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Thursday, March 2, 2017 - 14:00 ,
Location: Skiles 006 ,
Professor Kui Ren ,
University of Texas, Austin ,
Organizer: Sung Ha Kang

Two-photon photoacoustic tomography (TP-PAT) is a non-invasive optical molecular imaging modality that aims at inferring two-photon absorption property of heterogeneous media from photoacoustic measurements. In this work, we analyze an inverse problem in quantitative TP-PAT where we intend to reconstruct optical coefficients in a semilinear elliptic PDE, the mathematical model for the propagation of near infra-red photons in tissue-like optical media, from the internal absorbed energy data. We derive uniqueness and stability results on the reconstructions of single and multiple coefficients, and perform numerical simulations based on synthetic data to validate the theoretical analysis.

Monday, February 27, 2017 - 14:00 ,
Location: Skiles 005 ,
Gunay Dogan ,
National Institute of Standards and Technology ,
Organizer: Sung Ha Kang

For many problems in science and engineering, one needs to quantitatively compare shapes of objects in images, e.g., anatomical structures in medical images, detected objects in images of natural scenes. One might have large databases of such shapes, and may want to cluster, classify or compare such elements. To be able to perform such analyses, one needs the notion of shape distance quantifying dissimilarity of such entities. In this work, we focus on the elastic shape distance of Srivastava et al. [PAMI, 2011] for closed planar curves. This provides a flexible and intuitive geodesic distance measure between curve shapes in an appropriate shape space, invariant to translation, scaling, rotation and reparametrization. Computing this distance, however, is computationally expensive. The original algorithm proposed by Srivastava et al. using dynamic programming runs in cubic time with respect to the number of nodes per curve. In this work, we propose a new fast hybrid iterative algorithm to compute the elastic shape distance between shapes of closed planar curves. The asymptotic time complexity of our iterative algorithm is O(N log(N)) per iteration. However, in our experiments, we have observed almost a linear trend in the total running times depending on the type of curve data.

Saturday, February 25, 2017 - 09:00 ,
Location: University of Georgia, Paul D. Coverdell Center for Biomedical & Health Sciences, Athens, GA 30602 ,
Haomin Zhou ,
GT Math ,
Organizer: Sung Ha Kang

The Georgia Scientific Computing Symposium (GSCS) is a forum for
professors, postdocs, graduate students and other researchers in Georgia
to meet in an informal setting, to exchange ideas, and to highlight
local scientific computing research. The symposium has been held every
year since 2009 and is open to the entire research community.
The format of the day-long symposium is a set of invited
presentations, poster sessions and a poster blitz, and plenty of time to
network with other attendees. More information at http://euler.math.uga.edu/cms/GSCS-2017

Monday, November 28, 2016 - 14:05 ,
Location: Skiles 005 ,
Prof. Enlu Zhou ,
Georgia Tech ISyE ,
Organizer: Martin Short

Many real-life systems require simulation techniques to evaluate the system performance and facilitate decision making. Stochastic simulation is driven by input model — a collection of probability distributions that model the system stochasticity. The choice of the input model is crucial for successful modeling and analysis via simulation. When there are past observed data of the system stochasticity, we can utilize these data to construct an input model. However, there is only a finite amount of data in practice, so the input model based on data is always subject to uncertainty, which is the so-called input (model) uncertainty. Therefore, a typical stochastic simulation faces two types of uncertainties: one is the input (model) uncertainty, and the other is the intrinsic stochastic uncertainty. In this talk, I will discuss our recent work on how to assess the risk brought by the two types of uncertainties and how to make decisions under these uncertainties.

Monday, November 21, 2016 - 14:05 ,
Location: Skiles 005 ,
Dr. Christina Frederick ,
Georgia Tech Mathematics ,
Organizer: Martin Short

We present a multiscale approach for identifying features in ocean beds
by solving inverse problems in high frequency seafloor acoustics. The
setting is based on Sound Navigation And Ranging (SONAR) imaging used in
scientific, commercial, and military applications. The forward model
incorporates multiscale simulations, by coupling Helmholtz equations and
geometrical optics for a wide range of spatial scales in the seafloor
geometry. This allows for detailed recovery of seafloor parameters
including material type. Simulated backscattered data is generated using
numerical microlocal analysis techniques. In order to lower the
computational cost of the large-scale simulations in the inversion
process, we take advantage of a \r{pre-computed} library of
representative acoustic responses from various seafloor
parameterizations.

