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Physics-Based Signal and Image ProcessingPhysics-Based Signal and Image Processing
Prof. Eric Miller, Dr. Basak Ulker KarbeyazDept. of Electrical and Computer Engineering
Northeastern [email protected]. Robin Cleveland
Dept. Mechanical and Aeronautical Eng.Boston [email protected]
Prof. Eric Miller, Dr. Basak Ulker KarbeyazDept. of Electrical and Computer Engineering
Northeastern [email protected]. Robin Cleveland
Dept. Mechanical and Aeronautical Eng.Boston [email protected]
OverviewOverview
Introduction to physics-based signal and image processingOverview of research projects and collaboratorsRepresentative effort
Quantitative ultrasound imaging for guidance of cancer treatment
Future work
Introduction to physics-based signal and image processingOverview of research projects and collaboratorsRepresentative effort
Quantitative ultrasound imaging for guidance of cancer treatment
Future work
Physics Based Signal ProcessingPhysics Based Signal Processing
Goal: extract information regarding internal structure
ImageObjects: what & where
Data from transducers on the boundary
Time or frequency domainProblems
Sparse noisy dataLimited apertureCluttered backgroundComplicated mapping from unknowns to data
ApplicationsUltrasoundDiffuse optical tomographyResistance tomography
Goal: extract information regarding internal structure
ImageObjects: what & where
Data from transducers on the boundary
Time or frequency domainProblems
Sparse noisy dataLimited apertureCluttered backgroundComplicated mapping from unknowns to data
ApplicationsUltrasoundDiffuse optical tomographyResistance tomography
The FrameworkThe Framework
Computational sensormodels
Experimentallaboratory facilities
Informationextraction methods
Our strengthsWhere we look for collaboration
CollaborationCollaboration
Wide variety of institutionsOther universities (BU, Ole Miss, U Toronto)Industry (Textron, BAE/Alphatech, Coherent)Hospitals (MGH, BWH)Gov’t labs (INL)
Wide variety of ways we work togetherA place for my students to immerse themselves in the problemIntellectual exchange (problem statements, data, models)Joint proposalsFunding
Wide variety of institutionsOther universities (BU, Ole Miss, U Toronto)Industry (Textron, BAE/Alphatech, Coherent)Hospitals (MGH, BWH)Gov’t labs (INL)
Wide variety of ways we work togetherA place for my students to immerse themselves in the problemIntellectual exchange (problem statements, data, models)Joint proposalsFunding
Geometric Imaging MethodsGeometric Imaging Methods
Discrete “objects” against (possibly) inhomogeneous backgroundMany examples
Defects/crack in NDETumors in medical imagingTreated regions in image guided surgeryAreas of functional brain activityPollution plumes in environmental remediation
Discrete “objects” against (possibly) inhomogeneous backgroundMany examples
Defects/crack in NDETumors in medical imagingTreated regions in image guided surgeryAreas of functional brain activityPollution plumes in environmental remediation
Geometric Methods (cont)Geometric Methods (cont)
Option 1Estimate many, many pixels and then “segment” out objectsMany difficulties if a priori you have an “object” problem
Option 2Use data to determine size, shape, perhaps number, and contrast of objects as well as something about backgroundFar fewer geometric unknowns than pixelsBetter adapted to underlying problem
Option 1Estimate many, many pixels and then “segment” out objectsMany difficulties if a priori you have an “object” problem
Option 2Use data to determine size, shape, perhaps number, and contrast of objects as well as something about backgroundFar fewer geometric unknowns than pixelsBetter adapted to underlying problem
UltrasoundUltrasound
Medical imaging & nondestructive evaluation (NDE)Scan transmitter and receiverBuild up an image of
“Reflectivity”Sound speedDensityAbsorption
Time-of-flight pretty easyMore sophisticated methods not so simple
Medical imaging & nondestructive evaluation (NDE)Scan transmitter and receiverBuild up an image of
“Reflectivity”Sound speedDensityAbsorption
Time-of-flight pretty easyMore sophisticated methods not so simple
Skin
Fig. 0.1. Focused Ultrasound Surgery.
