- You are here:
- GT Home
- Home
- News & Events

Friday, January 25, 2013 - 14:00 ,
Location: Skiles 005 ,
Sangwoon Yun ,
Sung Kyun Kwan Univ. (Korea) ,
yswmathedu@skku.edu ,
Organizer: Sung Ha Kang

In this talk, we introduce coordinate gradient descent methods for nonsmooth separable minimization whose objective function is the sum of a smooth function and a convex separable function and for linearly constrained smooth minimization. We also introduce incremental gradient methods for nonsmooth minimization whose objective function is the sum of smooth functions and a convex function.

Friday, January 18, 2013 - 14:00 ,
Location: Skiles 005 ,
Michael Klibanov ,
University of North Carolina, Charlotte ,
Organizer: Haomin Zhou

Coefficient Inverse Problems (CIPs) are the hardest ones to work with in the field of Inverse Problems. Indeed, they are both nonlinear and ill-posed. Conventional numerical methods for CIPs are based on the least squares minimization. Therefore, these methods suffer from the phenomenon of multiple local minima and ravines. This means in turn that those methods are locally convergent ones. In other words, their convergence is guaranteed only of their starting points of iterations are located in small neighborhoods of true solutions. In the past five years we have developed a new numerical method for CIPs for an important hyperbolic Partial Differential Equation, see, e.g. [1,2] and references cited there. This is a globally convergent method. In other words, there is a rigorous guarantee that this method delivers a good approximation for the exact solution without any advanced knowledge of a small neighborhood of this solution. In simple words, a good first guess is not necessary. This method is verified on many examples of computationally simulated data. In addition, it is verified on experimental data. In this talk we will outline this method and present many numerical examples with the focus on experimental data.REFERENCES [1] L. Beilina and M.V. Klibanov, Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, Springer, New York, 2012. [2] A.V. Kuzhuget, L. Beilina and M.V. Klibanov, A. Sullivan, L. Nguyen and M.A. Fiddy, Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm, Inverse Problems, 28, 095007, 2012.

Monday, January 14, 2013 - 14:00 ,
Location: Skiles 005 ,
Xue-Cheng Tai ,
University of Bergen, Department of Mathematics, Norway ,
Organizer: Sung Ha Kang

In this talk, we present a new global optimization based approach to contour evolution, with or without the novel variational shape constraint that imposes a generic star shape using a continuous max-flow framework. In theory, the proposed continuous max-flow model provides a dual perspective to the reduced continuous min-cut formulation of the contour evolution at each discrete time frame, which proves the global optimality of the discrete time contour propagation. The variational analysis of the flow conservation condition of the continuous max-flow model shows that the proposed approach does provide a fully time implicit solver to the contour convection PDE, which allows a large time-step size to significantly speed up the contour evolution. For the contour evolution with a star shape prior, a novel variational representation of the star shape is integrated to the continuous max-flow based scheme by introducing an additional spatial flow. In numerics, the proposed continuous max-flow formulations lead to efficient duality-based algorithms using modern convex optimization theories. Our approach is implemented in a GPU, which significantly improves computing efficiency. We show the high performance of our approach in terms of speed and reliability to both poor initialization and large evolution step-size, using numerous experiments on synthetic, real-world and 2D/3D medical images.This talk is based in a joint work by: J. Yuan, E. Ukwatta, X.C. Tai, A. Fenster, and C. Schnorr.

Monday, November 26, 2012 - 14:00 ,
Location: Skiles 005 ,
Prashant Athavale ,
Fields Institute, Dep. of Math, University of Toronto, ,
prashant@math.utoronto.ca ,
Organizer: Sung Ha Kang

Images consist of features of varying scales. Thus, multiscale image processing techniques are extremely valuable, especially for medical images. We will discuss multiscale image processing techniques based onvariational methods, specifically (BV, L^2) and (BV, L^1) decompositions. We will discuss the applications to real time denoising, deblurring and image registration.

Monday, November 19, 2012 - 14:00 ,
Location: Skiles 005 ,
Hao Gao ,
Dep of Math and CS/ Dep of Radiology and Imaging Sciences, Emory University ,
haog@mathcs.emory.edu ,
Organizer: Sung Ha Kang

I will talk about (1) a few sparsity models for 4DCBCT; (2) the split Bregman method as an efficient algorithm for solving L1-type minimization problem; (3) an efficient implementation through fast and highly parallelizable algorithms for computing the x-ray transform and its adjoint.

