|
Probability
and Statistics in Complex Systems: Genomics, Networks, and Financial
Engineering, September 1, 2003 - June 30, 2004
Abstracts:
IMA
"Hot Topics" Workshop:
June
27-30, 2004
Photo
Gallery Material
from Talk
Liliana
Borcea (Computational
and Applied Mathematics, Rice University) borcea@caam.rice.edu
Coherent
Interferometric Array Imaging in Clutter, Part I Theory
We
describe a new coherent interferometric approach to imaging
small or extended sources hidden in clutter, via passive arrays
of transducers. The uncertainty in the index of refraction in
clutter is modeled as a random process and the imaging method
is based on the asymptotic stochastic analysis of wave propagation
in random media, in regimes with strong multipath. To achieve
stable results, our method uses cross-correlations of nearby
traces recorded at the array, the interferograms. We also exploit
the existence of a frequency coherence band in order to achieve
good resolution of the images. Naturally, the spatial and frequency
coherence of the data at the array depend on the random medium
and, as we show here, they quantify explicitly the resolution
of the images. The efficiency and robustness of the proposed
method in clutter will be illustrated with several numerical
results.
Parcifal
Bourgeois (ETRO, Faculty of Applied Sciences, Vrije
Universiteit Brussel (VUB)) pbourgeo@etro.vub.ac.be
The
Residual Least Squares Method, a New Variational Approach to
Electrical Impedance Tomography Part II. Computational considerations
Electrical Impedance Tomography (EIT), which is concerned with
the reconstruction of a spatially varying conductivity distribution
inside a bounded domain from partial knowledge of the Neumann-to-Dirichlet
or Dirichlet-to-Neumann map, is a notoriously difficult to solve
inverse problem, due to its nonlinear and severely ill-posed
nature. Despite its theoretical limitations and often disappointing
performance, output least squares (OLS) based reconstruction
methods continue to play a prominent role in most practical
applications of EIT. Recently, we suggested a new variational
method, which, unlike OLS, is guaranteed to deliver solutions
that satisfy both the associated Thompson and Dirichlet variational
principles, irrespective of any additional smoothness assumptions
on the conductivity distribution.
In the first part of this presentation, we will introduce the
variational formulation, establish its convergence properties,
and elucidate how its discretization gives rise to a conventional
subspace approximation problem. Whereas the OLS method can
be regarded as minimizing a certain error norm, solutions are
recovered here as the minimizers of a closely related residual
norm problem arising directly from the governing differential
equations. This key difference is found to have a profound
effect on the numerical properties of the proposed method.
The derivation of a nonlinear conjugate gradient based solution
scheme is shown to lead to a sequence of structured sparse matrix
problems, the conditioning of which appears to be far more favorable
than typically observed in OLS iterations.
In the second part of this presentation, we identify the sparsity
structure in the discretized problem formulation as the distinguishing
feature underlying the superior computational efficiency and
robustness of our variational method. In particular, it will
be illustrate how multi-frontal QR factorization and displacement
rank concepts combine with the conjugate gradient scheme, to
yield a nonlinear solution method that requires significantly
less computations than OLS, while restricting the iterations
to a confined subspace of valid solutions. When tested on a
set of numerical experiments, the results are found to confirm
the anticipated computational savings.
Lawrence
Carin (Department of Electrical & Computer Engineering,
Duke University) lcarin@ee.duke.edu
http://www.ee.duke.edu/~lcarin/
Semi-Supervised and Adaptive Multi-Aspect Sensing of General
Targets
Joint work with Shihao Ji.
In design of statistical inversion algorithms, one typically
assumes access to a set of labeled training data, represented
by observed data and associated labels (a given label denotes
the target/clutter type). A supervised algorithm is trained
entirely on the labeled data. In practice the amount of available
labeled training data is quite small, and this data does not
account for environmental changes the sensor may encounter.
By contrast, one typically has access to a large quantity of
unlabeled data, with this changing as the environment changes.
A semi-supervised classifier utilizes the labeled data and unlabeled
data (i.e., all available data) to build an inversion algorithm.
