170 research outputs found
Limits to the representation capacity of imaging in random media
The information capacity of an image in the atmosphere, ocean, or biological media does not grow indefinitely with increasing light power but has well defined limits. Here, the exact effects of the propagation of light in random inhomogeneous media are elucidated and upper bounds to the capacity of image pixels to represent a corresponding point in the object are described.Peer ReviewedPostprint (published version
Array imaging of localized objects in homogeneous and heterogeneous media
We present a comprehensive study of the resolution and stability properties
of sparse promoting optimization theories applied to narrow band array imaging
of localized scatterers. We consider homogeneous and heterogeneous media, and
multiple and single scattering situations. When the media is homogeneous with
strong multiple scattering between scatterers, we give a non-iterative
formulation to find the locations and reflectivities of the scatterers from a
nonlinear inverse problem in two steps, using either single or multiple
illuminations. We further introduce an approach that uses the top singular
vectors of the response matrix as optimal illuminations, which improves the
robustness of sparse promoting optimization with respect to additive noise.
When multiple scattering is negligible, the optimization problem becomes linear
and can be reduced to a hybrid- method when optimal illuminations are
used. When the media is random, and the interaction with the unknown
inhomogeneities can be primarily modeled by wavefront distortions, we address
the statistical stability of these methods. We analyze the fluctuations of the
images obtained with the hybrid- method, and we show that it is stable
with respect to different realizations of the random medium provided the
imaging array is large enough. We compare the performance of the
hybrid- method in random media to the widely used Kirchhoff migration
and the multiple signal classification methods
Recovery of the absorption coefficient in radiative transport from a single measurement
In this paper, we investigate the recovery of the absorption coefficient from
boundary data assuming that the region of interest is illuminated at an initial
time. We consider a sufficiently strong and isotropic, but otherwise unknown
initial state of radiation. This work is part of an effort to reconstruct
optical properties using unknown illumination embedded in the unknown medium.
We break the problem into two steps. First, in a linear framework, we seek
the simultaneous recovery of a forcing term of the form (with known) and an isotropic initial condition using
the single measurement induced by these data. Based on exact boundary
controllability, we derive a system of equations for the unknown terms and
. The system is shown to be Fredholm if satisfies a certain
positivity condition. We show that for generic term and weakly
absorbing media, this linear inverse problem is uniquely solvable with a
stability estimate. In the second step, we use the stability results from the
linear problem to address the nonlinearity in the recovery of a weak absorbing
coefficient. We obtain a locally Lipschitz stability estimate
Statistical stability in time reversal
When a signal is emitted from a source, recorded by an array of transducers,
time reversed and re-emitted into the medium, it will refocus approximately on
the source location. We analyze the refocusing resolution in a high frequency,
remote sensing regime, and show that, because of multiple scattering, in an
inhomogeneous or random medium it can improve beyond the diffraction limit. We
also show that the back-propagated signal from a spatially localized
narrow-band source is self-averaging, or statistically stable, and relate this
to the self-averaging properties of functionals of the Wigner distribution in
phase space. Time reversal from spatially distributed sources is self-averaging
only for broad-band signals. The array of transducers operates in a
remote-sensing regime so we analyze time reversal with the parabolic or
paraxial wave equation
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