| Date: | January 27, 2017 |
| Time: | 1:50pm |
| Location: | BLOC 628 |
| Speaker: | Prof. L. Kunyansky, University of Arizona |
| Title: | Lorentz force impedance tomography in 2D: Theory and Experiments |
| Abstract: | We will start with a brief overview of the emerging family of
"multi-physics" modalities of medical imaging. After discussing
the general ideas underlying these techniques, and the advantages they
promise to deliver, we will concentrate on the Lorentz force impedance
tomography --- a novel modality that should yield stable, high-resolution
images of the conductivity distribution in the tissues. After a short
theoretical introduction into the Lorentz force tomography, I will present
the design of a simplified 2D MAET scanner we have built, and will discuss
new mathematical problems associated with this device, and the methods
that can be used to solve them.
(Joint work with R.S. Witte and C.P. Ingram) |
|
| Date: | March 29, 2017 |
| Time: | Noon |
| Location: | Bloc 628 |
| Speaker: | Isaac Harris, TAMU |
| Title: | A Direct Method for reconstructing inclusions from Electrostatic Data |
| Abstract: | In this talk, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. Sampling Methods allow one to recover unknown obstacles with little to no a prior information. These methods are computationally simple to implement and analytically rigorous. We consider the case of an Impedance (Robin) inclusion where we show that the Dirichlet-to-Neumann mapping can be used to reconstruct such impenetrable sub-regions. We also propose a non-iterative method based on Boundary Integral Equations to reconstruct the impedance parameter from the knowledge of multiple Cauchy pairs. Some numerical reconstructions will be presented in two dimensions. We will also briefly discuss the extension to other Inverse Boundary Value Problems.
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| Date: | April 5, 2017 |
| Time: | Noon |
| Location: | Blocker 628 |
| Speaker: | Mohammad Latifi, UT Arlington |
| Title: | Inversion of Broken-Ray and Conical Radon Transforms Using Cone Differentiation |
| Abstract: | The talk discusses a new approach to inversion of generalized Radon
transforms integrating a function along broken-rays or polyhedral cones.
These types of transformations appear in mathematical models of single
scattering optical tomography, Compton camera imaging and some other
applications. Our approach is based on a natural generalization of the fundamental theorem of calculus to vector spaces with partial order uniquely
defined by positive cones. We apply our method to derive a new inversion
formula for the broken-ray transform (BRT) with a fixed opening angle and
axis of symmetry in R^2. Our formula is much simpler than two previously
known results on inversion of BRT in the same setup and allows generalizations to BRT with weights and to higher dimensions. It also leads to a range description of BRT using absolute continuity in R^n and Radon-Nikodym theorem. The efficiency of our reconstruction algorithm is demonstrated throughsome simple numerical examples. |
|
| Date: | April 12, 2017 |
| Time: | Noon |
| Location: | Blocker 628 |
| Speaker: | Anrea Bonito, Texas A&M |
| Title: | DIFFUSION COEFFICIENTS ESTIMATION FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS |
| Abstract: | In this talk, we are concerned with parameter estimation in elliptic partial differential equations with homogeneous Dirichlet boundary conditions.
For a fixed right hand side, we discuss under which conditions the diffusion coefficients can be stably recovered from the full knowledge of the corresponding elliptic solutions.
We provide a new argumentation mainly based on techniques taught in Math 612, which guarantees that the inverse map is stable from $L_2$ to $H^1_0$ whenever the right hand side is strictly positive and the diffusion coefficients are in $H^s$ for some $s$ between $1/2$ and $1$.
In this theory, the physical domain is not required to be more than Lipschitz continuous.
Worth mentioning - and open to discussion - this recovery theory could be put forward in the second step of hybrid inverse problems.
In this context, parameters of elliptic partial differential equations are recovered from the knowledge of internal functionals.
This is joint work with R. DeVore, A. Cohen, G. Petrova and G. Welper. |
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