By utilizing the unlabeled data in the classifier design, the
algorithm naturally accounts for changes in the properties of
the environment, as seen by the sensor. We investigate a semi-supervised
statistical inversion algorithm, employing a hidden Markov model
(HMM), thereby accounting for multi-aspect sensing. In addition,
the semi-supervised algorithm employs active sensing, wherein
the inversion and sensing missions are combined. In this context
the algorithm determines which new data would be most informative,
if it were measured by the sensor. The active-sensing algorithm
also defines those unlabeled signatures that would be most informative
to classifier design if the associated labels were acquired.
In this talk we summarize the underlying algorithmic developments,
and show example results for measured underwater-acoustic scattering
data.
David
Castañón (Department of Electrical
& Computer Engineering, Boston University) dac@bu.edu
Non-Myopic
Approaches to Adaptive Sensing: Challenges and New Results
Slides: pdf
In this talk, we discuss formulations and approaches for adaptive
sensing problems with non-myopic objectives. We focus on problems
related to object classification. The talk presents a mathematical
framework for adaptive sensing, and develops a lower bound to
the optimal achievable performance that can be used for practical
adaptive sensing control. Numerical experiments demonstrate
the relative advantages of non-myopic adaptive strategies versus
myopic strategies.
David
Castanon (Department of Electrical & Computer Engineering,
Boston University) dac@bu.edu
Multimodal
Data Fusion for Atherosclerotic Plaque Imaging (poster)
Slides:
pdf
Joint
work with Robert Weisenseel and
Clem Karl.
In many subsurface sensing problems, single sensor information
quality is poor. In these cases, the solution of inverse problems
in each modality can be ill-conditioned and lead to artifacts
that make it hard to co-register and fuse the data. We present
a joint inversion framework for fusing and estimating images
from multimodal data directly as a single inverse problem based
on shared boundary structure. The approach is based on generalizations
of the Mumford-Shah variational approach to image enhancement,
to account for simultaneous registration and inversion. The
approach is demonstrated with examples for imaging of vulnerable
atherosclerotic plaque with MRI and CT modalities.
Margaret
Cheney (Department of Mathematical Sciences, Rensselaer
Polytechnic Institute) cheney@rpi.edu
Optimal
Measurements, Time-Reversal, and Frequency Tuning
Slides:
pdf
We consider the problem of obtaining information about an inaccessible
half-space from acoustic or electromagnetic measurements made
in the accessible half-space. If the measurements are of limited
precision, some scatterers will be undetectable because their
scattered fields are below the precision of the measuring instrument.
How can we make optimal measurements? In other words, what incident
fields should we apply that will result in the biggest measurements?
There are many ways to formulate this question, depending on
the measuring instruments. In this paper we consider a formulation
involving wave-splitting in the accessible half-space: what
downgoing wave will result in an upgoing wave of greatest energy?
This formulation is most natural for far-field problems.
A closely related question arises in the case when we have a
guess about the configuration of the inaccessible half-space.
What measurements should we make to determine whether our guess
is accurate? In this case we compare the scattered field to
the field computed from the guessed configuration. Again we
look for the incident field that results in the greatest energy
difference.
We show that the optimal incident field can be found by an iterative
process involving time reversal "mirrors." For band-limited
incident fields and compactly supported scatterers, in general
this iterative process converges to a time-harmonic field at
the frequency that gives the most scattering. In other words,
the time-reversal process "tunes" automatically to the best
frequency.
Leslie M. Collins (Department of Electrical & Computer
Engineering, Duke University) lcollins@ee.duke.edu http://www.ee.duke.edu/Research/lcollins/
Uncertainty
Mitigation Using Adaptive Multi-Modality Processing (poster)
Gregoire
Derveaux (Department of Mathematics, Stanford University)
derveaux@stanford.edu
Near-Field
Imaging: A Study of the SNR Issue
Slides:
pdf
We investigate the use of near-field data collected by GPR for
imaging the surface displacement induced by the propagation
of a seismic wave used to detect the presence of landmines underground.
The information carried by evanescent waves can be used to achieve
subwavelength resolution, but since they decay rapidly this
information is easily corrupted by noise. Using a simple propagating
model for the scalar wave equation, the effect of noise is analyzed
theoretically and is illustrated by numerical examples. The
interest of the use of broadband signals for enhancing the resolution
while reducing the level of noise is shown.
