Campuses:

Poster session

Thursday, October 20, 2005 - 4:30pm - 6:00pm
Lind 400
  • Regularization and Prior Error Distributions in Ill-posed

    Problems

    Jodi Mead (Boise State University)
    We will examine the validity of parameter estimates in ill-posed
    problems when errors in data and initial parameter estimates are
    from normal and non-normal distributions. Given appropriate
    initial parameter estimates and the data error covariance matrix, the
    covariance matrix for errors in initial parameter estimates can be
    recovered and highly accurate parameter estimates can be found. This
    approach allows the regularization to be varied with each parameter.
  • Ultrasound Breast Tomography with Full-Wave Non-Linear Inverse

    Scattering

    Michael Andre (University of California, San Diego)
    The fundamentals of medical ultrasound imaging have not changed since its
    inception 60 or more years ago. 180-degree pulse-echo backscatter is used for
    image formation without accounting for refraction, diffraction, multiple
    scattering, etc. Various forms of ultrasound computed tomography that
    incorporate the transmitted wave component have been proposed and investigated
    for many years with mixed success. These methods apply approximations of
    inverse scattering tomography: time-of-flight, Born, Rytov, Diffraction
    Tomography, etc. Techniscan Medical Systems (Salt Lake City, Utah) and the
    University of California, San Diego are beginning pre-clinical evaluation of a
    new system for breast imaging that applies novel inverse scattering methods to
    provide a unique method for calculating ultrasound characteristics of speed and
    attenuation of sound traveling through human tissue. We have developed an
    efficient inversion method for the coefficients of the partial differential
    equation that governs wave propagation in the human breast. The procedure is
    based on nonlinear minimization, fast computation of the forward problem and
    analytic computational formulas for actions of the Jacobian of the forward
    operator and its Hermitian adjoint. The goal of the development is to provide
    quantitative, high-resolution two- and three-dimensional ultrasonic imaging
    combined with unique information about tissue properties at sub millimeter
    resolution in an effort to improve diagnosis of breast cancer. Details of the
    imaging system design and the inversion method will be summarized. Sample
    images from human subjects and preliminary results in 26 patients with known
    breast masses will be presented.
  • Imaging of Physiological Properties of Human Skin from Spectral Reflectance Data
    Jakob Stamnes (University of Bergen)
    Joint with K.P. Nielsen, M. Biryulina, G.Ryzhikov, K.
    Stamnes, and L. Zhao.

    We present a new method, based on inverse radiative transfer
    modelling, for retrieving physiological parameters of human skin
    tissue from multi-spectral reflectance data. Whereas previous
    attempts of such retrievals have been based either on empirical
    formulas or simplified, inaccurate forward models, such as the
    Kubelka-Munk theory, our forward model is based on the
    discrete-ordinate solution of the radiative transfer equation, which
    is both fast and accurate. Examples are given of retrievals based on
    simulated reflectance data or in-vivo measurements.
  • Convergence of Approximations of Solutions to First-order Pseudodifferential Wave Equations with Products of Fourier Integral Operators
    Jerome Le Rousseau (Université d'Aix-Marseille I (Université de Provence))
    An approximation of the solution to a hyperbolic equation with
    a damping term is introduced. It is built as the composition of Fourier
    integral operators (FIO). We prove the convergence of this
    approximation in the sense of Sobolev norms as well as for the
    wavefront set of the solution. We apply the introduced method to
    numerically image seismic data.
  • Imaging Cardiac Activity by the D-bar Method for

