334 research outputs found
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Mathematical Methods in Tomography
This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century
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Mathematical Challenges in Electron Microscopy
Development of electron microscopes first started nearly 100 years ago and they are now a mature imaging modality with many applications and vast potential for the future. The principal feature of electron microscopes is their resolution; they can be up to 1000 times more powerful than a visible light microscope and resolve even the smallest atoms. Furthermore, electron microscopes are also sensitive to many material properties due to the very rich interactions between electrons and other matter. Because of these capabilities, electron microscopy is used in applications as diverse as drug discovery, computer chip manufacture, and the development of solar cells.
In parallel to this, the mathematical field of inverse problems has also evolved dramatically. Many new methods have been introduced to improve the recovery of unknown structures from indirect data, typically an ill-posed problem. In particular, sparsity promoting functionals such as the total variation and its extensions have been shown to be very powerful for recovering accurate physical quantities from very little and/or poor quality data. While sparsity-promoting reconstruction methods are powerful, they can also be slow, especially in a big-data setting. This trade-off forms an eternal cycle as new numerical tools are found and more powerful models are developed.
The work presented in this thesis aims to marry the tools of inverse problems with the problems of electron microscopy: bringing state-of-the-art image processing techniques to bear on challenges specific to electron microscopy, developing new optimisation methods for these problems, and modelling new inverse problems to extend the capabilities of existing microscopes. One focus is the application of a directional total variation to overcome the limited angle problem in electron tomography, another is the proposal of a new inverse problem for the reconstruction of 3D strain tensor fields from electron microscopy diffraction data. The remaining contributions target numerical aspects of inverse problems, from new algorithms for non-convex problems to convex optimisation with adaptive meshes.Cantab Capital Institute for Mathematics of Informatio
Modern GPR Target Recognition Methods
Traditional GPR target recognition methods include pre-processing the data by
removal of noisy signatures, dewowing (high-pass filtering to remove
low-frequency noise), filtering, deconvolution, migration (correction of the
effect of survey geometry), and can rely on the simulation of GPR responses.
The techniques usually suffer from the loss of information, inability to adapt
from prior results, and inefficient performance in the presence of strong
clutter and noise. To address these challenges, several advanced processing
methods have been developed over the past decade to enhance GPR target
recognition. In this chapter, we provide an overview of these modern GPR
processing techniques. In particular, we focus on the following methods:
adaptive receive processing of range profiles depending on the target
environment; adoption of learning-based methods so that the radar utilizes the
results from prior measurements; application of methods that exploit the fact
that the target scene is sparse in some domain or dictionary; application of
advanced classification techniques; and convolutional coding which provides
succinct and representatives features of the targets. We describe each of these
techniques or their combinations through a representative application of
landmine detection.Comment: Book chapter, 56 pages, 17 figures, 12 tables. arXiv admin note:
substantial text overlap with arXiv:1806.0459
Adorym: A multi-platform generic x-ray image reconstruction framework based on automatic differentiation
We describe and demonstrate an optimization-based x-ray image reconstruction
framework called Adorym. Our framework provides a generic forward model,
allowing one code framework to be used for a wide range of imaging methods
ranging from near-field holography to and fly-scan ptychographic tomography. By
using automatic differentiation for optimization, Adorym has the flexibility to
refine experimental parameters including probe positions, multiple hologram
alignment, and object tilts. It is written with strong support for parallel
processing, allowing large datasets to be processed on high-performance
computing systems. We demonstrate its use on several experimental datasets to
show improved image quality through parameter refinement
A Comprehensive Survey of Deep Learning in Remote Sensing: Theories, Tools and Challenges for the Community
In recent years, deep learning (DL), a re-branding of neural networks (NNs),
has risen to the top in numerous areas, namely computer vision (CV), speech
recognition, natural language processing, etc. Whereas remote sensing (RS)
possesses a number of unique challenges, primarily related to sensors and
applications, inevitably RS draws from many of the same theories as CV; e.g.,
statistics, fusion, and machine learning, to name a few. This means that the RS
community should be aware of, if not at the leading edge of, of advancements
like DL. Herein, we provide the most comprehensive survey of state-of-the-art
RS DL research. We also review recent new developments in the DL field that can
be used in DL for RS. Namely, we focus on theories, tools and challenges for
the RS community. Specifically, we focus on unsolved challenges and
opportunities as it relates to (i) inadequate data sets, (ii)
human-understandable solutions for modelling physical phenomena, (iii) Big
Data, (iv) non-traditional heterogeneous data sources, (v) DL architectures and
learning algorithms for spectral, spatial and temporal data, (vi) transfer
learning, (vii) an improved theoretical understanding of DL systems, (viii)
high barriers to entry, and (ix) training and optimizing the DL.Comment: 64 pages, 411 references. To appear in Journal of Applied Remote
Sensin
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