Joaquim
Fortuny Guasch
(DG Joint Research Centre) joaquim.fortuny@jrc.it
http://www.jrc.cec.eu.int
Retrieval
of Biophysical Parameters Using Polarimetric Interferometry
Techniques: Theory and Experimental Results (poster)
Bojan
Guzina (Department of Civil Engineering, University
of Minnesota) guzina@wave.ce.umn.edu
An
Alternate Course to 3D Seismic Imaging
In
the context of seismic exploration, a comprehensive 3D imaging
of subterranean structures is commonly associated with the interpretation
of thousands of motion measurements via elastodynamic models
that are inherently based on domain discretization. In contrast,
this investigation is concerned with the mapping of major underground
openings where only a few measurements can be made, usually
on the ground surface. In such instances boundary integral equation
(BIE) methods, which target only the outline of a hidden structure,
can be used to deal with the limited field data. This boundary-only
imaging approach, which offers formidable computational savings,
has its origins in radar and sonar technologies. So far, however,
it has been largely unexplored in the context of seismic surveys.
On
modeling the subterranean domain as a semi-infinite solid, the
problem of active imaging is reduced to the minimization of
a misfit between experiment and theory in the context of surface
seismic waveforms. For a rigorous treatment of the gradient
search technique used to solve the inverse problem, sensitivities
of the predictive BIE model with respect to cavity parameters
are evaluated using an adjoint field approach. Despite its computational
advantages, however, this method suffers from the lack of robustness
owing to its critical dependence on a suitable choice of initial
"guess." To provide the BIE imaging method with a rationally
selected initial "guess" (in terms of obstacle location, topology,
and geometry), the concept of topological derivative, rooted
in the theory of structural shape optimization, is extended
to elastic wave scattering and applied to the featured inverse
problem. As a viable alternative to the topological derivative
approach, this talk will also highlight a near-field elastodynamic
generalization of the linear sampling method in acoustics and
electromagnetics as it pertains to "rapid" ground probing. A
set of numerical examples is included to illustrate the performance
of proposed imaging tools. The results suggest a possibility
of rendering 3D seismic imaging tractable for everyday engineering
applications.
Alfred
O. Hero III (Department of Electrical Engineering
and Computer Science, University of Michigan) hero@eecs.umich.edu
http://www.eecs.umich.edu/~hero/
Non-Myopic
Strategies Adaptive Multi-Modal Sensor Management for Target
Tracking and Acquisition
Joint work with C. Kreucher and
D. Blatt.
Myopic approaches for scheduling multi-modality sensors are
computationally simpler than optimal non-myopic strategies but
can have significantly poorer performance. This performance
loss translates into a longer time to detection of targets,
less efficient use of resources, and higher tracking errors
for multiple target tracking and acquisition applications. We
will illustrate the causes underlying myopic performance degradation
and present a hybrid reinforcement-learning and particle-filtering
framework for improving performance.
Alfred
O. Hero III (Department of Electrical Engineering
and Computer Science, University of Michigan) hero@eecs.umich.edu
http://www.eecs.umich.edu/~hero/
Analysis
of a Multistatic Adaptive Target Illumination and Detection
Approach (MATILDA) to Time Reversal Imaging (poster)
Slides: pdf
Joint
work with Raghuram Rangarajan.
An iterative physical time reversal method using an array of
antennas or transducers is presented for imaging random media.
The Cramer-Rao bound (CRB) is used to explore the imaging performance
advantages of this method, which we call MATILDA, as compared
to conventional techniques that do not exploit time reversal
retrofocusing. The analysis is performed under a narrowband
far-field approximation to the scatter medium. Our principal
conclusions are: 1) for a calibrated array (known antenna positions)
use of time reversal results in a significant reduction of variance
of estimates of scatter cross-section in the far-field; 2) for
an uncalibrated array (unknown sensor positions) variance reduction
can still be achieved if statistically efficient estimates (estimates
attaining the CRB) of the sensor positions can be implemented;
3) the analysis suggests an time-reversal autocalibration method
for uncalibrated arrays. Simulation results will be presented
that illustrate these theoretical predictions.
