75,161 research outputs found
On the Reconstruction of Static and Dynamic Discrete Structures
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in ). The main emphasis is on recent mathematical developments and new applications, which emerge in scientific areas such as physics and materials science, but also in inner mathematical fields such as number theory, optimization, and imaging. Along with a concise introduction to the field of discrete tomography, we give pointers to related aspects of computerized tomography in order to contrast the worlds of continuous and discrete inverse problems
Time-Dependent Tomographic Reconstruction of the Solar Corona
Solar rotational tomography (SRT) applied to white-light coronal images
observed at multiple aspect angles has been the preferred approach for
determining the three-dimensional (3D) electron density structure of the solar
corona. However, it is seriously hampered by the restrictive assumption that
the corona is time-invariant which introduces significant errors in the
reconstruction. We first explore several methods to mitigate the temporal
variation of the corona by decoupling the "fast-varying" inner corona from the
"slow-moving" outer corona using multiple masking (either by juxtaposition or
recursive combination) and radial weighting. Weighting with a radial
exponential profile provides some improvement over a classical reconstruction
but only beyond 3 Rsun. We next consider a full time-dependent tomographic
reconstruction involving spatio-temporal regularization and further introduce a
co-rotating regularization aimed at preventing concentration of reconstructed
density in the plane of the sky. Crucial to testing our procedure and properly
tuning the regularization parameters is the introduction of a time-dependent
MHD model of the corona based on observed magnetograms to build a time-series
of synthetic images of the corona. Our procedure, which successfully reproduces
the time-varying model corona, is finally applied to a set of of 53 LASCO-C2 pB
images roughly evenly spaced in time from 15 to 29 March 2009. Our procedure
paves the way to a time-dependent tomographic reconstruction of the coronal
electron density to the whole set of LASCO-C2 images presently spanning 20
years.Comment: 24 pages, 18 figure
Dynamical system analysis and forecasting of deformation produced by an earthquake fault
We present a method of constructing low-dimensional nonlinear models
describing the main dynamical features of a discrete 2D cellular fault zone,
with many degrees of freedom, embedded in a 3D elastic solid. A given fault
system is characterized by a set of parameters that describe the dynamics,
rheology, property disorder, and fault geometry. Depending on the location in
the system parameter space we show that the coarse dynamics of the fault can be
confined to an attractor whose dimension is significantly smaller than the
space in which the dynamics takes place. Our strategy of system reduction is to
search for a few coherent structures that dominate the dynamics and to capture
the interaction between these coherent structures. The identification of the
basic interacting structures is obtained by applying the Proper Orthogonal
Decomposition (POD) to the surface deformations fields that accompany
strike-slip faulting accumulated over equal time intervals. We use a
feed-forward artificial neural network (ANN) architecture for the
identification of the system dynamics projected onto the subspace (model space)
spanned by the most energetic coherent structures. The ANN is trained using a
standard back-propagation algorithm to predict (map) the values of the observed
model state at a future time given the observed model state at the present
time. This ANN provides an approximate, large scale, dynamical model for the
fault.Comment: 30 pages, 12 figure
SOM-VAE: Interpretable Discrete Representation Learning on Time Series
High-dimensional time series are common in many domains. Since human
cognition is not optimized to work well in high-dimensional spaces, these areas
could benefit from interpretable low-dimensional representations. However, most
representation learning algorithms for time series data are difficult to
interpret. This is due to non-intuitive mappings from data features to salient
properties of the representation and non-smoothness over time. To address this
problem, we propose a new representation learning framework building on ideas
from interpretable discrete dimensionality reduction and deep generative
modeling. This framework allows us to learn discrete representations of time
series, which give rise to smooth and interpretable embeddings with superior
clustering performance. We introduce a new way to overcome the
non-differentiability in discrete representation learning and present a
gradient-based version of the traditional self-organizing map algorithm that is
more performant than the original. Furthermore, to allow for a probabilistic
interpretation of our method, we integrate a Markov model in the representation
space. This model uncovers the temporal transition structure, improves
clustering performance even further and provides additional explanatory
insights as well as a natural representation of uncertainty. We evaluate our
model in terms of clustering performance and interpretability on static
(Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST
images, a chaotic Lorenz attractor system with two macro states, as well as on
a challenging real world medical time series application on the eICU data set.
Our learned representations compare favorably with competitor methods and
facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on
Learning Representations (ICLR 2019
Temporally coherent 4D reconstruction of complex dynamic scenes
This paper presents an approach for reconstruction of 4D temporally coherent
models of complex dynamic scenes. No prior knowledge is required of scene
structure or camera calibration allowing reconstruction from multiple moving
cameras. Sparse-to-dense temporal correspondence is integrated with joint
multi-view segmentation and reconstruction to obtain a complete 4D
representation of static and dynamic objects. Temporal coherence is exploited
to overcome visual ambiguities resulting in improved reconstruction of complex
scenes. Robust joint segmentation and reconstruction of dynamic objects is
achieved by introducing a geodesic star convexity constraint. Comparative
evaluation is performed on a variety of unstructured indoor and outdoor dynamic
scenes with hand-held cameras and multiple people. This demonstrates
reconstruction of complete temporally coherent 4D scene models with improved
nonrigid object segmentation and shape reconstruction.Comment: To appear in The IEEE Conference on Computer Vision and Pattern
Recognition (CVPR) 2016 . Video available at:
https://www.youtube.com/watch?v=bm_P13_-Ds
Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing
Current 3D photoacoustic tomography (PAT) systems offer either high image
quality or high frame rates but are not able to deliver high spatial and
temporal resolution simultaneously, which limits their ability to image dynamic
processes in living tissue. A particular example is the planar Fabry-Perot (FP)
scanner, which yields high-resolution images but takes several minutes to
sequentially map the photoacoustic field on the sensor plane, point-by-point.
However, as the spatio-temporal complexity of many absorbing tissue structures
is rather low, the data recorded in such a conventional, regularly sampled
fashion is often highly redundant. We demonstrate that combining variational
image reconstruction methods using spatial sparsity constraints with the
development of novel PAT acquisition systems capable of sub-sampling the
acoustic wave field can dramatically increase the acquisition speed while
maintaining a good spatial resolution: First, we describe and model two general
spatial sub-sampling schemes. Then, we discuss how to implement them using the
FP scanner and demonstrate the potential of these novel compressed sensing PAT
devices through simulated data from a realistic numerical phantom and through
measured data from a dynamic experimental phantom as well as from in-vivo
experiments. Our results show that images with good spatial resolution and
contrast can be obtained from highly sub-sampled PAT data if variational image
reconstruction methods that describe the tissues structures with suitable
sparsity-constraints are used. In particular, we examine the use of total
variation regularization enhanced by Bregman iterations. These novel
reconstruction strategies offer new opportunities to dramatically increase the
acquisition speed of PAT scanners that employ point-by-point sequential
scanning as well as reducing the channel count of parallelized schemes that use
detector arrays.Comment: submitted to "Physics in Medicine and Biology
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