    Electrical Impedance Tomography

    Jennifer Mueller (Colorado State University)
    Electrical Impedance Tomography (EIT) is an imaging technique that uses the
    propagation of electromagnetic waves through a medium to form an image. In
    medical EIT, current is applied through electrodes on the surface of the body,
    the resulting voltages are measured on the electrodes, and the inverse
    conductivity problem is solved numerically to reconstruct the conductivity
    distribution in the interior. Here results are shown from EIT data taken on
    electrodes placed around the circumference of a human chest to reconstruct a 2-D
    cross-section of the torso. The images show changes in conductivity during a
    cardiac cycle made from the D-bar reconstruction algorithm based on the 1996
    uniqueness proof of A. Nachman [Ann.Math. 143].
  • Ultrawideband Microwave Breast Cancer Detection: Beamforming for 3-D MRI-derived Numerical Phantoms
    Shakti Davis (University of Wisconsin, Madison)
    Microwave imaging has the potential to be a highly sensitive modality
    for breast cancer detection due to the dielectric-properties
    contrast that exists between malignant and normal breast tissue at
    microwave frequencies. One microwave imaging approach is to transmit
    ultrawideband (UWB) microwave pulses into the breast, record the
    scattered fields, and use radar methods such as beamforming to detect
    and localize significant scatterers such as tumors. We previously
    proposed a beamforming technique and demonstrated its accuracy and
    robustness for tumor detection using 2-D MRI-derived numerical breast
    phantoms (Davis, et. al, JEMWA, 17(2):357-381, 2003) and simple 3-D
    physical phantoms (Li, et. al, IEEE T-MTT, 52(8):1856-1865, 2004). In
    this poster we extend our investigation to 3-D MRI-derived numerical
    breast phantoms. These anatomically realistic breast phantoms
    represent a prone patient with an antenna array surrounding the
    breast. Small (properties in a region to represent a specified malignant-to-normal
    tissue contrast. We solve for backscattered fields at each antenna
    position using the FDTD-method and construct a 3-D image of scattered
    energy in the breast using our beamforming technique. The resulting
    images exhibit localized high-energy peaks within a few mm of the
    true tumor locations as expected. This work represents our first
    successful demonstration of detecting and localizing very small
    tumors in 3-D MRI-derived numerical breast models.
  • Iterative Solver for the Wave Equation in the Frequency Domain
    Rene-Edouard Plessix (The Shell Group)
    Joint work with Wim Mulder.

    To retrieve the long and short spatial frequencies of the velocity model from seismic data,
    several authors have proposed to work in the frequency-domain. The data are inverted per
    frequency going from the low to the high. This approach has been used for long
    offset data in two dimensional space. It relies on the solution of the wave equation in the
    frequency domain (Helmholtz equation). Whereas in two dimensional space, a direct solver of the frequency-domain
    wave equation provides an efficient method, in three dimensional space, this approach
    is not feasible because the linear system becomes too large. This difficulty may be
    overcome with an iterative solver for the Helmholtz equation.
    During his Ph. D work, Y. Erlangga has studied an iterative approach based on a
    preconditioned bicgstab (conjugate-gradient type) method. The efficiency of the method
    depends on the preconditioner. It was proposed to use a damped wave equation
    as a preconditioner and to approximate the inverse of the damped equation with a multigrid
    method. Strong damping is required for the preconditioner, otherwise the
    multigrid method does not convergence. Two-dimensional examples show that this approach is robust and that the number of iterations
    depends linearly on the frequency when the number of grid points
    per wavelength is kept constant. Thus, this approach provides a sub-optimal solution.
    In the poster, several numerical examples will be
    presented to assess the efficiency of the iterative approach.
    Its relevance for migration in two and three dimensions and for
    inversion algorithms will also be discussed.
  • Wideband Through-The-Wall Radar Imaging Experimentations
    Uttam Majumder (US Air Force Research Laboratory)
    The Center for Advanced Communications (CAC) at Villanova
    University
    along with Air Force Research Laboratory (AFRL) has conducted
    several
    preliminary experimentations on through-the-wall imaging and
    collected
    real data on different settings behind the wall using a
    newly-integrated
    RF instrumentation suite. The full-polarization, 2D aperture
    data measurements
    are taken using an Agilent network analyzer, Model ENA 5071B,
    implementing a
    step frequency waveform over a 2-3 GHz frequency range. The
    imaging room is
    a typical computer lab that has been lined with radar absorbing
    material.
    Three different arrangements of the room's contents are
    considered: empty scene,
    calibration scene, and populated scene. The empty scene allows
    measurement
    of the noise/clutter background and supports coherent
    subtraction with the other two scenes. The calibration scene
    contains
    isolated reflectors that may be used to determine a
    fully-polarimetric
    radiometric calibration solution for the experimental system.
    The populated scene contains a number of common objects such as
    a phone, computer, tables, chair and filing cabinet and a jug of
    saline solution.
    Data was collected each scene with and without a wall. The wall
    is composed of plywood and gypsum board on a wood frame.
    The antennas are mounted on a 2D scanner that moves the
    antennas along and adjacent to the wall and is
    controlled by the network analyzer.
    Two additional antennas are fixed to the scanner frame and act
    as bistatic receivers.
  • Progress in Quantitative Biomechanical Imaging
    Paul Barbone (Boston University)
    Joint work with Michael S. Richards, Nachiket H. Gokhale,
    Carlos Rivas Aroni, Ricardo Leiderman, Jeffrey C. Bamber,
    and Assad A. Oberai.

