963 research outputs found
A penalty method for PDE-constrained optimization in inverse problems
Many inverse and parameter estimation problems can be written as
PDE-constrained optimization problems. The goal, then, is to infer the
parameters, typically coefficients of the PDE, from partial measurements of the
solutions of the PDE for several right-hand-sides. Such PDE-constrained
problems can be solved by finding a stationary point of the Lagrangian, which
entails simultaneously updating the paramaters and the (adjoint) state
variables. For large-scale problems, such an all-at-once approach is not
feasible as it requires storing all the state variables. In this case one
usually resorts to a reduced approach where the constraints are explicitly
eliminated (at each iteration) by solving the PDEs. These two approaches, and
variations thereof, are the main workhorses for solving PDE-constrained
optimization problems arising from inverse problems. In this paper, we present
an alternative method that aims to combine the advantages of both approaches.
Our method is based on a quadratic penalty formulation of the constrained
optimization problem. By eliminating the state variable, we develop an
efficient algorithm that has roughly the same computational complexity as the
conventional reduced approach while exploiting a larger search space. Numerical
results show that this method indeed reduces some of the non-linearity of the
problem and is less sensitive the initial iterate
Sequential Experimental Design for X-Ray CT Using Deep Reinforcement Learning
In X-ray Computed Tomography (CT), projections from many angles are acquired
and used for 3D reconstruction. To make CT suitable for in-line quality
control, reducing the number of angles while maintaining reconstruction quality
is necessary. Sparse-angle tomography is a popular approach for obtaining 3D
reconstructions from limited data. To optimize its performance, one can adapt
scan angles sequentially to select the most informative angles for each scanned
object. Mathematically, this corresponds to solving and optimal experimental
design (OED) problem. OED problems are high-dimensional, non-convex, bi-level
optimization problems that cannot be solved online, i.e., during the scan. To
address these challenges, we pose the OED problem as a partially observable
Markov decision process in a Bayesian framework, and solve it through deep
reinforcement learning. The approach learns efficient non-greedy policies to
solve a given class of OED problems through extensive offline training rather
than solving a given OED problem directly via numerical optimization. As such,
the trained policy can successfully find the most informative scan angles
online. We use a policy training method based on the Actor-Critic approach and
evaluate its performance on 2D tomography with synthetic data
Deep data compression for approximate ultrasonic image formation
In many ultrasonic imaging systems, data acquisition and image formation are
performed on separate computing devices. Data transmission is becoming a
bottleneck, thus, efficient data compression is essential. Compression rates
can be improved by considering the fact that many image formation methods rely
on approximations of wave-matter interactions, and only use the corresponding
part of the data. Tailored data compression could exploit this, but extracting
the useful part of the data efficiently is not always trivial. In this work, we
tackle this problem using deep neural networks, optimized to preserve the image
quality of a particular image formation method. The Delay-And-Sum (DAS)
algorithm is examined which is used in reflectivity-based ultrasonic imaging.
We propose a novel encoder-decoder architecture with vector quantization and
formulate image formation as a network layer for end-to-end training.
Experiments demonstrate that our proposed data compression tailored for a
specific image formation method obtains significantly better results as opposed
to compression agnostic to subsequent imaging. We maintain high image quality
at much higher compression rates than the theoretical lossless compression rate
derived from the rank of the linear imaging operator. This demonstrates the
great potential of deep ultrasonic data compression tailored for a specific
image formation method.Comment: IEEE International Ultrasonics Symposium 202
2DeteCT -- A large 2D expandable, trainable, experimental Computed Tomography dataset for machine learning
Recent research in computational imaging largely focuses on developing
machine learning (ML) techniques for image reconstruction, which requires
large-scale training datasets consisting of measurement data and ground-truth
images. However, suitable experimental datasets for X-ray Computed Tomography
(CT) are scarce, and methods are often developed and evaluated only on
simulated data. We fill this gap by providing the community with a versatile,
open 2D fan-beam CT dataset suitable for developing ML techniques for a range
of image reconstruction tasks. To acquire it, we designed a sophisticated,
semi-automatic scan procedure that utilizes a highly-flexible laboratory X-ray
CT setup. A diverse mix of samples with high natural variability in shape and
density was scanned slice-by-slice (5000 slices in total) with high angular and
spatial resolution and three different beam characteristics: A high-fidelity, a
low-dose and a beam-hardening-inflicted mode. In addition, 750
out-of-distribution slices were scanned with sample and beam variations to
accommodate robustness and segmentation tasks. We provide raw projection data,
reference reconstructions and segmentations based on an open-source data
processing pipeline
Electrical resistance of individual defects at a topological insulator surface
Three-dimensional topological insulators host surface states with linear
dispersion, which manifest as a Dirac cone. Nanoscale transport measurements
provide direct access to the transport properties of the Dirac cone in real
space and allow the detailed investigation of charge carrier scattering. Here,
we use scanning tunnelling potentiometry to analyse the resistance of different
kinds of defects at the surface of a (Bi0.53Sb0.47)2Te3 topological insulator
thin film. The largest localized voltage drop we find to be located at domain
boundaries in the topological insulator film, with a resistivity about four
times higher than that of a step edge. Furthermore, we resolve resistivity
dipoles located around nanoscale voids in the sample surface. The influence of
such defects on the resistance of the topological surface state is analysed by
means of a resistor network model. The effect resulting from the voids is found
to be small compared to the other defects
Electrical N\'eel-order switching in magnetron-sputtered CuMnAs thin films
Antiferromagnetic materials as active components in spintronic devices
promise insensitivity against external magnetic fields, the absence of own
magnetic stray fields, and ultrafast dynamics at the picosecond time scale.
