10,914 research outputs found
SEAGLE: Sparsity-Driven Image Reconstruction under Multiple Scattering
Multiple scattering of an electromagnetic wave as it passes through an object
is a fundamental problem that limits the performance of current imaging
systems. In this paper, we describe a new technique-called Series Expansion
with Accelerated Gradient Descent on Lippmann-Schwinger Equation (SEAGLE)-for
robust imaging under multiple scattering based on a combination of a new
nonlinear forward model and a total variation (TV) regularizer. The proposed
forward model can account for multiple scattering, which makes it advantageous
in applications where linear models are inaccurate. Specifically, it
corresponds to a series expansion of the scattered wave with an
accelerated-gradient method. This expansion guarantees the convergence even for
strongly scattering objects. One of our key insights is that it is possible to
obtain an explicit formula for computing the gradient of our nonlinear forward
model with respect to the unknown object, thus enabling fast image
reconstruction with the state-of-the-art fast iterative shrinkage/thresholding
algorithm (FISTA). The proposed method is validated on both simulated and
experimentally measured data
Optical tomography: forward and inverse problems
This paper is a review of recent mathematical and computational advances in
optical tomography. We discuss the physical foundations of forward models for
light propagation on microscopic, mesoscopic and macroscopic scales. We also
consider direct and numerical approaches to the inverse problems that arise at
each of these scales. Finally, we outline future directions and open problems
in the field.Comment: 70 pages, 2 figure
Kinetic Solvers with Adaptive Mesh in Phase Space for Low-Temperature Plasmas
We describe the implementation of 1d1v and 1d2v Vlasov and Fokker-Planck
kinetic solvers with adaptive mesh refinement in phase space (AMPS) and
coupling these kinetic solvers to Poisson equation solver for electric field.
We demonstrate that coupling AMPS kinetic and electrostatic solvers can be done
efficiently without splitting phase-space transport. We show that Eulerian
fluid and kinetic solvers with dynamically adaptive Cartesian mesh can be used
for simulations of collisionless plasma expansion into vacuum. The
Vlasov-Fokker-Planck solver is demonstrated for the analysis of electron
acceleration and scattering as well as the generation of runaway electrons in
spatially inhomogeneous electric fields
High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: Sampling Cost via Incident-Field Windowing and Recentering
This paper proposes a frequency/time hybrid integral-equation method for the
time dependent wave equation in two and three-dimensional spatial domains.
Relying on Fourier Transformation in time, the method utilizes a fixed
(time-independent) number of frequency-domain integral-equation solutions to
evaluate, with superalgebraically-small errors, time domain solutions for
arbitrarily long times. The approach relies on two main elements, namely, 1) A
smooth time-windowing methodology that enables accurate band-limited
representations for arbitrarily-long time signals, and 2) A novel Fourier
transform approach which, in a time-parallel manner and without causing
spurious periodicity effects, delivers numerically dispersionless
spectrally-accurate solutions. A similar hybrid technique can be obtained on
the basis of Laplace transforms instead of Fourier transforms, but we do not
consider the Laplace-based method in the present contribution. The algorithm
can handle dispersive media, it can tackle complex physical structures, it
enables parallelization in time in a straightforward manner, and it allows for
time leaping---that is, solution sampling at any given time at
-bounded sampling cost, for arbitrarily large values of ,
and without requirement of evaluation of the solution at intermediate times.
The proposed frequency-time hybridization strategy, which generalizes to any
linear partial differential equation in the time domain for which
frequency-domain solutions can be obtained (including e.g. the time-domain
Maxwell equations), and which is applicable in a wide range of scientific and
engineering contexts, provides significant advantages over other available
alternatives such as volumetric discretization, time-domain integral equations,
and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now
including direct comparisons to existing CQ and TDIE solver implementations)
(Part I of II
Mathematics of Hybrid Imaging. A Brief Review
The article provides a brief survey of the mathematics of some of the newly
being developed so called "hybrid" (also called "multi-physics" or
"multi-wave") imaging techniques.Comment: Dedicated to the memory of Professor Leon Ehrenprei
Lagrange Discrete Ordinates: a new angular discretization for the three dimensional linear Boltzmann equation
The classical equations of Carlson and Lee have been a mainstay in
multi-dimensional radiation transport calculations. In this paper, an
alternative to the equations, the "Lagrange Discrete Ordinate" (LDO)
equations are derived. These equations are based on an interpolatory framework
for functions on the unit sphere in three dimensions. While the LDO equations
retain the formal structure of the classical equations, they have a
number of important differences. The LDO equations naturally allow the angular
flux to be evaluated in directions other than those found in the quadrature
set. To calculate the scattering source in the LDO equations, no spherical
harmonic moments are needed--only values of the angular flux. Moreover, the LDO
scattering source preserves the eigenstructure of the continuous scattering
operator. The formal similarity of the LDO equations with the equations
should allow easy modification of mature 3D codes such as PARTISN or
PENTRAN to solve the LDO equations. Numerical results are shown that
demonstrate the spectral convergence (in angle) of the LDO equations for smooth
solutions and the ability to mitigate ray effects by increasing the angular
resolution of the LDO equations.Comment: Submitted to Nuclear Science and Engineerin
A numerical mode matching method for wave scattering in a layered medium with a stratified inhomogeneity
Numerical mode matching (NMM) methods are widely used for analyzing wave
propagation and scattering in structures that are piece-wise uniform along one
spatial direction. For open structures that are unbounded in transverse
directions (perpendicular to the uniform direction), the NMM methods use the
perfectly matched layer (PML) technique to truncate the transverse variables.