    It is widely recognized that tissue pathologies often change biomechanical properties.
    For instance, neoplastic tissue is typically highly vascularized, contains abnormal
    concentrations of extracellular proteins (i.e. collagen, proteoglycans) and has a high
    interstitial fluid pressure compared to most normal tissues. These differences in tissue
    microstructure effectively change a tissues response to mechanical stimuli. Our work
    focuses on noninvasively measuring and thereby imaging in vivo distributions of the
    biomechanical properties of soft tissues. The intended short term application of our
    work is the detection and diagnosis of breast cancer and other soft tissue pathologies.
    Our efforts include the development and computational implementation of
    mathematical models to describe soft tissue behavior, developing novel ultrasound techniques
    to accurately measure vector displacements of tissue deformation, the analysis of
    inverse problems associated with quantitative inference of material properties from
    measured displacements, and development of algorithms to solve those inverse problems.
    We present a combined ultrasound and image registration technique to quantitatively
    measure tissue response to mechanical manipulation. We further present several different mathematical models describing tissue responses
    for different experimental stimuli.
    Some of these models are motivated by microstructural considerations. Where possible,
    these model parameters are compared to values determined by independent mechanical
    testing.
  • Velocity Analysis in the Presence of Uncertainty
    Eric Dussaud (Rice University)
    Velocity Analysis resolves relatively long scales of earth
    structure, typically wavelengths larger than 500m. Migration produces
    images with length scales (wavelengths) on the order of 10's of m. In
    between these two scale regimes lies another, corresponding roughly to
    structures between 60 to 300m in extent, in which the resolution of
    velocity analysis is uncertain and the energy of images is small to
    non-existent. This work aims at assessing the impact on velocity analysis
    of uncertainty at these intermediate length scales, using ideas on time
    reversal and imaging in randomly inhomogeneous media developed by
    Papanicolaou and colleagues, in combination with velocity estimation
    methods of differential semblance type.
  • Nonlinear Inverse Scattering and Velocity Analysis
    William Symes (Rice University)
    Migration velocity analysis (MVA) can be viewed as a solution
    method for the linearized (Born) inverse scattering problem, in its
    reflection seismic incarnation. MVA is limited by the single scattering
    assumption - for example, it misinterprets multiply scattered waves - but
    it is capable of making large changes in the model, and moving estimated
    locations of scatterers by many wavelengths. The salient features of MVA
    is its use of an extended (nonphysical) scattering model. Nonlinear least
    squares inversion (NLS), on the other hand, incorporates whatever
    details of wave physics are built into its underlying modeling engine.
    However success appears to require that the initial estimate of wave
    velocity (in an iterative solution method) be accurate to within a
    wavelength, i.e. have kinematic properties very close to that of the
    optimal model.

    This poster will describe a nonlinear extended scattering model and a
    related optimization formulation of inverse scattering. I will present
    the results of some preliminary numerical explorations which suggest that
    this approach may combine the global nature of MVA with the capacity of
    NLS to accomodate nonlinear wave phenomena.
  • Signal Restoration Through Deconvolution Applied to Deep Mantle Seismic Probes
    Wolfgang Stefan (Arizona State University)
    We present a method of signal restoration to improve
    the signal to noise ratio, sharpen seismic arrival onset, and act as
    an empirical source deconvolution of specific seismic arrivals. The
    method is used on the shear wave time window containing SKS and
    S, whereby using a Gaussian PSF produces more impulsive, narrower,
    signals in the wave train. The resulting restored time series
    facilitates more accurate and objective relative travel time
    estimation of the individual seismic arrivals. Clean and sharp
    reconstructions are obtained with real data, even for signals with
    relatively high noise content. Reconstructed signals are simpler,
    more impulsive, and narrower, which allows highlighting of some details
    of arrivals that are not readily apparent in raw waveforms.
  • Local Tikhonov Regularization in n Dimensions
    Tom Scofield (Calvin College)
    Many ill-posed linear integral equations are solved using standard
    Tikhonov regularization. When solutions have edges, as is usually the
    case in the image deblurring problem, this procedure generally carries
    with it a choice between capturing the near-discontinuities found at edges
    at the expense of introducing oscillations in regions that should be
    smooth, or preserving smooth regions but oversmoothing edges. More
    recently, local Tikhonov regularization methods have been introduced,
    attempting to make this choice a local rather than global one. We prove
    the convergence of such methods in R^n for general n. We also carry out
    a discrete numerical implementation of such methods and provide examples
    in 1 and 2 dimensions of results using both these methods and standard
    Tikhonov regularization.
  • Seismic Velocity Analysis: In Time or Depth Domain?
    Herve Chauris (Mines-ParisTech)
    jointly with Gilles Lambare (Ecole des Mines de Paris)

