1,537 research outputs found
Multiscale Astronomical Image Processing Based on Nonlinear Partial Differential Equations
Astronomical applications of recent advances in the field of nonastronomical image processing are presented. These innovative methods, applied to multiscale astronomical images, increase signal-to-noise ratio, do not smear point sources or extended diffuse structures, and are thus a highly useful preliminary step for detection of different features including point sources, smoothing of clumpy data, and removal of contaminants from background maps. We show how the new methods, combined with other algorithms of image processing, unveil fine diffuse structures while at the same time enhance detection of localized objects, thus facilitating interactive morphology studies and paving the way for the automated recognition and classification of different features. We have also developed a new application framework for astronomical image processing that implements some recent advances made in computer vision and modern image processing, along with original algorithms based on nonlinear partial differential equations. The framework enables the user to easily set up and customize an image-processing pipeline interactively; it has various common and new visualization features and provides access to many astronomy data archives. Altogether, the results presented here demonstrate the first implementation of a novel synergistic approach based on integration of image processing, image visualization, and image quality assessment
Resolution learning in deep convolutional networks using scale-space theory
Resolution in deep convolutional neural networks (CNNs) is typically bounded
by the receptive field size through filter sizes, and subsampling layers or
strided convolutions on feature maps. The optimal resolution may vary
significantly depending on the dataset. Modern CNNs hard-code their resolution
hyper-parameters in the network architecture which makes tuning such
hyper-parameters cumbersome. We propose to do away with hard-coded resolution
hyper-parameters and aim to learn the appropriate resolution from data. We use
scale-space theory to obtain a self-similar parametrization of filters and make
use of the N-Jet: a truncated Taylor series to approximate a filter by a
learned combination of Gaussian derivative filters. The parameter sigma of the
Gaussian basis controls both the amount of detail the filter encodes and the
spatial extent of the filter. Since sigma is a continuous parameter, we can
optimize it with respect to the loss. The proposed N-Jet layer achieves
comparable performance when used in state-of-the art architectures, while
learning the correct resolution in each layer automatically. We evaluate our
N-Jet layer on both classification and segmentation, and we show that learning
sigma is especially beneficial for inputs at multiple sizes
PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering
Recovering high quality surfaces from noisy point clouds, known as point
cloud denoising, is a fundamental yet challenging problem in geometry
processing. Most of the existing methods either directly denoise the noisy
input or filter raw normals followed by updating point positions. Motivated by
the essential interplay between point cloud denoising and normal filtering, we
revisit point cloud denoising from a multitask perspective, and propose an
end-to-end network, named PCDNF, to denoise point clouds via joint normal
filtering. In particular, we introduce an auxiliary normal filtering task to
help the overall network remove noise more effectively while preserving
geometric features more accurately. In addition to the overall architecture,
our network has two novel modules. On one hand, to improve noise removal
performance, we design a shape-aware selector to construct the latent tangent
space representation of the specific point by comprehensively considering the
learned point and normal features and geometry priors. On the other hand, point
features are more suitable for describing geometric details, and normal
features are more conducive for representing geometric structures (e.g., sharp
edges and corners). Combining point and normal features allows us to overcome
their weaknesses. Thus, we design a feature refinement module to fuse point and
normal features for better recovering geometric information. Extensive
evaluations, comparisons, and ablation studies demonstrate that the proposed
method outperforms state-of-the-arts for both point cloud denoising and normal
filtering
L\'evy flights on a comb and the plasma staircase
We formulate the problem of confined L\'evy flight on a comb. The comb
represents a sawtooth-like potential field , with the asymmetric teeth
favoring net transport in a preferred direction. The shape effect is modeled as
a power-law dependence within the sawtooth period,
followed by an abrupt drop-off to zero, after which the initial power-law
dependence is reset. It is found that the L\'evy flights will be confined in
the sense of generalized central limit theorem if (i) the spacing between the
teeth is sufficiently broad, and (ii) , where is the fractal
dimension of the flights. In particular, for the Cauchy flights (),
. The study is motivated by recent observations of
localization-delocalization of transport avalanches in banded flows in the Tore
Supra tokamak and is intended to devise a theory basis to explain the observed
phenomenology.Comment: 13 pages; 3 figures; accepted for publication in Physical Review
Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations
Climate projections continue to be marred by large uncertainties, which
originate in processes that need to be parameterized, such as clouds,
convection, and ecosystems. But rapid progress is now within reach. New
computational tools and methods from data assimilation and machine learning
make it possible to integrate global observations and local high-resolution
simulations in an Earth system model (ESM) that systematically learns from
both. Here we propose a blueprint for such an ESM. We outline how
parameterization schemes can learn from global observations and targeted
high-resolution simulations, for example, of clouds and convection, through
matching low-order statistics between ESMs, observations, and high-resolution
simulations. We illustrate learning algorithms for ESMs with a simple dynamical
system that shares characteristics of the climate system; and we discuss the
opportunities the proposed framework presents and the challenges that remain to
realize it.Comment: 32 pages, 3 figure
Advanced VLBI Imaging
Very Long Baseline Interferometry (VLBI) is an observational technique developed in astronomy for combining multiple radio telescopes into a single virtual instrument with an effective aperture reaching up to many thousand kilometers and enabling measurements at highest angular resolutions. The celebrated examples of applying VLBI to astrophysical studies include detailed, high-resolution images of the innermost parts of relativistic outflows (jets) in active galactic nuclei (AGN) and recent pioneering observations of the shadows of supermassive black holes (SMBH) in the center of our Galaxy and in the galaxy M87.