Materials with certain crystal-symmetry show an intrinsic N\'eel-order
spin-orbit torque that can efficiently switch the magnetic order of an
antiferromagnet. The tetragonal variant of CuMnAs was shown to be electrically
switchable by this intrinsic spin-orbit effect and its use in memory cells with
memristive properties has been recently demonstrated for high-quality films
grown with molecular beam epitaxy. Here, we demonstrate that the magnetic order
of magnetron-sputtered CuMnAs films can also be manipulated by electrical
current pulses. The switching efficiency and relaxation as a function of
temperature, current density, and pulse width can be described by a
thermal-activation model. Our findings demonstrate that CuMnAs can be
fabricated with an industry-compatible deposition technique, which will
accelerate the development cycle of devices based on this remarkable material.Comment: 6 + 4 pages, 4 + 4 figures (main + appendix
Deep learning for multi-view ultrasonic image fusion
Ultrasonic imaging is being used to obtain information about the acoustic properties of a medium by emitting waves into it and recording their interaction using ultrasonic transducer arrays. The Delay-And-Sum (DAS) algorithm forms images using the main path on which reflected signals travel back to the transducers. In some applications, different insonification paths can be considered, for instance by placing the transducers at different locations or if strong reflectors inside the medium are known a-priori. These different modes give rise to multiple DAS images reflecting different geometric information about the scatterers and the challenge is to either fuse them into one image or to directly extract higher-level information regarding the materials of the medium, e.g., a segmentation map. Traditional image fusion techniques typically use ad-hoc combinations of predefined image transforms, pooling operations and thresholding. In this work, we propose a deep neural network (DNN) architecture that directly maps all available data to a segmentation map while explicitly incorporating the DAS image formation for the different insonification paths as network layers. This enables information flow between data pre-processing and image post-processing DNNs, trained end-to-end. We compare our proposed method to a traditional image fusion technique using simulated data experiments, mimicking a non-destructive testing application with four image modes, i.e., two transducer locations and two internal reflection boundaries. Using our approach, it is possible to obtain much more accurate segmentation of defects
Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantification
We present a novel approach to transcranial ultrasound computed tomography that utilizes normalizing flows to improve the speed of imaging and provide Bayesian uncertainty quantification. Our method combines physics-informed methods and data-driven methods to accelerate the reconstruction of the final image. We make use of a physics-informed summary statistic to incorporate the known ultrasound physics with the goal of compressing large incoming observations. This compression enables efficient training of the normalizing flow and standardizes the size of the data regardless of imaging configurations. The combinations of these methods results in fast uncertainty-aware image reconstruction that generalizes to a variety of transducer configurations. We evaluate our approach with in silico experiments and demonstrate that it can significantly improve the imaging speed while quantifying uncertainty. We validate the quality of our image reconstructions by comparing against the traditional physics-only method and also verify that our provided uncertainty is calibrated with the error
Single plane-wave imaging using physics-based deep learning
In plane-wave imaging, multiple unfocused ultrasound waves are transmitted into a medium of interest from different angles and an image is formed from the recorded reflections. The number of plane waves used leads to a tradeoff between frame-rate and image quality, with single-plane-wave (SPW) imaging being the fastest possible modality with the worst image quality. Recently, deep learning methods have been proposed to improve ultrasound imaging. One approach is to use image-to-image networks that work on the formed image and another is to directly learn a mapping from data to an image. Both approaches utilize purely data-driven models and require deep, expressive network architectures, combined with large numbers of training samples to obtain good results. Here, we propose a data-to-image architecture that incorporates a wave-physics-based image formation algorithm in-between deep convolutional neural networks. To achieve this, we implement the Fourier (FK) migration method as network layers and train the whole network end-to-end. We compare our proposed data-to-image network with an image-to-image network in simulated data experiments, mimicking a medical ultrasound application. Experiments show that it is possible to obtain high-quality SPW images, almost similar to an image formed using 75 plane waves over an angular range of ±16°. This illustrates the great potential of combining deep neural networks with physics-based image formation algorithms for SPW imaging
2DeteCT-A large 2D expandable, trainable, experimental Computed Tomography dataset for machine learning
Computer Systems, Imagery and Medi
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