David
Isaacson (Department of Mathematical Sciences, Rensselaer
Polytechnic Institute) isaacd@rpi.edu
Adaptive
Current Tomography
We explain how current patterns can be chosen adaptively in
order to yield the largest "distinguishability" of different
states of a body. Examples from monitoring heart and lung function
, breast cancer detection, geophysical sensing, and crack detection
in pipes will be shown that illustrate the theory.
Karl
J. Langenberg (Department of Electrical Engineering
and Computer Science, University of Kassel) langenberg@uni-kassel.de
Electromagnetic
and Elastic Wave Scattering and Imaging for Multi-Mode Non-Destructive
Testing
Non-destructive testing of concrete is a safety relevant task
in civil engineering. Therefore, particular attention must be
given to a quantitative analysis of measured data, and a combination
of different wave modes, i.e. electromagnetic and elastic waves,
is often required. A typical problem is the location of metallic
tendon ducts in concrete below the metallic reinforcement grid
and their subsequent check against corrosion; to achieve this
goal the physical scattering properties of electromagnetic and
elastic waves may be exploited to complement each other.
To locate metallic objects embedded in concrete we apply diffraction
tomographic imaging schemes either in reflection or transmission.
Applications to synthetic data obtained with a Finite Difference
Time Domain code reveals the resolution of the respective algorithms
with the reinforcement grid size as a parameter; yet the application
to experimental Ground Penetrating Radar data still exhibits
a better performance on synthetic data.
Grouting holes in the tendon duct are perfect targets for elastic
waves because they act as scattering voids. Yet for the ultrasonic
frequency regime under concern, concrete is a very heterogeneous
propagation medium. Therefore, detailed investigations were
performed with the numerical EFIT code (Elastodynamic Finite
Integration Technique) to understand elastic wave scattering
in concrete; this is demonstrated with wave propagation movies.
We confirm on synthetic as well as on experimental data that
diffraction tomographic imaging techniques can be equally applied
to ultrasonic data even in a highly random scattering environment.
Qing
H. Liu (Department of Electrical Engineering, Duke
University) qhliu@ee.duke.edu
http://www.ee.duke.edu/~qhliu
Multimodality
Inversion for Image Reconstruction of Objects Buried in Multilayered
Media with Radar and Seismic Measurements
Slides:
pdf
Image reconstruction of heterogeneous objects of arbitrary shape
buried in the multilayered earth is an important and challenging
research area in subsurface sensing. Such applications are common
to geophysical exploration, environmental characterization,
and subsurface sensing of landmines, unexploded ordnance and
underground structures.
Both electromagnetic and seismic waves have been widely used
to detect and characterize underground structures. However,
little has been done to combine electromagnetic and acoustic
measurements in a joint inversion for a better characterization
of targets. In this work, we explore the joint electromagnetic/seismic
characterization in order to improve the reconstruction of underground
structures.
The joint reconstruction problem is cast as an inverse scattering
problem in a multilayered medium. We have developed fast forward
and inverse solution methods for both 2-D and 3-D heterogeneous
objects in multilayered media based on the stabilized biconjugate-gradient
fast Fourier transform method for individual modalities. For
the joint inversion, we developed a technique based on a least-squares
criterion of the data misfit and mutual information theory to
combine electromagnetic and acoustic scattering data. Numerical
results show that the joint EM/Acoustic inversion method can
provide more information for the underground structures than
the stand-alone electromagnetic or acoustic imaging modalities.
These improved imaging results are due to the complementary
nature of electromagnetic and acoustic waves in underground
structures.
James
H. McClellan (School of Electrical and Computer Engineering,
Georgia Institute of Technology) jim.mcclellan@ece.gatech.edu
Processing
Algorithms for Near Field Imaging of Buried Targets
Joint
work with Mubashir Alam and Waymond
R. Scott, Jr.
One
class of imaging algorithms is based on the idea of time reversal.
A multi-static response matrix is built by using an array of
sources and receivers in which each source probes the medium
individually. The processing is carried out in the frequency
domain, one frequency at a time. By using the singular value
decomposition of the response matrix and an estimate of the
Green's function for the medium, an imaging algorithm is developed
which can determine the spatial positions of buried targets.
