6,084 research outputs found
One shot profilometry using iterative two-step temporal phase-unwrapping
This paper reviews two techniques that have been recently published for 3D
profilometry and proposes one shot profilometry using iterative two-step
temporal phase-unwrapping by combining the composite fringe projection and the
iterative two-step temporal phase unwrapping algorithm. In temporal phase
unwrapping, many images with different frequency fringe pattern are needed to
project which would take much time. In order to solve this problem, Ochoa
proposed a phase unwrapping algorithm based on phase partitions using a
composite fringe, which only needs projecting one composite fringe pattern with
four kinds of frequency information to complete the process of 3D profilometry.
However, we found that the fringe order determined through the construction of
phase partitions tended to be imprecise. Recently, we proposed an iterative
two-step temporal phase unwrapping algorithm, which can achieve high
sensitivity and high precision shape measurement. But it needs multiple frames
of fringe images which would take much time. In order to take into account both
the speed and accuracy of 3D shape measurement, we get a new, and more accurate
unwrapping method based on composite fringe pattern by combining these two
techniques. This method not only retains the speed advantage of Ochoa's
algorithm, but also greatly improves its measurement accuracy. Finally, the
experimental evaluation is conducted to prove the validity of the proposed
method, and the experimental results show that this method is feasible.Comment: 14 pages, 15 figure
Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources
Light incident on a layer of scattering material such as a piece of sugar or
white paper forms a characteristic speckle pattern in transmission and
reflection. The information hidden in the correlations of the speckle pattern
with varying frequency, polarization and angle of the incident light can be
exploited for applications such as biomedical imaging and high-resolution
microscopy. Conventional computational models for multi-frequency optical
response involve multiple solution runs of Maxwell's equations with
monochromatic sources. Exponential Krylov subspace time solvers are promising
candidates for improving efficiency of such models, as single monochromatic
solution can be reused for the other frequencies without performing full
time-domain computations at each frequency. However, we show that the
straightforward implementation appears to have serious limitations. We further
propose alternative ways for efficient solution through Krylov subspace
methods. Our methods are based on two different splittings of the unknown
solution into different parts, each of which can be computed efficiently.
Experiments demonstrate a significant gain in computation time with respect to
the standard solvers.Comment: 22 pages, 4 figure
Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging
This paper combines the use of high order finite element methods with
parallel preconditioners of domain decomposition type for solving
electromagnetic problems arising from brain microwave imaging. The numerical
algorithms involved in such complex imaging systems are computationally
expensive since they require solving the direct problem of Maxwell's equations
several times. Moreover, wave propagation problems in the high frequency regime
are challenging because a sufficiently high number of unknowns is required to
accurately represent the solution. In order to use these algorithms in practice
for brain stroke diagnosis, running time should be reasonable. The method
presented in this paper, coupling high order finite elements and parallel
preconditioners, makes it possible to reduce the overall computational cost and
simulation time while maintaining accuracy
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
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