PAPANICOLAOU
Array imaging, like synthetic aperture radar, does not produce good reflectivity images when there is clutter, or random scattering inhomogeneities, between the reflectors and the array. Can the blurring effects of clutter be controlled? I will discuss this issue in some detail and show that if bistatic array data is available and if the data is suitably preprocessed to stabilize clutter effects then a good deal can be done to minimize blurring.
SYLVESTER
I will give an introduction to scattering and inverse scattering for the Helmholtz equation (i.e. the time harmonic wave equation), trying as much as possible to follow an approach that extends to other models as well. The basic tool is the right hand side of Green's identity, which provides a direct analog of the familiar one dimensional Wronskian for ODE's. This provides a convenient link between so-called near field (observations made near the object of interest) and the far field (observations made far from the object of interest where simpler asymptotic formulas hold). Lastly, I will describe the notion of Scattering support. This is a method for locating a scatterer or a radiating source, using a single monochromatic far field. The novelty here is that a single far field is far from enough data to determine the scatterer or even its support. Nevertheless, this data does determine a subset which must be part of any scatterer that produces that field.
ROUX
We report on the latest results from our research group. These include work on noise-based time reversal and multiple focus ocean TRM results.
DOWLING
The inherent benefits of time reversal in wave propagation problems can be obtained to varying degrees with both active and passive time reversal. In the active case, the transducer array that performs the time reversal step must be able to receive and transmit signals. Such active arrays can spatially focus and temporally compress wave energy at the waves' source location without knowledge of the propagation environment, the source location, or even the array element locations. In the passive case, the transducer array merely receives signals and the benefits of time reversal emerge during signal processing. Here, temporal compression of the received signals can be achieved at the array without the back propagation step. In both cases, time variations in the environment may lead to degradation of time-reversal's benefits. This presentation will cover aspects of both active and passive time reversal with examples drawn from ocean-acoustic simulations and experiments. The discussion of active time reversal will address the influence that motion of the source, array, or medium has on spatial focusing. The discussion of passive time reversal will illustrate temporal compression from remote sound sources. Potential applications in underwater acoustic communication and blind deconvolution will be discussed.
ROUSEFF
Passive Phase Conjugation is a method for coherent underwater acoustic communication that uses multiple receive-only hydrophones. In its most basic formulation, the method begins with a source sending a single probe pulse. After waiting for the multipathed arrivals to clear, the source then transmits the data stream. At the distant receiving array, the measured probe responses act as estimates for the channel impulse response. The probe responses are cross-correlated with received data stream at that array element. The results are then combined coherently across the receiving array yielding the final communication signal ready for demodulation. To compensate for a time-varying environment, one approach is to break the data stream into short segments and intersperse new probe pulses. An alternative approach called Decision-Directed Passive Phase Conjugation uses a feedback loop to generate new estimates for the channel impulse response from the data stream itself. Passive Phase Conjugation was tested in a May 2000 experiment in Puget Sound near Seattle [Rouseff et al., IEEE J. Oceanic Eng. 26, pp. 821-831, 2001]. The experiment was conducted in water between 10 and 60 m deep and at ranges between 500 m and 5 km. Using binary phase shift keying (BPSK) and a center frequency of 12.5 kHz, data rates of 2.1 kbits/s were routinely achieved. Passive Phase Conjugation will also be a component of the High-Frequency Channel Characterization Experiment scheduled for May 2003 off the Kauai Island in Hawaii. The latter acoustics experiment should feature detailed synoptic oceanographic measurements. In the present talk, results from the two Passive Phase Conjugation experiments will be reviewed. Included will be results for what are known to be strongly range-dependent environments. The effects of array geometry and spatial sampling will be demonstrated. The goal will be to identify open research questions where interesting experimental results lack a satisfactory theoretical explanation.
JONES
The properties of super-resolution and stability in time-reversal focusing of an acoustic wave are investigated using perturbation theory in an unbounded scattering medium with weak sound speed fluctuations. Although super-resolution is obscured by weak scattering of the coherent field, the incoherent field still shows time-reversal enhanced focusing and the analytically tractable results may provide physical insight into time-reversal in stronger scattering media. Using first order perturbation theory, the correlation scales of focused time-reversed field are defined by the scales of the fluctuations in the medium, the scale of effective aperture of the time-reversal array due to scattering, the bandwidth of the system, and the array geometry. In this weak scattering example analytic expressions for the first and second moments of the time-reversal Green's function operator are found and provide physical insight into the mechanism of time-reversal focusing and the role of bandwidth in super-resolution and stability. Numerical simulation using discrete point scatterers are performed to compare with the analytic results and to investigate the transitional behavior of time-reversal focusing from weak to stronger scattering.
CHAMBERS
An computational study using the MUSIC method of subspace imaging is presented for the case of spheres above a reflecting boundary. The multistatic data matrix is calculated using a electromagnetic spectral code. The singular value decomposition of the data matrix is calculated and the singular vectors divided into signal and noise subspaces. Images showing the estimated sphere locations are obtained by calculating the MUSIC functional using either the free space Green's function or the Green's function that incorporates reflections from the boundary. We show that the latter Green's function improves imaging performance after applying a normalization that compensates for the interference between direct and reflected fields. We also show that the best images are obtained when the number of singular vectors in the signal subspace exceeds the number of spheres. This is consistent with previous analysis in acoustics showing multiple eigenvalues of the time reversal operator for spherical scatterers [Chambers and Gautesen, JASA 109(6)].