Ultrasound lesionUltrasoundtransducer
Target organ
Thanks to Prof. Ron Roy of BU
An Ultrasound ProblemAn Ultrasound Problem
• Ultrasonic image guided cancer treatmentapplication
• High intensity focused ultrasound (HIFU) transducer heats and kills tissue
• Necrosis causes changes in tissue properties: sound speed, attenuation, and maybe density
• Each focal area is small compared to the tumor and cigar shaped
• Can we use ultrasound (as opposed to MRI) to monitor treatment?
• Conventional image formation not adequate
• Brute force inverse scattering approachnot feasible
• Exploit prior information to obtain tractable solution
Problem FormulationProblem Formulation
The pressure signal scattered from an inhomegenity of sound speed attenuation and density in homogenous medium is given by:
Lossy, homogenous background.Contrast of the scatterer is weak. BORN Approximation is valid.
The pressure signal scattered from an inhomegenity of sound speed attenuation and density in homogenous medium is given by:
Lossy, homogenous background.Contrast of the scatterer is weak. BORN Approximation is valid.
ps (r,ω ) = − ks2 (ro,ω )G(r,ro,kb (ω ))
V '∫ pb (r,ro,kb (ω ))d 3ro
− σ p (ro )V '∫ ∇G(r,ro,kb (ω ))•∇pb (r,ro,kb (ω ))d 3ro
Density: σ p = ln 1+ρp (r)ρb
⎛
⎝⎜⎞
⎠⎟ks
2 = cp (r) −2ω 2
cb3
⎡
⎣⎢
⎤
⎦⎥ +α p (r,ω ) − j
2ωcb
⎡
⎣⎢
⎤
⎦⎥
kb2 =
ω 2
cb2
⎡
⎣⎢
⎤
⎦⎥ − j
2ωαb (ω )cb
⎡
⎣⎢
⎤
⎦⎥
Cylindrical TransducerCylindrical Transducer
Integral can not be solved analytically.It is oscillatory and numerical integration is not attractiveApproximation procedure:
Change integral from from dz to drExploit smallness of φDo φ integral first (analytically)Project slowly varying r integral onto Legendre basisIntegrate expansion analytically
Details depend on observation point where data are collectedThe computation time is 0.3 seconds in Matlab per observation point as opposed to 3 hours using numerical techniques.Validated with experimental data
Integral can not be solved analytically.It is oscillatory and numerical integration is not attractiveApproximation procedure:
Change integral from from dz to drExploit smallness of φDo φ integral first (analytically)Project slowly varying r integral onto Legendre basisIntegrate expansion analytically
Details depend on observation point where data are collectedThe computation time is 0.3 seconds in Matlab per observation point as opposed to 3 hours using numerical techniques.Validated with experimental data
φb (rp ) =R
4πe− jk (rp cos(φp )−R cos(φ ))2 +(rp sin(φp )−R sin(φ ))2 +(zp − z )2
(rp cos(φp )−R cos(φ ))2 +(rp sin(φp )−R sin(φ ))2 +(zp − z )2S∫ dφdz
Object ModelObject Model
Model treatment region as an ellipsoid
Linearized physical model (significant effort modeling real transducers)Estimate ellipsoid parameters from data
Model treatment region as an ellipsoid
Linearized physical model (significant effort modeling real transducers)Estimate ellipsoid parameters from data
DUT (r − c)2
2≤ 1
c = xo, yo, zo[ ]TD = diag(1 a ,1 b,1 c)U = F(θ1,θ2 ,θ3)
ab
(xo , yo , zo )
Object Model (2)Object Model (2)Formally, the contrast function for an ellipsoidal perturbation is defined as
Step is not smooth and we would like to use a gradient-dent type method for parameter estimation. Employ smooth version of step function
Formally, the contrast function for an ellipsoidal perturbation is defined as
Step is not smooth and we would like to use a gradient-dent type method for parameter estimation. Employ smooth version of step function