Monday, November 14, 2016 - 14:05 ,
Location: Skiles 005 ,
Dr. Maryam Yashtini ,
Georgia Tech Mathematics ,
Organizer: Martin Short

Many real-world problems reduce to optimization problems that are solved
by iterative methods. In this talk, I focus on recently developed
efficient algorithms for solving large-scale optimization problems that
arises in medical imaging and image
processing. In the first part of my talk, I will introduce the Bregman
Operator Splitting with Variable Stepsize (BOSVS) algorithm for solving
nonsmooth inverse problems. The proposed algorithm is designed to handle
applications where the matrix in the fidelity
term is large, dense, and ill-conditioned. Numerical results are provided
using test problems from parallel magnetic resonance imaging. In the
second part, I will focus on the Euler's Elastica-based model which is
non-smooth and non-convex, and involves high-order
derivatives. I introduce two efficient alternating minimization methods
based on operator splitting and alternating direction method of
multipliers, where subproblems can be solved efficiently by Fourier
transforms and shrinkage operators. I present the analytical
properties of each algorithm, as well as several numerical experiments
on image inpainting problems, including comparison with some existing
state-of-art methods to show the efficiency and the effectiveness of the
proposed methods.

Monday, November 7, 2016 - 14:05 ,
Location: Skiles 005 ,
JD Walsh ,
GA Tech Mathematics, doctoral candidate ,
Organizer: Martin Short

The boundary method is a new algorithm for solving semi-discrete
transport problems involving a variety of ground cost functions. By
reformulating a transport problem as an optimal coupling problem, one
can construct a partition of its continuous space whose boundaries allow
accurate determination of the transport map and its associated
Wasserstein distance. The boundary method approximates region boundaries
using the general auction algorithm, controlling problem size with a
multigrid discard approach. This talk describes numerical and
mathematical results obtained when the ground cost is a convex
combination of lp norms, and shares preliminary work involving other
ground cost functions.

Tuesday, November 1, 2016 - 14:05 ,
Location: Skiles 006 ,
Dr. Mehdi Vahab ,
Florida State University Math ,
Organizer: Martin Short

An adaptive hybrid level set moment-of-fluid method is developed to study
the material solidification of static and dynamic multiphase systems. The
main focus is on the solidification of water droplets, which may undergo
normal or supercooled freezing. We model the different regimes of freezing
such as supercooling, nucleation, recalescence, isothermal freezing and
solid cooling accordingly to capture physical dynamics during impact and
solidification of water droplets onto solid surfaces. The numerical
simulations are validated by comparison to analytical results and
experimental observations. The present simulations demonstrate the ability
of the method to capture sharp solidification front, handle contact line
dynamics, and the simultaneous impact, merging and freezing of a drop.
Parameter studies have been conducted, which show the influence of the
Stefan number on the regularity of the shape of frozen droplets. Also, it
is shown that impacting droplets with different sizes create ice shapes
which are uniform near the impact point and become dissimilar away from it.
In addition, surface wettability determines whether droplets freeze upon
impact or bounce away.

Monday, October 24, 2016 - 14:05 ,
Location: Skiles 005 ,
Prof. Lars Ruthotto ,
Emory University Math/CS ,
Organizer: Martin Short

Image registration is an essential task in almost all areas involving
imaging techniques. The goal of image registration is to find
geometrical correspondences between two or more images. Image
registration is commonly phrased as a variational problem that is known
to be ill-posed and thus regularization is commonly used to ensure
existence of solutions and/or introduce prior knowledge about the
application in mind. Many relevant applications, e.g., in biomedical
imaging, require that plausible transformations are diffeomorphic, i.e.,
smooth mappings with a smooth inverse.
This talk will present and compare two modeling strategies and numerical
approaches to diffeomorphic image registration. First, we will discuss
regularization approaches based on nonlinear elasticity. Second, we will
phrase image registration as an optimal control problem involving
hyperbolic PDEs which is similar to the popular framework of Large
Deformation Diffeomorphic Metric Mapping (LDDMM). Finally, we will
consider computational aspects and present numerical results for
real-life medical imaging problems.

Monday, October 17, 2016 - 14:05 ,
Location: Skiles 005 ,
Prof. Yanzhao Cao ,
Auburn University Mathematics ,
Organizer: Martin Short

A nonlinear filtering problem can be classified as a stochastic Bayesian
optimization problem of identifying the state of a stochastic dynamical
system based on noisy observations of the system. Well known numerical
simulation methods include unscented Kalman filters and particle
filters. In this talk, we consider a class of efficient numerical
methods based on forward backward stochastic differential equations.
The backward SDEs for nonlinear filtering problems are similar to the
Fokker-Planck equations for SDEs. We will describe the process of
deriving such backward SDEs as well as high order numerical algorithms
to solve them, which in turn solve nonlinear filtering problems.