1,187 research outputs found
Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation
Inverse problems play a key role in modern image/signal processing methods.
However, since they are generally ill-conditioned or ill-posed due to lack of
observations, their solutions may have significant intrinsic uncertainty.
Analysing and quantifying this uncertainty is very challenging, particularly in
high-dimensional problems and problems with non-smooth objective functionals
(e.g. sparsity-promoting priors). In this article, a series of strategies to
visualise this uncertainty are presented, e.g. highest posterior density
credible regions, and local credible intervals (cf. error bars) for individual
pixels and superpixels. Our methods support non-smooth priors for inverse
problems and can be scaled to high-dimensional settings. Moreover, we present
strategies to automatically set regularisation parameters so that the proposed
uncertainty quantification (UQ) strategies become much easier to use. Also,
different kinds of dictionaries (complete and over-complete) are used to
represent the image/signal and their performance in the proposed UQ methodology
is investigated.Comment: 5 pages, 5 figure
Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging
Computational image reconstruction algorithms generally produce a single
image without any measure of uncertainty or confidence. Regularized Maximum
Likelihood (RML) and feed-forward deep learning approaches for inverse problems
typically focus on recovering a point estimate. This is a serious limitation
when working with underdetermined imaging systems, where it is conceivable that
multiple image modes would be consistent with the measured data. Characterizing
the space of probable images that explain the observational data is therefore
crucial. In this paper, we propose a variational deep probabilistic imaging
approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging
(DPI) employs an untrained deep generative model to estimate a posterior
distribution of an unobserved image. This approach does not require any
training data; instead, it optimizes the weights of a neural network to
generate image samples that fit a particular measurement dataset. Once the
network weights have been learned, the posterior distribution can be
efficiently sampled. We demonstrate this approach in the context of
interferometric radio imaging, which is used for black hole imaging with the
Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging
(MRI).Comment: This paper has been accepted to AAAI 2021. Keywords: Computational
Imaging, Normalizing Flow, Uncertainty Quantification, Interferometry, MR
CHARA/MIRC observations of two M supergiants in Perseus OB1: temperature, Bayesian modeling, and compressed sensing imaging
Two red supergiants of the Per OB1 association, RS Per and T Per, have been
observed in H band using the MIRC instrument at the CHARA array. The data show
clear evidence of departure from circular symmetry. We present here new
techniques specially developed to analyze such cases, based on state-of-the-art
statistical frameworks. The stellar surfaces are first modeled as limb-darkened
discs based on SATLAS models that fit both MIRC interferometric data and
publicly available spectrophotometric data. Bayesian model selection is then
used to determine the most probable number of spots. The effective surface
temperatures are also determined and give further support to the recently
derived hotter temperature scales of red su- pergiants. The stellar surfaces
are reconstructed by our model-independent imaging code SQUEEZE, making use of
its novel regularizer based on Compressed Sensing theory. We find excellent
agreement between the model-selection results and the reconstructions. Our
results provide evidence for the presence of near-infrared spots representing
about 3-5% of the stellar flux
Non-Local Compressive Sensing Based SAR Tomography
Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse
reconstruction problem and, hence, can be solved using compressive sensing (CS)
algorithms. This paper proposes solutions for two notorious problems in this
field: 1) TomoSAR requires a high number of data sets, which makes the
technique expensive. However, it can be shown that the number of acquisitions
and the signal-to-noise ratio (SNR) can be traded off against each other,
because it is asymptotically only the product of the number of acquisitions and
SNR that determines the reconstruction quality. We propose to increase SNR by
integrating non-local estimation into the inversion and show that a reasonable
reconstruction of buildings from only seven interferograms is feasible. 2)
CS-based inversion is computationally expensive and therefore barely suitable
for large-scale applications. We introduce a new fast and accurate algorithm
for solving the non-local L1-L2-minimization problem, central to CS-based
reconstruction algorithms. The applicability of the algorithm is demonstrated
using simulated data and TerraSAR-X high-resolution spotlight images over an
area in Munich, Germany.Comment: 10 page
Interferometry of Aurigae: Characterization of the asymmetric eclipsing disk
We report on a total of 106 nights of optical interferometric observations of
the Aurigae system taken during the last 14 years by four beam
combiners at three different interferometric facilities. This long sequence of
data provides an ideal assessment of the system prior to, during, and after the
recent 2009-2011 eclipse. We have reconstructed model-independent images from
the 10 in-eclipse epochs which show that a disk-like object is indeed
responsible for the eclipse. Using new 3D, time-dependent modeling software, we
derive the properties of the F-star (diameter, limb darkening), determine
previously unknown orbital elements (, ), and access the global
structures of the optically thick portion of the eclipsing disk using both
geometric models and approximations of astrophysically relevant density
distributions. These models may be useful in future hydrodynamical modeling of
the system. Lastly, we address several outstanding research questions including
mid-eclipse brightening, possible shrinking of the F-type primary, and any
warps or sub-features within the disk.Comment: 105 pages, 57 figures. This is an author-created, un-copyedited
version of an article accepted for publication in Astrophysical Journal
Supplement Series. IOP Publishing Ltd is not responsible for any errors or
omissions in this version of the manuscript or any version derived from i
Computational Inverse Problems for Partial Differential Equations
The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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