The Green's function estimate used is for the Rayleigh wave
only. A generalized version of this algorithm has been developed
for near-field targets when wavefront curvature is significant.
A
second class of algorithms is based on the CLEAN algorithm used
in radio astronomy. A robust highresolution version, called
RELAX, can be modified to work in the scenario of passive buried
targets. These algorithms are based on a least-squares analysis
over the band of frequencies occupied by the Rayleigh wave.
From received data and an array model for the Green's function
of near-field targets, an iterative least-squares solution is
used to estimate both the target positions and the reflected
signals.
These
imaging algorithms require an estimate of various parameters
of surface waves in a nonhomogenous medium, like soil. An algorithm
for estimating dispersion curves (phase velocity vs. frequency)
for surface wave has been developed. This technique is based
on a combination of temporal Fourier transforms and spatial
pole-zero modeling. It is able to estimate the wave velocity,
wave number of individual wave packets, as well as extract the
Rayleigh wave. The parameters of the extracted Rayleigh wave
are then available for use in the imaging algorithms.
Eric
Miller (Department of Electrical and Computer Engineering,
Northeastern University) elmiller@ece.neu.edu
Geometric
Methods for Multi-Parameter, Multi-Source Inverse Problems
(poster)
George
C. Papanicolaou (Department of Mathematics,
Stanford University) papanico@math.stanford.edu
http://georgep.stanford.edu/
Adaptive
Multiresolution Interferometry
Interferometric array imaging in a cluttered environment works
well only if the residual space-time coherence of the array
data is taken into consideration appropriately. Is there a way
to account for coherence effects in an optimal way? We will
examine this question by using the adaptive local cosine transform.
We will review briefly adaptive multiresolution methods and
we will discuss how they can be used in imaging. We will also
show results of numerical simulations.
Fernando
Reitich (School of Mathematics, University of Minnesota)
reitich@math.umn.edu
A New High-Order High-Frequency Integral Equation Method - for
the Solution of Wave Scattering Problems
The effort and interest in the design of improved algorithms
for computational electromagnetics and acoustics applications
has consistently grown over the last twenty years as these simulations
have become relevant in an increasing number of fields and have
been facilitated by remarkable developments in computing resources.
Still, current state-of-the-art algorithms are limited by the
competing demands of accuracy, which typically requires an increasing
number of degrees of freedom to resolve on the scale of a wavelength,
and efficiency, which favors coarse discretizations. In this
talk we will present a new strategy for the solution of the
integral equations of electromagnetic and acoustic scattering
that successfully deals with these requirements by avoiding
the need to discretize on the scale of the wavelength at high-frequencies,
while retaining error-controllability and high-order convergence
characteristics. The approach is based the derivation of an
appropriate ansatz for the phase of the (unknown) currents,
on explicit treatment of shadow boundaries, and on localized
high-order integration around critical points. [This is joint
work with O. Bruno & C.
Geuzaine (Caltech)].
Jochen
Schulz (Institute for Numerical and Applied Mathematics,
University of Goettingen) schulz@math.uni-goettingen.de
A
Multiwave Range Test for Obstacle Reconstructions With Unknown
Physical Properties
Slides:
pdf
We propose a multi-wave version of the range test for obstacle
reconstruction in inverse scattering theory. The range test
has originally been proposed to obtain knowledge about an unknown
scatterer when the far field pattern for one plane wave only
is given. Here, we extend the method to the case of multi-wave
data in a way such that the full shape of the unknown obstacle
can be reconstructed. We provide a proof for the convergence
of the range test for the reconstruction of the shape of one
or several objects when the boundary condition of the scatterer
is not known. Numerical examples for the multi-wave reconstructions
are provided.
Waymond
R. Scott, Jr. (School of Electrical and Computer
Engineering, Georgia Institute of Technology) waymond.scott@ece.gatech.edu
Experimental
Investigation of Techniques for the Detection of Near Surface
Targets in Cluttered Media
Slides:
pdf
Joint
work with Pelham D. Norville, Kangwook
Kim, James H. McClellan,
and Gregg D. Larson.
