0041.005∑∑=yxyxkyxiyxoRatioFluxTotal,,)(),(),(The blurring should not alter the total number of photons detected.ε≤−+),(),(),()()()1(yxoyxoyxokkkWhere εis a small number"V. M. R. Banham and A. K. Katsaggelos (1997)Results – Dissipation fieldsObservedDissipation fieldRestoredDissipation fieldPixelDissipation10 20 30 40 50 60 70 80 90 100 110 12000.00010.00020.00030.00040.0005Dissipation - RestoredDissipation - ObservedPixelDissipation10 20 30 40 50 60 70 80 90 100 110 12000.00010.00020.00030.0004Dissipation - RestoredDissipation - OriginalVertical cutHorizontal cut3.51E-041.13E-053.51E-041.13E-05Results – Dissipation fieldsObserved RestoredPixelDissipation10 20 30 40 50 60 70 80 90 100 110 12000.00010.00020.00030.00040.00050.0006Dissipation - RestoredDissipation - Original5.95E-041.92E-055.95E-041.92E-051.08E-033.49E-051.08E-033.49E-05PixelDissipation10 20 30 40 50 60 70 80 90 100 110 12000.00020.00040.00060.00080.0010.0012Dissipation - RestoredDissipation - OriginalCross-cut profileWhat 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


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UT EE 381K - Application of Image Restoration

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