When incident waves are specified in homogeneous media surrounding the main
structure, the total field is not always outgoing, and the NMM methods rely on
reference solutions for each uniform segment. Existing NMM methods have
difficulty handing gracing incident waves and special incident waves related to
the onset of total internal reflection, and are not very efficient at computing
reference solutions for non-plane incident waves. In this paper, a new NMM
method is developed to overcome these limitations. A Robin-type boundary
condition is proposed to ensure that non-propagating and non-decaying wave
field components are not reflected by truncated PMLs. Exponential convergence
of the PML solutions based on the hybrid Dirichlet-Robin boundary condition is
established theoretically. A fast method is developed for computing reference
solutions for cylindrical incident waves. The new NMM is implemented for
two-dimensional structures and polarized electromagnetic waves. Numerical
experiments are carried out to validate the new NMM method and to demonstrate
its performance.Comment: 26 pages, 15 figure
Quasi-periodic Green's functions of the Helmholtz and Laplace equations
A classical problem of free-space Green's function
representations of the Helmholtz equation is studied in various quasi-periodic
cases, i.e., when an underlying periodicity is imposed in less dimensions than
is the dimension of an embedding space. Exponentially convergent series for the
free-space quasi-periodic and for the expansion coefficients
of in the basis of regular (cylindrical in two
dimensions and spherical in three dimension (3D)) waves, or lattice sums, are
reviewed and new results for the case of a one-dimensional (1D) periodicity in
3D are derived. From a mathematical point of view, a derivation of
exponentially convergent representations for Schl\"{o}milch series of
cylindrical and spherical Hankel functions of any integer order is
accomplished. The quasi-periodic Green's functions of the Laplace equation are
obtained from the corresponding representations of of the
Helmholtz equation by taking the limit of the wave vector magnitude going to
zero. The derivation of relevant results in the case of a 1D periodicity in 3D
highlights the common part which is universally applicable to any of remaining
quasi-periodic cases. The results obtained can be useful for numerical solution
of boundary integral equations for potential flows in fluid mechanics, remote
sensing of periodic surfaces, periodic gratings, in many contexts of simulating
systems of charged particles, in molecular dynamics, for the description of
quasi-periodic arrays of point interactions in quantum mechanics, and in
various ab-initio first-principle multiple-scattering theories for the analysis
of diffraction of classical and quantum waves.Comment: 60 pages, 5 figures; no change in the results; introduction
rewritten, refined sectioning, Fig. 1 amended, 3 references adde
A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
On X-ray scattering model for single particles, Part I: The legacy of protein crystallography
Emerging coherent X-ray scattering patterns of single particles have shown
dominant morphological signatures in agreement with predictions of the
scattering model used for conventional protein crystallography. The key
question is if and to what extent these scattering patterns contain volumetric
information, and what model can retrieve it. The scattering model of protein
crystallography is valid for very small crystals or those like crystalized
biomolecules with small coherent subunits. But in the general case, it fails to
model the integrated intensities of diffraction spots, and cannot even find the
size of the crystal. The more rigorous and less employed alternative is a
purely-classical crystal-specific model, which bypasses the fundamental notion
of bulk and hence the non-classical X-ray scattering from bulk. This
contribution is Part 1 out of two reports, in which we seek to clarify the
assumptions of some different regimes and models of X-ray scattering and their
implications for single particle imaging. In this part, first basic concepts
and existing models are briefly reviewed. Then the predictions of the
conventional and the rigorous models for emerging scattering patterns of
protein nanocrystals (intermediate case between conventional crystals and
single particles) are contrasted, and the terminology conflict regarding
"Diffraction Theory" is addressed. With a clearer picture of crystal
scattering, Part 2 will focus on additional concepts, limitations, correction
schemes, and alternative models relevant to single particles. Aside from such
optical details, protein crystallography is an advanced tool of analytical
chemistry and not a self-contained optical imaging technique (despite
significant instrumental role of optical data). As such, its final results can
be neither confirmed nor rejected on mere optical grounds; i.e., no
jurisdiction for optics.Comment: Some of the reviews and discussions were moved to new appendice
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