Despite these and many other proven successes of VLBI, analysis and imaging of VLBI data still remain difficult, owing in part to the fact that VLBI imaging inherently constitutes an ill-posed inverse problem. Historically, this problem has been addressed in radio interferometry by the CLEAN algorithm, a matching-pursuit inverse modeling method developed in the early 1970-s and since then established as a de-facto standard approach for imaging VLBI data.
In recent years, the constantly increasing demand for improving quality and fidelity of interferometric image reconstruction has resulted in several attempts to employ new approaches, such as forward modeling and Bayesian estimation, for application to VLBI imaging.
While the current state-of-the-art forward modeling and Bayesian techniques may outperform CLEAN in terms of accuracy, resolution, robustness, and adaptability, they also tend to require more complex structure and longer computation times, and rely on extensive finetuning of a larger number of non-trivial hyperparameters. This leaves an ample room for further searches for potentially more effective imaging approaches and provides the main motivation for this dissertation and its particular focusing on the need to unify algorithmic frameworks and to study VLBI imaging from the perspective of inverse problems in general.
In pursuit of this goal, and based on an extensive qualitative comparison of the existing methods, this dissertation comprises the development, testing, and first implementations of two novel concepts for improved interferometric image reconstruction. The concepts combine the known benefits of current forward modeling techniques, develop more automatic and less supervised algorithms for image reconstruction, and realize them within two different frameworks.
The first framework unites multiscale imaging algorithms in the spirit of compressive sensing with a dictionary adapted to the uv-coverage and its defects (DoG-HiT, DoB-CLEAN). We extend this approach to dynamical imaging and polarimetric imaging. The core components of this framework are realized in a multidisciplinary and multipurpose software MrBeam, developed as part of this dissertation.
The second framework employs a multiobjective genetic evolutionary algorithm (MOEA/D) for the purpose of achieving fully unsupervised image reconstruction and hyperparameter optimization.
These new methods are shown to outperform the existing methods in various metrics such as angular resolution, structural sensitivity, and degree of supervision. We demonstrate the great potential of these new techniques with selected applications to frontline VLBI observations of AGN jets and SMBH.
In addition to improving the quality and robustness of image reconstruction, DoG-HiT, DoB-CLEAN and MOEA/D also provide such novel capabilities as dynamic reconstruction of polarimetric images on minute time-scales, or near-real time and unsupervised data analysis (useful in particular for application to large imaging surveys).
The techniques and software developed in this dissertation are of interest for a wider range of inverse problems as well. This includes such versatile fields such as Ly-alpha tomography (where we improve estimates of the thermal state of the intergalactic medium), the cosmographic search for dark matter (where we improve forecasted bounds on ultralight dilatons), medical imaging, and solar spectroscopy
Multiscale Modelling for Tokamak Pedestals
Pedestal modelling is crucial to predict the performance of future fusion
devices. Current modelling efforts suffer either from a lack of kinetic
physics, or an excess of computational complexity. To ameliorate these
problems, we take a first-principles multiscale approach to the pedestal. We
will present three separate sets of equations, covering the dynamics of Edge
Lo- calised Modes, the inter-ELM pedestal, and pedestal turbulence,
respectively. Precisely how these equations should be coupled to each other are
covered in detail. This framework is completely self-consistent; it is derived
from first principles by means an asymptotic expansion in appropriate small
parameters. The derivation exploits the narrowness of the pedestal region, the
smallness of the thermal gyroradius, and the low plasma typical of
current pedestal operation to achieve its simplifications. The relationship
between this framework and gyrokinetics is analysed, and possibilities to
directly match this framework onto multiscale gyrokinetics are explored. A
detailed comparison between our model and other models in the literature is
performed. Finally, the potential for matching this framework onto an
open-field-line region is discussed.Comment: 49 pages; Accepted for publication in the Journal of Plasma Physic
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