cp r( )= cpu 1− DUT (r − c)2
2( ) u x( )=1 x ≥ 00 else⎧⎨⎩
cp r( )= exp(Msech(α DUT (r − c)2
16)) −1
exp(M) −1
ProcessingProcessing
One ellipse for each physical property:Sound speedAttenuationDensity
Model is nonlinear in ellipsoid parameters but differentiableUse Gauss-Newton method to estimate parameters from data assuming least-squares cost function (Gaussian noise)
One ellipse for each physical property:Sound speedAttenuationDensity
Model is nonlinear in ellipsoid parameters but differentiableUse Gauss-Newton method to estimate parameters from data assuming least-squares cost function (Gaussian noise)
Numerical ExperimentNumerical Experiment
• Linear array of 5 point sources• ROI is 5mm x 5mm x 5 mm
(16 x 16 x 16)• 6 frequencies between 300
kHz-425kHz.• Array scanned across aperture
(6 measurement points)• Homogeneous, lossy
background • Power law attenuation• Homogeneous sound speed,
density and attenuation anomaly
• Unknown contrasts • 25dB SNR • cb = 1551 m/s, αbo =3.6 Np/m,• ρb=1045 kg/m3
ResultsResults
cp= 3.5m/s αpo= 3.5 Np/m
Estimated Speed
True
Estimated Density
ρp= 5 kg/m3
Estimated Attenuation
Initial guess
Real Data ResultsReal Data Results((Bovine Serum Albumin) BSA PhantomBovine Serum Albumin) BSA Phantom
Enhanced ImagePhotograph of the BSA Phantom
H= 125 mm
R=65 mm
z
x
ResultsResults
cp= 5m/scp= 20m/sαpo= 440 Np/m
cp= 5.8m/sαpo= 46.34 Np/m αpo= 48.7 Np/m
Initial Estimate True
Future Opportunities:Driving ApplicationsFuture Opportunities:Driving Applications
Medical Bio-optical: Cancer screening, brain imaging, molecular imaging, microscopy, …Acoustic: continuation of ultrasound work
EnvironmentalUnexploded ordnanceMonitor and control of the fate and transport of species moving through the underground
Homeland SecurityExplosives detection, baggage inspection, …
Medical Bio-optical: Cancer screening, brain imaging, molecular imaging, microscopy, …Acoustic: continuation of ultrasound work
EnvironmentalUnexploded ordnanceMonitor and control of the fate and transport of species moving through the underground
Homeland SecurityExplosives detection, baggage inspection, …
Future Opportunities:Technical IssuesFuture Opportunities:Technical Issues
Non-trivial multi-sensor processing for single, coherent characterization of the mediumNew physical models (e.g. flow and transport)Imaging over space and timeNew methods for characterizing shapeIntegration of experiment and theory
Non-trivial multi-sensor processing for single, coherent characterization of the mediumNew physical models (e.g. flow and transport)Imaging over space and timeNew methods for characterizing shapeIntegration of experiment and theory
Future Opportunities:Teaming and CollaborationFuture Opportunities:Teaming and Collaboration
Success in the present (and likely future) funding environment requires real collaborationTeams of people with expertise in
Analytics ExperimentsComputationDriving applications
Drawn from academia, industry, and government labsExist opportunities out there (NSF, NIH, DoD) for well-seeded groups to succeed in acquisition of large scale, long term, interesting research funding
Success in the present (and likely future) funding environment requires real collaborationTeams of people with expertise in
Analytics ExperimentsComputationDriving applications
Drawn from academia, industry, and government labsExist opportunities out there (NSF, NIH, DoD) for well-seeded groups to succeed in acquisition of large scale, long term, interesting research funding