3,385 research outputs found
On the Adjoint Operator in Photoacoustic Tomography
Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from
coupled physics" technique, in which the image contrast is due to optical
absorption, but the information is carried to the surface of the tissue as
ultrasound pulses. Many algorithms and formulae for PAT image reconstruction
have been proposed for the case when a complete data set is available. In many
practical imaging scenarios, however, it is not possible to obtain the full
data, or the data may be sub-sampled for faster data acquisition. In such
cases, image reconstruction algorithms that can incorporate prior knowledge to
ameliorate the loss of data are required. Hence, recently there has been an
increased interest in using variational image reconstruction. A crucial
ingredient for the application of these techniques is the adjoint of the PAT
forward operator, which is described in this article from physical, theoretical
and numerical perspectives. First, a simple mathematical derivation of the
adjoint of the PAT forward operator in the continuous framework is presented.
Then, an efficient numerical implementation of the adjoint using a k-space time
domain wave propagation model is described and illustrated in the context of
variational PAT image reconstruction, on both 2D and 3D examples including
inhomogeneous sound speed. The principal advantage of this analytical adjoint
over an algebraic adjoint (obtained by taking the direct adjoint of the
particular numerical forward scheme used) is that it can be implemented using
currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems
Reconstruction-classification method for quantitative photoacoustic tomography
We propose a combined reconstruction-classification method for simultaneously recovering absorption and scattering in turbid media from images of absorbed optical energy. This method exploits knowledge that optical parameters are determined by a limited number of classes to iteratively improve their estimate. Numerical experiments show that the proposed approach allows for accurate recovery of absorption and scattering in two and three dimensions, and delivers superior image quality with respect to traditional reconstruction-only approaches
Models of competitive learning: complex dynamics, intermittent conversions and oscillatory coarsening
We present two models of competitive learning, which are respectively
interfacial and cooperative learning. This learning is outcome-related, so that
spatially and temporally local environments influence the conversion of a given
site between one of two different types. We focus here on the behavior of the
models at coexistence, which yields new critical behavior and the existence of
a phase involving a novel type of coarsening which is oscillatory in nature.Comment: 23 pages, 11 figures. To appear in Phys. Rev.
A Learned Born Series for Highly-Scattering Media
A new method for solving the wave equation is presented, called the learned
Born series (LBS), which is derived from a convergent Born Series but its
components are found through training. The LBS is shown to be significantly
more accurate than the convergent Born series for the same number of
iterations, in the presence of high contrast scatterers, while maintaining a
comparable computational complexity. The LBS is able to generate a reasonable
prediction of the global pressure field with a small number of iterations, and
the errors decrease with the number of learned iterations.Comment: 6 pages, 1 figur
A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound
Transcranial ultrasound therapy is increasingly used for the non-invasive
treatment of brain disorders. However, conventional numerical wave solvers are
currently too computationally expensive to be used online during treatments to
predict the acoustic field passing through the skull (e.g., to account for
subject-specific dose and targeting variations). As a step towards real-time
predictions, in the current work, a fast iterative solver for the heterogeneous
Helmholtz equation in 2D is developed using a fully-learned optimizer. The
lightweight network architecture is based on a modified UNet that includes a
learned hidden state. The network is trained using a physics-based loss
function and a set of idealized sound speed distributions with fully
unsupervised training (no knowledge of the true solution is required). The
learned optimizer shows excellent performance on the test set, and is capable
of generalization well outside the training examples, including to much larger
computational domains, and more complex source and sound speed distributions,
for example, those derived from x-ray computed tomography images of the skull.Comment: 23 pages, 13 figure
High Resolution 3D Ultrasonic Breast Imaging by Time-Domain Full Waveform Inversion
Ultrasound tomography (UST) scanners allow quantitative images of the human
breast's acoustic properties to be derived with potential applications in
screening, diagnosis and therapy planning. Time domain full waveform inversion
(TD-FWI) is a promising UST image formation technique that fits the parameter
fields of a wave physics model by gradient-based optimization. For high
resolution 3D UST, it holds three key challenges: Firstly, its central building
block, the computation of the gradient for a single US measurement, has a
restrictively large memory footprint. Secondly, this building block needs to be
computed for each of the measurements, resulting in a massive
parallel computation usually performed on large computational clusters for
days. Lastly, the structure of the underlying optimization problem may result
in slow progression of the solver and convergence to a local minimum. In this
work, we design and evaluate a comprehensive computational strategy to overcome
these challenges: Firstly, we introduce a novel gradient computation based on
time reversal that dramatically reduces the memory footprint at the expense of
one additional wave simulation per source. Secondly, we break the dependence on
the number of measurements by using source encoding (SE) to compute stochastic
gradient estimates. Also we describe a more accurate, TD-specific SE technique
with a finer variance control and use a state-of-the-art stochastic LBFGS
method. Lastly, we design an efficient TD multi-grid scheme together with
preconditioning to speed up the convergence while avoiding local minima. All
components are evaluated in extensive numerical proof-of-concept studies
simulating a bowl-shaped 3D UST breast scanner prototype. Finally, we
demonstrate that their combination allows us to obtain an accurate 442x442x222
voxel image with a resolution of 0.5mm using Matlab on a single GPU within 24h
open-UST: An Open-Source Ultrasound Tomography Transducer Array System
Fast imaging methods are needed to promote widespread clinical adoption of Ultrasound Tomography (UST), and more widely available UST hardware could support the experimental validation of new measurement configurations. In this work, an open-source 256-element transducer ring array was developed (morganjroberts.github.io/open-UST) and manufactured using rapid prototyping, for only £2k. Novel manufacturing techniques were used, resulting in a 1.17° mean beam axis skew angle, a 104 μm mean element position error, and a ±13.6 μm deviation in matching layer thickness. The nominal acoustic performance was measured using hydrophone scans and watershot data, and the 61.2 dB SNR, 55.4° opening angle, 10.2 mm beamwidth and 54% transmit-receive bandwidth (-12 dB), were found to be similar to existing systems, and compatible with state of the art full-waveform-inversion image reconstruction methods. The inter-element variation in acoustic performance was typically <10% without using normalisation, meaning that the elements can be modelled identically during image reconstruction, removing the need for individual source definitions based on hydrophone measurements. Finally, data from a phantom experiment was successfully reconstructed. These results demonstrate that the open-UST system is accessible for users, and suitable for UST imaging research
Testing systems of identical components
We consider the problem of testing sequentially the components of a multi-component reliability system in order to figure out the state of the system via costly tests. In particular, systems with identical components are considered. The notion of lexicographically large binary decision trees is introduced and a heuristic algorithm based on that notion is proposed. The performance of the heuristic algorithm is demonstrated by computational results, for various classes of functions. In particular, in all 200 random cases where the underlying function is a threshold function, the proposed heuristic produces optimal solutions
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