Systems
are under development at the Georgia Institute of Technology
for the detection of near surface targets that use electromagnetic
or seismic waves individually or in combination. One system
utilizes a seismic source to propagate Rayleigh waves through
a medium such as soil. Non-surface-contacting electromagnetic
sensors are used to detect the displacement of the medium created
by interaction of the Rayleigh waves with a target, such as
a landmine. In another system using ground penetrating radar
(GPR), only electromagnetic waves are used to detect buried
targets. Both these system have been tested in a relatively
uncluttered medium and have yielded encouraging results, demonstrating
that the systems are effective for the detection of buried targets.
However, when the medium is filled with a large number of scattering
objects, the waves will be broken up by the scatterers in the
medium to the point that the wave front no longer interacts
with the target as it would in an uncluttered medium. This causes
detection of a target to be uncertain or impossible.
In
an effort to extend the application of the seismic system to
a highly cluttered medium, the time reversal method is applied
to the seismic system, and evaluated for focusing Rayleigh wave
fronts at a desired location. Experimental results are presented
for a propagation medium with no scatterers present, and with
multiple scatterers present. Time-reverse focusing results are
also compared to uniform excitation and time-delay beamforming
methods.
In
addition, multistatic arrays of sensors are investigated to
see if they are more robust in a highly cluttered medium than
are bistatic sensors. Experiment results for mutistatic arrays
of seismic and GPR sensors are presented with and without scatters
present. These results will be compared to the bistatic results.
Imaging techniques will be investigated using this data.
John
Sylvester (Department of Mathematics, University
of Washington) sylvest@math.washington.edu
Deductions
About Size and Location Based On Scattering Data
Slides: pdf
There are many successful techniques for deducing the location
of point sources or scatterers from a limited number of acoustic
or electromagnetic measurements. These measurements are far
too few to uniquely identify a general source or even give an
upper bound on its support. Nevertheless, the task of remote
sensing is to infer what we can about size and location from
exactly such limited data sets.
In several cases, will show that this data does uniquely determine
a lower bound on a suitably defined notion of support of a source
or scatterer.
We will take the Helmholtz equation as a model and consider
some specific data sets, i.e.
1) broadband (many frequencies) measurements at a few angles
2) a single frequency far field measured from multiple angles
(i.e one monochromatic incident wave, many sensors)
3) single frequency (multi-angle) backscattering data
In the last two cases we can find a lower bound on the convex
hull of the support and a similar but weaker notion in the first
case.
We will discuss the spectrum of the operator which maps sources
to far fields and describe the role it plays in the computation
of what we wil call the convex scattering support of the data.
Bart
Truyen (Department of Electronics and Information
Processing (ETRO), Vrije Universiteit Brussel (VUB)) batruyen@etro.vub.ac.be
The
Residual Least Squares Method, a New Variational Approach to
Electrical Impedance Tomography Part
I. Problem Formulation, Solution Method, and Properties
Electrical
Impedance Tomography (EIT), which is concerned with the reconstruction
of a spatially varying conductivity distribution inside a bounded
domain from partial knowledge of the Neumann-to-Dirichlet or
Dirichlet-to-Neumann map, is a notoriously difficult to solve
inverse problem, due to its nonlinear and severely ill-posed
nature. Despite its theoretical limitations and often disappointing
performance, output least squares (OLS) based reconstruction
methods continue to play a prominent role in most practical
applications of EIT. Recently, we suggested a new variational
method, which, unlike OLS, is guaranteed to deliver solutions
that satisfy both the associated Thompson and Dirichlet variational
principles, irrespective of any additional smoothness assumptions
on the conductivity distribution.
In the first part of this presentation, we will introduce the
variational formulation, establish its convergence properties,
and elucidate how its discretization gives rise to a conventional
subspace approximation problem. Whereas the OLS method can
be regarded as minimizing a certain error norm, solutions are
recovered here as the minimizers of a closely related residual
norm problem arising directly from the governing differential
equations. This key difference is found to have a profound
effect on the numerical properties of the proposed method.
