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ºtÁ¿¥DÃD¡G2014 CMMSC Seminar on Scientific Computing with Applications

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Speaker¡G(i) Prof. Jijun Liu (Southeast University, China)

15:20-16:10pm

(ii) Prof. Haibing Wang (Southeast University, China)

16:10-17:00pm

Venue¡GNCTU SA223(¥æ³q¤j¾Ç ¬ì¾Ç¤@À]223«Ç)

(i)Title¡GTotal variation regularization for backward time-fractional diffusion problem

Consider a 2-dimensional backward problem for time-fractional diffusion process, which can be considered as image de-blurring where the blurring process is assumed to be slow diffusion. In order to avoid the over-smoothing effect for object image with

edges and to construct a fast reconstruction scheme, the total variation regularizing term and the data residual error in the frequency domain are coupled to construct the cost functional. The well-posedness of this optimization problem is studied. The minimizer is sought approximately using the iteration process for a series of optimization problems with Bregman distance as penalty term. This iteration reconstruction scheme is essentially

a new regularizing scheme with coupling parameter in the cost functional and the iteration stopping times as two regularizing parameters.

We give the choice strategy for the regularizing parameters in terms of the noise level of measurement data, which yields the optimal error estimate on the iterative solution. The series optimization problems are solved by alternative iteration with explicit exact solution and therefore the amount of computation is much weakened.

(ii)Title¡GInverse obstacle scattering problems with impedance boundary conditions

The theory of inverse obstacle scattering has been an active research led in applied mathematics for a long time. The aim of research in this led is to identify unknown objects through the use of acoustic, electromagnetic or elastic waves. It is found that

impedance boundary conditions could be used to approximately describe some scattering problems involving complex geometric structures or physical properties. In this case, our task is to reconstruct both the shape of an unknown obstacle and the boundary impedance from the measured data of scattered elds. In this talk, I will present our recent works on inverse obstacle scattering problems with impedance boundary conditions.

In particular, we are concerned with the inverse problems for the scattering of time-harmonic electromagnetic plane waves by an impedance cylinder. Both normal and oblique incidences are considered. The talk is based on the joint works with Prof. Jijun Liu (Southeast University) and Prof. Gen Nakamura (Inha University).