Monday, November 12, 2012 - 14:00 ,
Location: Skiles 005 ,
Antonio Cicone ,
GT Math ,
cicone@math.gatech.edu ,
Organizer: Sung Ha Kang

Given F, finite set of square matrices of dimension n, it is possible to define the Joint Spectral Radius or simply JSR as a generalization of the well known spectral radius of a matrix. The JSR evaluation proves to be useful for instance in the analysis of the asymptotic behavior of solutions of linear difference equations with variable coefficients, in the construction of compactly supported wavelets of and many others contexts. This quantity proves, however, to be hard to compute in general. Gripenberg in 1996 proposed an algorithm for the computation of lower and upper bounds to the JSR based on a four member inequality and a branch and bound technique. In this talk we describe a generalization of Gripenberg's method based on ellipsoidal norms that achieve a tighter upper bound, speeding up the approximation of the JSR. We show the performance of this new algorithm compared with Gripenberg's one. This talk is based on joint work with V.Y.Protasov.

Monday, October 29, 2012 - 14:00 ,
Location: Skiles 005 ,
Hyenkyun Woo ,
Georiga Tech CSE ,
hyenkyun@gmail.com ,
Organizer: Sung Ha Kang

The fully developed speckle(multiplicative noise) naturally appears in coherent imaging systems, such as synthetic aperture radar imaging systems. Since the speckle is multiplicative, it makes difficult to interpret observed data. In this talk, we introduce total variation based variational model and convex optimization algorithm(linearized proximal alternating minimization algorithm) to efficiently remove speckle in synthetic aperture radar imaging systems. Numerical results show that our proposed methods outperform the augmented Lagrangian based state-of-the-art algorithms.

Monday, October 22, 2012 - 14:00 ,
Location: Skiles 005 ,
Alessio Medda ,
Aerospace Transportation and Advanced System Laboratory, Georgia Tech Research Institute ,
Alessio.Medda@gtri.gatech.edu ,
Organizer: Sung Ha Kang

In this talk, I will present two
examples of the application of wavelet analysis to the understanding of mild Traumatic
Brain Injury (mTBI). First, the talk will focus on how wavelet-based features
can be used to define important characteristics of blast-related acceleration
and pressure signatures, and how these can be used to drive a Naïve Bayes
classifier using wavelet packets. Later, some recent progress on the use of
wavelets for data-driven clustering of brain regions and the characterization
of functional network dynamics related to mTBI will be discussed. In
particular, because neurological time series such as the ones obtained from an
fMRI scan belong to the class of long term memory processes
(also referred to as 1/f-like
processes), the use of wavelet
analysis guarantees optimal theoretical whitening properties and leads to
better clusters compared to classical seed-based approaches.

Monday, October 8, 2012 - 14:00 ,
Location: 005 ,
Xiaobing Feng ,
University of Tennessee ,
Organizer: Haomin Zhou

In this talk I shall present some latest advances on developing
numerical methods (such as finite difference methods, Galerkin methods,
discontinuous Galerkin methods) for fully nonlinear second order PDEs
including Monge-Ampere type equations and Hamilton-Jacobi-Bellman
equations. The focus of this talk is to present a new framework for
constructing finite difference methods which can reliably approximate
viscosity solutions of these fully nonlinear PDEs. The
connection between this new framework with the well-known finite difference
theory for first order fully nonlinear Hamilton-Jacobi equations will be
explained. Extensions of these finite difference techniques
to discontinuous Galerkin settings will also be discussed.

Monday, October 1, 2012 - 14:00 ,
Location: Skiles 005 ,
Martin Short ,
UCLA Math department ,
Organizer: Luca Dieci

In this era of "big data", Mathematics as it applies to human behavior is becoming a much more relevant and penetrable topic of research. This holds true even for some of the less desirable forms of human behavior, such as crime. In this talk, I will discuss the mathematical modeling of crime on two different "scales", as well as the results of experiments that are being performed to test the usefulness and accuracy of these models. First, I will present a data-driven model of crime hotspots at the scale of neighborhoods -- adapted from literature on earthquake predictions -- along with the results of this model's application within the LAPD. Second, I will describe a game-theoretic model of crime and punishment at the scale of a society, and compare the model to results of lab-based economic experiments performed by myself and collaborators.