864 research outputs found
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast
Ultrasound Tomography has seen a revival of interest in the past decade,
especially for breast imaging, due to improvements in both ultrasound and
computing hardware. In particular, three-dimensional ultrasound tomography, a
fully tomographic method in which the medium to be imaged is surrounded by
ultrasound transducers, has become feasible. In this paper, a comprehensive
derivation and study of a robust framework for large-scale bent-ray ultrasound
tomography in 3D for a hemispherical detector array is presented. Two
ray-tracing approaches are derived and compared. More significantly, the
problem of linking the rays between emitters and receivers, which is
challenging in 3D due to the high number of degrees of freedom for the
trajectory of rays, is analysed both as a minimisation and as a root-finding
problem. The ray-linking problem is parameterised for a convex detection
surface and three robust, accurate, and efficient ray-linking algorithms are
formulated and demonstrated. To stabilise these methods, novel
adaptive-smoothing approaches are proposed that control the conditioning of the
update matrices to ensure accurate linking. The nonlinear UST problem of
estimating the sound speed was recast as a series of linearised subproblems,
each solved using the above algorithms and within a steepest descent scheme.
The whole imaging algorithm was demonstrated to be robust and accurate on
realistic data simulated using a full-wave acoustic model and an anatomical
breast phantom, and incorporating the errors due to time-of-flight picking that
would be present with measured data. This method can used to provide a
low-artefact, quantitatively accurate, 3D sound speed maps. In addition to
being useful in their own right, such 3D sound speed maps can be used to
initialise full-wave inversion methods, or as an input to photoacoustic
tomography reconstructions
Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization
This paper proposes an algorithmic framework for solving parametric
optimization problems which we call adjoint-based predictor-corrector
sequential convex programming. After presenting the algorithm, we prove a
contraction estimate that guarantees the tracking performance of the algorithm.
Two variants of this algorithm are investigated. The first one can be used to
solve nonlinear programming problems while the second variant is aimed to treat
online parametric nonlinear programming problems. The local convergence of
these variants is proved. An application to a large-scale benchmark problem
that originates from nonlinear model predictive control of a hydro power plant
is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure
A Closer Look at the Adversarial Robustness of Deep Equilibrium Models
Deep equilibrium models (DEQs) refrain from the traditional layer-stacking
paradigm and turn to find the fixed point of a single layer. DEQs have achieved
promising performance on different applications with featured memory
efficiency. At the same time, the adversarial vulnerability of DEQs raises
concerns. Several works propose to certify robustness for monotone DEQs.
However, limited efforts are devoted to studying empirical robustness for
general DEQs. To this end, we observe that an adversarially trained DEQ
requires more forward steps to arrive at the equilibrium state, or even
violates its fixed-point structure. Besides, the forward and backward tracks of
DEQs are misaligned due to the black-box solvers. These facts cause gradient
obfuscation when applying the ready-made attacks to evaluate or adversarially
train DEQs. Given this, we develop approaches to estimate the intermediate
gradients of DEQs and integrate them into the attacking pipelines. Our
approaches facilitate fully white-box evaluations and lead to effective
adversarial defense for DEQs. Extensive experiments on CIFAR-10 validate the
adversarial robustness of DEQs competitive with deep networks of similar sizes.Comment: Accepted at NeurIPS 2022. Our code is available at
https://github.com/minicheshire/DEQ-White-Box-Robustnes
Shuttle ascent trajectory optimization with function space quasi-Newton techniques
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76144/1/AIAA-1974-824-585.pd
Optimal mistuning for enhanced aeroelastic stability of transonic fans
An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom
Finite reduction and Morse index estimates for mechanical systems
A simple version of exact finite dimensional reduction for the variational
setting of mechanical systems is presented. It is worked out by means of a
thorough global version of the implicit function theorem for monotone
operators. Moreover, the Hessian of the reduced function preserves all the
relevant information of the original one, by Schur's complement, which
spontaneously appears in this context. Finally, the results are
straightforwardly extended to the case of a Dirichlet problem on a bounded
domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential
Equations and Application
Bayesian data assimilation in shape registration
In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud
for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem
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