KIM
We discuss fundamental aspects of wireless communication systems. It is well understood that with multiple antennas at the transmitter and receiver, capacity is greatly improved. However, current multiple input/multiple output (MIMO) wireless systems do not optimally use capacity and energy focusing leverages gained from broadband signals. With time-reversal theory, a broadband communication system can deliver power to a spatially localized region that is nearly free of noise. With numerical simulations, we investigate the potential use of this time-reversal system in broadband wireless communication systems.
RYZHIK
Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the simplified regime of the parabolic wave equation in a random medium. The mathematical theory of the convergence and statistical properties of the algorithm is based on the analysis of the Wigner transforms in random media. This is a joint work with G. Bal.
JACKSON
Laboratory and field experiments have demonstrated the feasibility of acoustic time-reversal focusing in the ocean. Formal developments relating to this problem lag experiment somewhat, and the purpose of this talk is to outline some previous theoretical approaches, some current work, and some problems for the future. One general issue is generalization of theoretical results obtained for unbounded media to the waveguide. This is readily done for homogenous and stratified oceans, but issues arise when scattering is considered. The assumption of weak multiple forward volume scattering has led to useful results showing improved focusing, the relation between focus stability to bandwidth, and the effect of time variation of the medium. Questions remain regarding volume and interface scattering in waveguides, and the effect of three-dimensional scattering when vertical linear arrays are used.
CARIN
Time-reversal imaging is addressed for sensing an elastic target situated in an acoustic waveguide. It is assumed that the target-sensor range is large relative to the channel depth. We first investigate the theory of wideband time-reversal imaging of an extended target, for which the target dimensions are large relative to the principal wavelengths. When performing time-reversal imaging one requires a forward model for propagation through the channel, and the quality of the resulting image may be used as a measure of the match between the modeled and actual (measured) channel parameters. It is demonstrated that the channel parameters associated with a given measurement may be determined via a genetic-algorithm (GA) search in parameter space, employing a cost function based on the time-reversal image quality. Example GA channel-parameter-inversion results are presented for measured data. Target classification based on time-reversal imagery is also considered, wherein the main focus is on classification-performance sensitivity to knowledge of the uncertain channel parameters. The classifier is implemented via a relevance-vector machine.
LIU
Detection and identification of 3-D objects embedded in earth or in ocean by electromagnetic and/or acoustic waves is a great challenge. In spite of the importance of this problem, little progress has been made in the area of inverse scattering methods because of the complex interactions between 3-D objects and the underlying multilayer medium. In this talk, I will present our recent efforts in developing fast electromagnetic inverse scattering methods for the 3-D vectorial integral equation derived from Maxwell's equations for layered media. Numerical examples will be illustrated. I will also discuss about several remaining challenging issues.
GARNIER
This talk addresses the impact of time fluctuations of the medium on refocusing during a time-reversal experiment. The statistical properties of the refocused pulse are discussed. In some experimental configurations, it is shown that a time modification of the medium reduces the amplitude of the refocused pulse without changing the pulse shape. In other configurations the time modifications only filter high frequencies.
NACHBIN
The simplest model for water waves in coastal regions is the (hyperbolic) shallow water system of equations. At the next level of approximation one has the (dispersive) Boussinesq system. We present theoretical and numerical time-reversed refocusing results in both cases. Linear and weakly nonlinear regimes are considered.
BERRYMAN
The time-reversal operator for a planar array of crossed dipole elements illuminating a small conducting and/or dielectric sphere has been investigated to obtain general properties of a RADAR imaging and/or tracking system. Results obtained (with D. H. Chambers, LLNL) show that the maximum number of singular vectors is six total for a conducting dielectric sphere, but only three for a non-conducting dielectric sphere. Numerical results will be presented for various cases including both linear and circular arrays.
DORN
We will present some first results of a very recently started project which has the goal to locate, identify and, if possible, track one or more extended penetrable objects from limited-view data. In the talk, we will address three different approaches: (a) Identifying objects from data with sufficient view by a level set based shape evolution method; (b) Locating objects with a gradient-based method iterating on the location of the extended object; (c) Locating extended objects from limited view scattering data by a simple sampling scheme which is based on the singular value decomposition (SVD) of the scattering response matrix (residual matrix) and the Born approximation. All numerical experiments have been done in 2D using a finite differences frequency domain scheme for the Helmholtz equation with absorbing boundary conditions (PML).
SØ LNA
A multiscale flow field in the turbulent atmosphere gives rise to multiscale variation in the index of refraction. We consider a situation where waves propagate through a random medium with an index of refraction which exhibit multiscale variations. We examine how the wave field is affected by such medium heterogeneity. We also discuss results from analysis of physical measurements from the turbulent atmosphere with a view toward modeling of the random medium.