The derivation of a nonlinear conjugate gradient based solution
scheme is shown to lead to a sequence of structured sparse matrix
problems, the conditioning of which appears to be far more favorable
than typically observed in OLS iterations.
In the second part of this presentation, we identify the sparsity
structure in the discretized problem formulation as the distinguishing
feature underlying the superior computational efficiency and
robustness of our variational method. In particular, it will
be illustrate how multi-frontal QR factorization and displacement
rank concepts combine with the conjugate gradient scheme, to
yield a nonlinear solution method that requires significantly
less computations than OLS, while restricting the iterations
to a confined subspace of valid solutions. When tested on a
set of numerical experiments, the results are found to confirm
the anticipated computational savings.
Yen-Hsi
Richard Tsai (Department of Mathematics and PACM,
Princeton University) ytsai@Math.Princeton.EDU
A
Level Set Framework for Visibility Related Variational Problems
We introduce a frameowrk and construct algorithms based on it
to handle optimization problems that deal with the maximization
of visibility information for observers when obstacles to vision
are present in the environment. Related applications include
certain types of path-planning and pursuer-evader problems.
This framework uses a function that encodes visibility information
in a continuous way. This continuity allows for powerful techniques
to be used in the discrete setting for interpolation, integration,
differentiation, and set operations. Using these tools, we are
able to limit the scope of search and produce locally optimized
solutions.
Chrysoula
Tsogka (Department of Mathematics, Stanford University)
tsogka@math.Stanford.EDU
Coherent
interferometric Array Imaging in Clutter, Part II Numerical
Results
We describe a new coherent interferometric approach to imaging
small or extended sources hidden in clutter, via passive arrays
of transducers. The uncertainty in the index of refraction in
clutter is modeled as a random process and the imaging method
is based on the asymptotic stochastic analysis of wave propagation
in random media, in regimes with strong multipath. To achieve
stable results, our method uses cross-correlations of nearby
traces recorded at the array, the interferograms. We also exploit
the existence of a frequency coherence band in order to achieve
good resolution of the images. Naturally, the spatial and frequency
coherence of the data at the array depend on the random medium
and, as we show here, they quantify explicitly the resolution
of the images. The efficiency and robustness of the proposed
method in clutter will be illustrated with several numerical
results.
Michael
S. Vogelius (Department of Mathematics Rutgers, The
State University of New Jersey) vogelius@math.rutgers.edu
http://www.math.rutgers.edu/~vogelius
Effective
Imaging of Small Inhomogeneities
I
shall give a review of the perturbation formulae (generalized
Born Approximations) and the direct numerical reconstruction
algorithms (of a linear samling nature) that are at the center
of a very effective method to accurately image small inhomogeneities
using electromagnetic measurements.
Tim
Zajic (Lockheed Martin MS2 Tactical Systems)
zajic@math.umn.edu
Probabilistic
Objective Functions for Sensor Management
Joint
work with Ronald P. Mahler.
Multi-sensor,
multi-target sensor management is at root a problem in nonlinear
control theory. Several previous talks have been concerned with
the problem of formulating a foundational and yet practical
basis for control-theoretic sensor management, using a comprehensive
and yet intuitive Bayesian paradigm. Single-sensor, single-target
control requires a core objective function that determines the
degree to which the sensor Field of View (FoV) overlaps the
predicted target track. In the multi-sensor, multi-target case
we have formulated the control problem, and in particular the
problem of formulating objective functions, in Bayesian terms-i.e.,
in terms of posterior distributions. We have also proposed an
approximate multisensor-multitarget sensor management approach.
This approach is based on multi-hypothesis trackers as approximations
to the general multitarget Bayes filter, in conjunction with
"natural" probabilistic objective functions (such as, the probability
that all predicted tracks will be contained in the field of
view of at least one sensor). We have also shown how to extend
this reasoning to multistep look-ahead sensor management. In
this talk we describe preliminary simulations illustrating the
approach. We also show how both the general and approximate
approaches can be modified to incorporate prioritizations due
to the tactical importance of targets.
Photo
Gallery Material
from Talk
IMA
"Hot Topics" Workshops
Probability
and Statistics in Complex Systems: Genomics, Networks, and Financial
Engineering, September 1, 2003 - June 30, 2004
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