Physics-Based Signal and Image Processing

Transkript

1 Physics-Based Signal and Image Processing Prof. Eric Miller, Dr. Basak Ulker Karbeyaz Dept. of Electrical and Computer Engineering Northeastern University Prof. Robin Cleveland Dept. Mechanical and Aeronautical Eng. Boston University

2 Overview Introduction to physics-based signal and image processing Overview of research projects and collaborators Representative effort Quantitative ultrasound imaging for guidance of cancer treatment Future work

3 Physics Based Signal Processing Goal: extract information regarding internal structure Image Objects: what & where Data from transducers on the boundary Time or frequency domain Problems Sparse noisy data Limited aperture Cluttered background Complicated mapping from unknowns to data Applications Ultrasound Diffuse optical tomography Resistance tomography

4 The Framework Computational sensor models Information extraction methods Experimental laboratory facilities Our strengths Where we look for collaboration

5 Collaboration Wide variety of institutions Other universities (BU, Ole Miss, U Toronto) Industry (Textron, BAE/Alphatech, Coherent) Hospitals (MGH, BWH) Gov t labs (INL) Wide variety of ways we work together A place for my students to immerse themselves in the problem Intellectual exchange (problem statements, data, models) Joint proposals Funding

6 Geometric Imaging Methods Discrete objects against (possibly) inhomogeneous background Many examples Defects/crack in NDE Tumors in medical imaging Treated regions in image guided surgery Areas of functional brain activity Pollution plumes in environmental remediation

7 Geometric Methods (cont) Option 1 Estimate many, many pixels and then segment out objects Many difficulties if a priori you have an object problem Option 2 Use data to determine size, shape, perhaps number, and contrast of objects as well as something about background Far fewer geometric unknowns than pixels Better adapted to underlying problem

8 Ultrasound Ultrasound transducer Ultrasound lesion Medical imaging & nondestructive evaluation (NDE) Scan transmitter and receiver Build up an image of Reflectivity Sound speed Density Absorption Time-of-flight pretty easy More sophisticated methods not so simple Skin Target organ Fig Focused Ultrasound Surgery. Thanks to Prof. Ron Roy of BU

9 An Ultrasound Problem Ultrasonic image guided cancer treatment application 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 approach not feasible Exploit prior information to obtain tractable solution

10 Problem Formulation The pressure signal scattered from an inhomegenity of sound speed attenuation and density in homogenous medium is given by: p s (r,ω) = k 2 s (r o,ω)g(r,r o,k b (ω)) p b (r,r o, k b (ω))d 3 r o V ' σ p (r o ) G(r,r o,k b (ω)) p b (r,r o,k b (ω))d 3 r o V ' Lossy, homogenous background. Contrast of the scatterer is weak. BORN Approximation is valid. Density: σ p = ln 1 + ρ p(r) ρ b k 2 s = c p (r) 2ω 2 3 c b k 2 b = ω 2 2 c j 2ωα b (ω) b c b + α p(r,ω) j 2ω c b

11 Cylindrical Transducer φ b (r p ) = R jk (r e p cos(φ p ) R cos(φ ))2 +(r p sin(φ p ) R sin(φ )) 2 +(z p z) 2 4π (r p cos(φ p ) R cos(φ )) 2 +(r p sin(φ p ) R sin(φ )) 2 +(z p z) S 2 dφdz Integral can not be solved analytically. It is oscillatory and numerical integration is not attractive Approximation procedure: Change integral from from dz to dr Exploit smallness of φ Do φ integral first (analytically) Project slowly varying r integral onto Legendre basis Integrate expansion analytically Details depend on observation point where data are collected The computation time is 0.3 seconds in Matlab per observation point as opposed to 3 hours using numerical techniques. Validated with experimental data

12 Object Model Model treatment region as an ellipsoid b a (x o, y o, z o ) DU T (r c) c = [ x o, y o, z ] T o D = diag(1 a,1 b,1 c) U = F(θ 1,θ 2,θ 3 ) Linearized physical model (significant effort modeling real transducers) Estimate ellipsoid parameters from data

13 Object Model (2) Formally, the contrast function for an ellipsoidal perturbation is defined as c p ( ()= r c p u 1 DU T 2 ) (r c) u x 2 ()= 1 x 0 0 else Step is not smooth and we would like to use a gradient-dent type method for parameter estimation. Employ smooth version of step function c p ()= r exp(msech(α DU T 16 exp(m) 1 (r c) 2 )) 1

14 Processing One ellipse for each physical property: Sound speed Attenuation Density Model is nonlinear in ellipsoid parameters but differentiable Use Gauss-Newton method to estimate parameters from data assuming leastsquares cost function (Gaussian noise)

15 Numerical 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 c b = 1551 m/s, α bo =3.6 Np/m, ρ b =1045 kg/m3

16 Results True Initial guess Estimated Speed Estimated Attenuation Estimated Density c p = 3.5m/s α po = 3.5 Np/m ρ p = 5 kg/m 3

17 Real Data Results (Bovine Serum Albumin) BSA Phantom R=65 mm H= 125 mm x z Photograph of the BSA Phantom Enhanced Image

18 Results Initial Estimate True c p = 20m/s c p = 5.8m/s c p = 5m/s α po = 440 Np/m α po = Np/m α po = 48.7 Np/m

19 Future Opportunities: Driving Applications Medical Bio-optical: Cancer screening, brain imaging, molecular imaging, microscopy, Acoustic: continuation of ultrasound work Environmental Unexploded ordnance Monitor and control of the fate and transport of species moving through the underground Homeland Security Explosives detection, baggage inspection,

20 Future Opportunities: Technical Issues Non-trivial multi-sensor processing for single, coherent characterization of the medium New physical models (e.g. flow and transport) Imaging over space and time New methods for characterizing shape Integration of experiment and theory

21 Future Opportunities: Teaming and Collaboration Success in the present (and likely future) funding environment requires real collaboration Teams of people with expertise in Analytics Experiments Computation Driving applications Drawn from academia, industry, and government labs Exist opportunities out there (NSF, NIH, DoD) for well-seeded groups to succeed in acquisition of large scale, long term, interesting research funding