194 research outputs found
Distributed-memory large deformation diffeomorphic 3D image registration
We present a parallel distributed-memory algorithm for large deformation
diffeomorphic registration of volumetric images that produces large isochoric
deformations (locally volume preserving). Image registration is a key
technology in medical image analysis. Our algorithm uses a partial differential
equation constrained optimal control formulation. Finding the optimal
deformation map requires the solution of a highly nonlinear problem that
involves pseudo-differential operators, biharmonic operators, and pure
advection operators both forward and back- ward in time. A key issue is the
time to solution, which poses the demand for efficient optimization methods as
well as an effective utilization of high performance computing resources. To
address this problem we use a preconditioned, inexact, Gauss-Newton- Krylov
solver. Our algorithm integrates several components: a spectral discretization
in space, a semi-Lagrangian formulation in time, analytic adjoints, different
regularization functionals (including volume-preserving ones), a spectral
preconditioner, a highly optimized distributed Fast Fourier Transform, and a
cubic interpolation scheme for the semi-Lagrangian time-stepping. We
demonstrate the scalability of our algorithm on images with resolution of up to
on the "Maverick" and "Stampede" systems at the Texas Advanced
Computing Center (TACC). The critical problem in the medical imaging
application domain is strong scaling, that is, solving registration problems of
a moderate size of ---a typical resolution for medical images. We are
able to solve the registration problem for images of this size in less than
five seconds on 64 x86 nodes of TACC's "Maverick" system.Comment: accepted for publication at SC16 in Salt Lake City, Utah, USA;
November 201
Spectral-Element and Adjoint Methods in Seismology
We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem
Integrated Heart - Coupling multiscale and multiphysics models for the simulation of the cardiac function
Mathematical modelling of the human heart and its function can expand our understanding of various cardiac
diseases, which remain the most common cause of death in the developed world. Like other physiological
systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the
molecular, cellular, tissue, and organ levels. This article addresses the numerical modelling of many aspects
of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle
tissue, the sub-cellular activation-contraction mechanisms, as well as the hemodynamics inside the heart
chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially
developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we
also look at systemic stability, and explain for example how physiological concepts such as microscopic force
generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability
properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate
three fundamental challenges of developing multiphysics and multiscale numerical models for simulating
heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the
proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii)
the stable simulation of ventricular hemodynamics during rapid valve opening and closure
Piecewise smoothed value picking regularization applied to 2-D TM and TE inverse scattering
The Stepwise Relaxed Value Picking (SRVP) regularization technique, proposed earlier for the iterative reconstruction of piecewise (quasi-) homogeneous objects, is a non-spatial technique, whereby the reconstruction unknowns are clustered around a limited number of-a-priori unknown-reference values. Artifacts have been observed in some 2-D and 3D complex permittivity reconstructions. This paper therefore combines the non-spatial SRVP technique with a spatial smoothing technique, whereby the reference values provided by the former-in each iteration-are employed by the latter to define separate smoothing regions. This way edges are preserved, since the spatial smoothing constraints in the cost function are active within but not across the region boundaries. This combined technique, denoted as Stepwise Relaxed Piecewise Smoothed Value Picking (SRPSVP) regularization, is formulated for the 2.5D microwave inverse scattering problem and is illustrated with reconstructions from the Institut Fresnel 2-D scattering database
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