538 research outputs found
Detection and imaging in strongly backscattering randomly layered media
Abstract. Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and enhancing the echoes from the reflectors that we wish to locate. We consider a filtering and detection approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm is general and can be used for detection and imaging in heavy clutter, but its analysis depends on the model of the cluttered medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the filtering algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging
Enhanced statistical stability in coherent interferometric imaging
http://iopscience.iop.org/0266-5611/International audienc
Adaptive time-frequency detection and filtering for imaging in heavy clutter
Abstract. We introduce an adaptive approach for the detection of a reflector in a strongly scattering medium using a timefrequency representation of the array response matrix followed by a Singular Value Decomposition (SVD). We use the Local Cosine Transform (LCT) for the time-frequency representation and introduce a detection criterion that identifies anomalies in the top singular values, across frequencies and in different time windows, that are due to the reflector. The detection is adaptive because the time windows that contain the primary echoes from the reflector are not determined in advance. Their location and width is identified by searching through the time-frequency binary tree of the LCT. After detecting the presence of the reflector we filter the array response matrix to retain information only in the time windows that have been selected. We also project the filtered array response matrix to the subspace associated with the top singular value and then image using travel time migration. We show with extensive numerical simulations that this approach to detection and imaging works well in heavy clutter that is calibrated using random matrix theory so as to simulate regimes close to the experiments in [3]. While the detection and filtering algorithm presented here works well in general clutter it has been analyzed theoretically only for the case of randomly layered media [1]
Phase transitions with four-spin interactions
Using an extended Lee-Yang theorem and GKS correlation inequalities, we
prove, for a class of ferromagnetic multi-spin interactions, that they will
have a phase transition(and spontaneous magnetization) if, and only if, the
external field (and the temperature is low enough). We also show the
absence of phase transitions for some nonferromagnetic interactions. The FKG
inequalities are shown to hold for a larger class of multi-spin interactions
The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus
We present necessary and sufficient conditions for the generic rigidity of
body-bar frameworks on the three-dimensional fixed torus. These frameworks
correspond to infinite periodic body-bar frameworks in with a
fixed periodic lattice.Comment: 31 pages, 12 figure
Filtering Deterministic Layer Effects in Imaging
Sensor array imaging arises in applications such as nondestructive evaluation of materials
with ultrasonic waves, seismic exploration, and radar. The sensors probe a medium with
signals and record the resulting echoes, which are then processed to determine the location
and reflectivity of remote reflectors. These could be defects in materials such as voids,
fault lines or salt bodies in the earth, and cars, buildings, or aircraft in radar applications.
Imaging is relatively well understood when the medium through which the signals
propagate is smooth, and therefore nonscattering. But in many problems the medium is
heterogeneous, with numerous small inhomogeneities that scatter the waves. We refer to
the collection of inhomogeneities as clutter, which introduces an uncertainty in imaging
because it is unknown and impossible to estimate in detail. We model the clutter as a
random process. The array data is measured in one realization of the random medium,
and the challenge is to mitigate cumulative clutter scattering so as to obtain robust images
that are statistically stable with respect to different realizations of the inhomogeneities.
Scatterers that are not buried too deep in clutter can be imaged reliably with the coherent
interferometric (CINT) approach. But in heavy clutter the signal-to-noise ratio (SNR)
is low and CINT alone does not work. The “signal,” the echoes from the scatterers to be
imaged, is overwhelmed by the “noise,” the strong clutter reverberations. There are two
existing approaches for imaging at low SNR: The first operates under the premise that data
are incoherent so that only the intensity of the scattered field can be used. The unknown
coherent scatterers that we want to image are modeled as changes in the coefficients of
diffusion or radiative transport equations satisfied by the intensities, and the problem becomes
one of parameter estimation. Because the estimation is severely ill-posed, the results
have poor resolution, unless very good prior information is available and large arrays are
used. The second approach recognizes that if there is some residual coherence in the data,
that is, some reliable phase information is available, it is worth trying to extract it and
use it with well-posed coherent imaging methods to obtain images with better resolution.
This paper takes the latter approach and presents a first attempt at enhancing the SNR
of the array data by suppressing medium reverberations. It introduces filters, or annihilators of layer backscatter, that are designed to remove primary echoes from strong, isolated
layers in a medium with additional random layering at small, subwavelength scales. These
strong layers are called deterministic because they can be imaged from the data. However,
our goal is not to image the layers, but to suppress them and thus enhance the echoes
from compact scatterers buried deep in the medium. Surprisingly, the layer annihilators
work better than intended, in the sense that they suppress not only the echoes from the
deterministic layers, but also multiply scattered ones in the randomly layered structure.
Following the layer annihilators presented here, other filters of general, nonlayered
heavy clutter have been developed. We review these more recent developments and the
challenges of imaging in heavy clutter in the introduction in order to place the research
presented here in context. We then present in detail the layer annihilators and show with
analysis and numerical simulations how they work
Uniform stability estimates for the discrete Calderon problems
In this article, we focus on the analysis of discrete versions of the
Calderon problem in dimension d \geq 3. In particular, our goal is to obtain
stability estimates for the discrete Calderon problems that hold uniformly with
respect to the discretization parameter. Our approach mimics the one in the
continuous setting. Namely, we shall prove discrete Carleman estimates for the
discrete Laplace operator. A main difference with the continuous ones is that
there, the Carleman parameters cannot be taken arbitrarily large, but should be
smaller than some frequency scale depending on the mesh size. Following the
by-now classical Complex Geometric Optics (CGO) approach, we can thus derive
discrete CGO solutions, but with limited range of parameters. As in the
continuous case, we then use these solutions to obtain uniform stability
estimates for the discrete Calderon problems.Comment: 38 pages, 2 figure
Generalized Borcea-Voisin Construction
C. Voisin and C. Borcea have constructed mirror pairs of families of
Calabi-Yau threefolds by taking the quotient of the product of an elliptic
curve with a K3 surface endowed with a non-symplectic involution. In this
paper, we generalize the construction of Borcea and Voisin to any prime order
and build three and four dimensional Calabi-Yau orbifolds. We classify the
topological types that are obtained and show that, in dimension 4, orbifolds
built with an involution admit a crepant resolution and come in topological
mirror pairs. We show that for odd primes, there are generically no minimal
resolutions and the mirror pairing is lost.Comment: 15 pages, 2 figures. v2: typos corrected & references adde
2D and 3D reconstructions in acousto-electric tomography
We propose and test stable algorithms for the reconstruction of the internal
conductivity of a biological object using acousto-electric measurements.
Namely, the conventional impedance tomography scheme is supplemented by
scanning the object with acoustic waves that slightly perturb the conductivity
and cause the change in the electric potential measured on the boundary of the
object. These perturbations of the potential are then used as the data for the
reconstruction of the conductivity. The present method does not rely on
"perfectly focused" acoustic beams. Instead, more realistic propagating
spherical fronts are utilized, and then the measurements that would correspond
to perfect focusing are synthesized. In other words, we use \emph{synthetic
focusing}. Numerical experiments with simulated data show that our techniques
produce high quality images, both in 2D and 3D, and that they remain accurate
in the presence of high-level noise in the data. Local uniqueness and stability
for the problem also hold
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