13,638 research outputs found
A parametric level-set method for partially discrete tomography
This paper introduces a parametric level-set method for tomographic
reconstruction of partially discrete images. Such images consist of a
continuously varying background and an anomaly with a constant (known)
grey-value. We represent the geometry of the anomaly using a level-set
function, which we represent using radial basis functions. We pose the
reconstruction problem as a bi-level optimization problem in terms of the
background and coefficients for the level-set function. To constrain the
background reconstruction we impose smoothness through Tikhonov regularization.
The bi-level optimization problem is solved in an alternating fashion; in each
iteration we first reconstruct the background and consequently update the
level-set function. We test our method on numerical phantoms and show that we
can successfully reconstruct the geometry of the anomaly, even from limited
data. On these phantoms, our method outperforms Total Variation reconstruction,
DART and P-DART.Comment: Paper submitted to 20th International Conference on Discrete Geometry
for Computer Imager
Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network
Efficient and high-fidelity prior sampling and inversion for complex
geological media is still a largely unsolved challenge. Here, we use a deep
neural network of the variational autoencoder type to construct a parametric
low-dimensional base model parameterization of complex binary geological media.
For inversion purposes, it has the attractive feature that random draws from an
uncorrelated standard normal distribution yield model realizations with spatial
characteristics that are in agreement with the training set. In comparison with
the most commonly used parametric representations in probabilistic inversion,
we find that our dimensionality reduction (DR) approach outperforms principle
component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform
(DCT) DR techniques for unconditional geostatistical simulation of a
channelized prior model. For the considered examples, important compression
ratios (200 - 500) are achieved. Given that the construction of our
parameterization requires a training set of several tens of thousands of prior
model realizations, our DR approach is more suited for probabilistic (or
deterministic) inversion than for unconditional (or point-conditioned)
geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D
transient hydraulic tomography data are used to demonstrate the DR-based
inversion. For the 2D case study, the performance is superior compared to
current state-of-the-art multiple-point statistics inversion by sequential
geostatistical resampling (SGR). Inversion results for the 3D application are
also encouraging
Quantum characterization of bipartite Gaussian states
Gaussian bipartite states are basic tools for the realization of quantum
information protocols with continuous variables. Their complete
characterization is obtained by the reconstruction of the corresponding
covariance matrix. Here we describe in details and experimentally demonstrate a
robust and reliable method to fully characterize bipartite optical Gaussian
states by means of a single homodyne detector. We have successfully applied our
method to the bipartite states generated by a sub-threshold type-II optical
parametric oscillator which produces a pair of thermal cross-polarized
entangled CW frequency degenerate beams. The method provide a reliable
reconstruction of the covariance matrix and allows to retrieve all the physical
information about the state under investigation. These includes observable
quantities, as energy and squeezing, as well as non observable ones as purity,
entropy and entanglement. Our procedure also includes advanced tests for
Gaussianity of the state and, overall, represents a powerful tool to study
bipartite Gaussian state from the generation stage to the detection one
Non-maximally entangled states: production, characterization and utilization
Using a spontaneous-downconversion photon source, we produce true
non-maximally entangled states, i.e., without the need for post-selection. The
degree and phase of entanglement are readily tunable, and are characterized
both by a standard analysis using coincidence minima, and by quantum state
tomography of the two-photon state. Using the latter, we experimentally
reconstruct the reduced density matrix for the polarization. Finally, we use
these states to measure the Hardy fraction, obtaining a result that is from any local-realistic result.Comment: 4 pages, 4 figures. To appear in Phys. Rev. Let
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