    Seismic velocity analysis is a crucial step needed to obtain consistent
    images of the subsurface. Several new methods appeared in the last 10 years, among them Slope Tomography and Differential Semblance
    Optimization. We want to discuss here the link between these a priori different methods.

    Slope Tomography is formulated in the prestack unmigrated time domain
    and uses not only time information picked on seismic gathers,
    but also associated slopes that better constrain the inversion scheme.
    On the other side, Differential Semblance Optimization is formulated
    in the depth migrated domain where adjacent images are compared
    to obtain a final consistent image of the subsurface.

    We analyse these two types of methods to show that they are in fact
    equivalent from a theoretical point of view despite the different
    formulation.
  • Direct Reconstruction-Segmentation, as Motivated by Electron

    Microscopy

    Hstau Liao (University of Minnesota, Twin Cities)
    Quite often in electron microscopy it is desired to segment the
    reconstructed volumes of biological macromolecules, whose 3D structural
    inference is crucial for the understanding of biological functions. We
    propose approaches that directly produce a label (segmented) image from
    the tomograms (projections).

    Knowing that there are only a finitely many possible labels and by
    postulating Gibbs priors on the underlying distribution of label images,
    it is possible to recover the unknown image from only a few noisy
    projections.
  • Problems in Sub-salt Imaging due to Layered-Earth Assumptions
    Scott Morton (Amerada Hess Corporation)
    The standard approach to seismic imaging is rife with limitations due
    to the assumption that the earth is approximately a layered medium.
    Unfortunately much of the current petroleum exploration in the Gulf of
    Mexico is around or beneath salt bodies which have complex 3-D shapes.
    We illustrate several problems attributable to the layered-earth approach
    in the standard model building process, state-of-the-art imaging algorithms
    and available data interpretation tools used in sub-salt imaging.
  • Adjoint Method in Time Domain Ultrasound Tomography
    Frank Natterer (Westfälische Wilhelms-Universität Münster)
    We model ultrasound tomography by the wave equation. Adjoint methods can
    be used for the inversion. Unfortunately, due to the large number of
    sources, adjoint methods are very time consuming. By preprocessing of the
    data (wavefront synthesizing, plane wave stacking), adjoint methods can be
    sped up by orders of magnitude. We analyse the preprocessed data in
    Fourier domain. We present numerical results for the Salt Lake City breast
    phantom and for the Marmousi data.
  • Texture Discrimination, Nonlinear Filtering, and Segmentation in Mammography
    Walter Richardson Jr. (University of Texas)
    There are two primary signs used by the radiologist to
    detect lesions. The first is mass: a benign neoplasm is smoothly
    marginated whereas a malignancy is characterized by an indistinct border
    which becomes more spiculated with time.
    The second sign is microcalcification.
    An essential ingredient of these indicators is
    texture, used by the radiologist in many subtle ways to discriminate
    between normal and cancerous tissue.
    The irregular boundaries of suspect lesions suggest that they
    could be identified by their local fractal signature.
    Any real image is corrupted by some noise and it is necessary
    to prefilter the data. Results are presented for two
    edge-enhancing filters: the Weighted Majority - Minimum Range
    filter and the mean-curvature dependent PDE filter of
    Morel. Once the image has been filtered/transformed, the
    Mumford-Shah approach is used for segmentation.
  • Exponential Radon Transform Inversion Based on Harmonic Analysis of the Euclidean Motion Group
    Can Yarman (Rensselaer Polytechnic Institute)
    This paper presents a new method for the exponential Radon transform inversion based on harmonic analysis of the Euclidean motion
    group (M(2)). The exponential Radon transform is modified to be formulated as a convolution over M(2). The convolution
    representation leads to a block diagonalization of the modified exponential Radon transform in the Euclidean motion group Fourier
    domain, which provides a deconvolution type inversion for the exponential Radon transform. Numerical examples are presented to show
    the viability of the proposed method.